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

Percentage Accurate: 84.8% → 93.7%

Time: 15.9s

Alternatives: 22

Speedup: 1.0×

• 50.4% 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: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, t, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(k, j \cdot 27, \left(4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(t\_1, t, b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma z (* (* x 18.0) y) (* a -4.0))))
   (if (<= t -3.4e+115)
     (fma t_1 t (fma c b (- (fma k (* j 27.0) (* (* 4.0 x) i)))))
     (if (<= t 1.16e-12)
       (fma
        -27.0
        (* j k)
        (fma (fma -4.0 i (* (* (* z t) y) 18.0)) x (fma (* a t) -4.0 (* b c))))
       (fma (* -27.0 j) k (fma (* -4.0 x) i (fma t_1 t (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(z, ((x * 18.0) * y), (a * -4.0));
	double tmp;
	if (t <= -3.4e+115) {
		tmp = fma(t_1, t, fma(c, b, -fma(k, (j * 27.0), ((4.0 * x) * i))));
	} else if (t <= 1.16e-12) {
		tmp = fma(-27.0, (j * k), fma(fma(-4.0, i, (((z * t) * y) * 18.0)), x, fma((a * t), -4.0, (b * c))));
	} else {
		tmp = fma((-27.0 * j), k, fma((-4.0 * x), i, fma(t_1, t, (b * c))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(z, Float64(Float64(x * 18.0) * y), Float64(a * -4.0))
	tmp = 0.0
	if (t <= -3.4e+115)
		tmp = fma(t_1, t, fma(c, b, Float64(-fma(k, Float64(j * 27.0), Float64(Float64(4.0 * x) * i)))));
	elseif (t <= 1.16e-12)
		tmp = fma(-27.0, Float64(j * k), fma(fma(-4.0, i, Float64(Float64(Float64(z * t) * y) * 18.0)), x, fma(Float64(a * t), -4.0, Float64(b * c))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * x), i, fma(t_1, t, Float64(b * c))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(z * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+115], N[(t$95$1 * t + N[(c * b + (-N[(k * N[(j * 27.0), $MachinePrecision] + N[(N[(4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e-12], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(-4.0 * i + N[(N[(N[(z * t), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(t$95$1 * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4000000000000001e115

   1. Initial program 87.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. distribute-rgt-out-- N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 92.4%

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

   if -3.4000000000000001e115 < t < 1.1599999999999999e-12

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.3%

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

   7. Applied rewrites 96.4%

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

   if 1.1599999999999999e-12 < t

   1. Initial program 92.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 96.0

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 100.0%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(k, j \cdot 27, \left(4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, b \cdot c\right)\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(-j, 27 \cdot k, t\_1\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -4.0 x)
          i
          (fma (fma z (* (* x 18.0) y) (* a -4.0)) t (* b c)))))
   (if (<= t -3.4e+115)
     (fma (- j) (* 27.0 k) t_1)
     (if (<= t 1.06e-51)
       (fma
        -27.0
        (* j k)
        (fma (fma -4.0 i (* (* (* z t) y) 18.0)) x (fma (* a t) -4.0 (* b c))))
       (fma (* -27.0 j) k t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-4.0 * x), i, fma(fma(z, ((x * 18.0) * y), (a * -4.0)), t, (b * c)));
	double tmp;
	if (t <= -3.4e+115) {
		tmp = fma(-j, (27.0 * k), t_1);
	} else if (t <= 1.06e-51) {
		tmp = fma(-27.0, (j * k), fma(fma(-4.0, i, (((z * t) * y) * 18.0)), x, fma((a * t), -4.0, (b * c))));
	} else {
		tmp = fma((-27.0 * j), k, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-4.0 * x), i, fma(fma(z, Float64(Float64(x * 18.0) * y), Float64(a * -4.0)), t, Float64(b * c)))
	tmp = 0.0
	if (t <= -3.4e+115)
		tmp = fma(Float64(-j), Float64(27.0 * k), t_1);
	elseif (t <= 1.06e-51)
		tmp = fma(-27.0, Float64(j * k), fma(fma(-4.0, i, Float64(Float64(Float64(z * t) * y) * 18.0)), x, fma(Float64(a * t), -4.0, Float64(b * c))));
	else
		tmp = fma(Float64(-27.0 * j), k, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+115], N[((-j) * N[(27.0 * k), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 1.06e-51], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(-4.0 * i + N[(N[(N[(z * t), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4000000000000001e115

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 87.4

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 89.9%

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

   if -3.4000000000000001e115 < t < 1.0600000000000001e-51

   1. Initial program 81.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.3%

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

   7. Applied rewrites 96.7%

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

   if 1.0600000000000001e-51 < t

   1. Initial program 91.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 95.0

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 98.5%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(-j, 27 \cdot k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, b \cdot c\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, b \cdot c\right)\right)\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -27.0 j)
          k
          (fma
           (* -4.0 x)
           i
           (fma (fma z (* (* x 18.0) y) (* a -4.0)) t (* b c))))))
   (if (<= t -3.4e+115)
     t_1
     (if (<= t 1.06e-51)
       (fma
        -27.0
        (* j k)
        (fma (fma -4.0 i (* (* (* z t) y) 18.0)) x (fma (* a t) -4.0 (* b c))))
       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((-27.0 * j), k, fma((-4.0 * x), i, fma(fma(z, ((x * 18.0) * y), (a * -4.0)), t, (b * c))));
	double tmp;
	if (t <= -3.4e+115) {
		tmp = t_1;
	} else if (t <= 1.06e-51) {
		tmp = fma(-27.0, (j * k), fma(fma(-4.0, i, (((z * t) * y) * 18.0)), x, fma((a * t), -4.0, (b * c))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * x), i, fma(fma(z, Float64(Float64(x * 18.0) * y), Float64(a * -4.0)), t, Float64(b * c))))
	tmp = 0.0
	if (t <= -3.4e+115)
		tmp = t_1;
	elseif (t <= 1.06e-51)
		tmp = fma(-27.0, Float64(j * k), fma(fma(-4.0, i, Float64(Float64(Float64(z * t) * y) * 18.0)), x, fma(Float64(a * t), -4.0, Float64(b * c))));
	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[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+115], t$95$1, If[LessEqual[t, 1.06e-51], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(-4.0 * i + N[(N[(N[(z * t), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000001e115 or 1.0600000000000001e-51 < t

   1. Initial program 89.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 91.9

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 95.0%

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

   if -3.4000000000000001e115 < t < 1.0600000000000001e-51

   1. Initial program 81.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.3%

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

   7. Applied rewrites 96.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, b \cdot c\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-51}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(x \cdot 18\right) \cdot y, a \cdot -4\right), t, b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot z\right) \cdot x\right) \cdot 18\right), t, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -5e+14)
   (fma
    -27.0
    (* j k)
    (fma (* a t) -4.0 (fma c b (* (fma -4.0 i (* (* (* y z) t) 18.0)) x))))
   (if (<= t 2.5e+88)
     (fma
      -27.0
      (* j k)
      (fma (fma -4.0 i (* (* (* z t) y) 18.0)) x (fma (* a t) -4.0 (* b c))))
     (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* y z) x) 18.0)) t (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -5e+14) {
		tmp = fma(-27.0, (j * k), fma((a * t), -4.0, fma(c, b, (fma(-4.0, i, (((y * z) * t) * 18.0)) * x))));
	} else if (t <= 2.5e+88) {
		tmp = fma(-27.0, (j * k), fma(fma(-4.0, i, (((z * t) * y) * 18.0)), x, fma((a * t), -4.0, (b * c))));
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((y * z) * x) * 18.0)), t, (b * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -5e+14)
		tmp = fma(-27.0, Float64(j * k), fma(Float64(a * t), -4.0, fma(c, b, Float64(fma(-4.0, i, Float64(Float64(Float64(y * z) * t) * 18.0)) * x))));
	elseif (t <= 2.5e+88)
		tmp = fma(-27.0, Float64(j * k), fma(fma(-4.0, i, Float64(Float64(Float64(z * t) * y) * 18.0)), x, fma(Float64(a * t), -4.0, Float64(b * c))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(y * z) * x) * 18.0)), t, Float64(b * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -5e+14], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(-4.0 * i + N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+88], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(-4.0 * i + N[(N[(N[(z * t), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5e14

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 83.5%

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

   7. Applied rewrites 89.0%

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

   if -5e14 < t < 2.49999999999999999e88

   1. Initial program 83.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.7%

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

   7. Applied rewrites 96.9%

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

   if 2.49999999999999999e88 < 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 i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

   5. Applied rewrites 95.1%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot t\right) \cdot y\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot z\right) \cdot x\right) \cdot 18\right), t, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{if}\;4 \cdot a \leq -1 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;4 \cdot a \leq 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right), x, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma i x (* a t)) -4.0 (fma c b (* (* j k) -27.0)))))
   (if (<= (* 4.0 a) -1e+190)
     t_1
     (if (<= (* 4.0 a) 1e+48)
       (fma -27.0 (* j k) (fma (fma -4.0 i (* (* (* y z) t) 18.0)) x (* b c)))
       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(i, x, (a * t)), -4.0, fma(c, b, ((j * k) * -27.0)));
	double tmp;
	if ((4.0 * a) <= -1e+190) {
		tmp = t_1;
	} else if ((4.0 * a) <= 1e+48) {
		tmp = fma(-27.0, (j * k), fma(fma(-4.0, i, (((y * z) * t) * 18.0)), x, (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(i, x, Float64(a * t)), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)))
	tmp = 0.0
	if (Float64(4.0 * a) <= -1e+190)
		tmp = t_1;
	elseif (Float64(4.0 * a) <= 1e+48)
		tmp = fma(-27.0, Float64(j * k), fma(fma(-4.0, i, Float64(Float64(Float64(y * z) * t) * 18.0)), x, Float64(b * c)));
	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[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(4.0 * a), $MachinePrecision], -1e+190], t$95$1, If[LessEqual[N[(4.0 * a), $MachinePrecision], 1e+48], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(-4.0 * i + N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 4 binary64)) < -1.0000000000000001e190 or 1.00000000000000004e48 < (*.f64 a #s(literal 4 binary64))

   1. Initial program 83.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.5%

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

   7. Applied rewrites 86.7%

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

   8. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--r- N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 86.3%

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

   if -1.0000000000000001e190 < (*.f64 a #s(literal 4 binary64)) < 1.00000000000000004e48

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 84.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;4 \cdot a \leq -1 \cdot 10^{+190}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{elif}\;4 \cdot a \leq 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right), x, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.7 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= b 2.7e+76)
   (fma
    -27.0
    (* j k)
    (fma (* a t) -4.0 (fma c b (* (fma -4.0 i (* (* (* y z) t) 18.0)) x))))
   (fma (* -27.0 k) j (* b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= 2.7e+76) {
		tmp = fma(-27.0, (j * k), fma((a * t), -4.0, fma(c, b, (fma(-4.0, i, (((y * z) * t) * 18.0)) * x))));
	} else {
		tmp = fma((-27.0 * k), j, (b * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (b <= 2.7e+76)
		tmp = fma(-27.0, Float64(j * k), fma(Float64(a * t), -4.0, fma(c, b, Float64(fma(-4.0, i, Float64(Float64(Float64(y * z) * t) * 18.0)) * x))));
	else
		tmp = fma(Float64(-27.0 * k), j, Float64(b * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[b, 2.7e+76], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(-4.0 * i + N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.6999999999999999e76

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.5%

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

   7. Applied rewrites 90.5%

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

   if 2.6999999999999999e76 < b

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.4%

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

   7. Applied rewrites 82.3%

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

   8. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 69.1

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

   10. Applied rewrites 69.1%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 60.1%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.7 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot z\right) \cdot x\right) \cdot 18\right), t, b \cdot c\right)\right)\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -27.0 j)
          k
          (fma (fma -4.0 a (* (* (* y z) x) 18.0)) t (* b c)))))
   (if (<= t -5.9e-118)
     t_1
     (if (<= t 2.65e+132)
       (fma (fma i x (* a t)) -4.0 (fma c b (* (* j k) -27.0)))
       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((-27.0 * j), k, fma(fma(-4.0, a, (((y * z) * x) * 18.0)), t, (b * c)));
	double tmp;
	if (t <= -5.9e-118) {
		tmp = t_1;
	} else if (t <= 2.65e+132) {
		tmp = fma(fma(i, x, (a * t)), -4.0, fma(c, b, ((j * k) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(y * z) * x) * 18.0)), t, Float64(b * c)))
	tmp = 0.0
	if (t <= -5.9e-118)
		tmp = t_1;
	elseif (t <= 2.65e+132)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	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[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.9e-118], t$95$1, If[LessEqual[t, 2.65e+132], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9e-118 or 2.65e132 < t

   1. Initial program 88.5%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

   5. Applied rewrites 88.8%

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

   if -5.9e-118 < t < 2.65e132

   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 0

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

   5. Applied rewrites 87.4%

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

   7. Applied rewrites 88.9%

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

   8. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--r- N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 87.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{-118}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot z\right) \cdot x\right) \cdot 18\right), t, b \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot z\right) \cdot x\right) \cdot 18\right), t, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -270:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* (fma (* (* y z) x) 18.0 (* a -4.0)) t) (* (* j 27.0) k))))
   (if (<= t -270.0)
     t_1
     (if (<= t 5.6e+132)
       (fma (fma i x (* a t)) -4.0 (fma c b (* (* j k) -27.0)))
       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(((y * z) * x), 18.0, (a * -4.0)) * t) - ((j * 27.0) * k);
	double tmp;
	if (t <= -270.0) {
		tmp = t_1;
	} else if (t <= 5.6e+132) {
		tmp = fma(fma(i, x, (a * t)), -4.0, fma(c, b, ((j * k) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t <= -270.0)
		tmp = t_1;
	elseif (t <= 5.6e+132)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	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[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -270.0], t$95$1, If[LessEqual[t, 5.6e+132], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -270 or 5.5999999999999998e132 < t

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 35.1

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

   5. Applied rewrites 35.1%

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

   6. Taylor expanded in b around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. associate-*r* N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

      13. distribute-lft-out N/A

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

      14. lower-*.f64 N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-*.f64 87.0

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

   8. Applied rewrites 87.0%

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

   9. Taylor expanded in i around 0

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

   11. Applied rewrites 84.9%

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

   if -270 < t < 5.5999999999999998e132

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.1%

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

   7. Applied rewrites 88.7%

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

   8. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--r- N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 84.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -270:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+231}:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-124}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(b, c, \left(-27 \cdot k\right) \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 0.0028:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, b \cdot c\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -6e+231)
   (* (fma (* (* x y) z) 18.0 (* a -4.0)) t)
   (if (<= t -3.35e-124)
     (fma (* -4.0 t) a (fma b c (* (* -27.0 k) j)))
     (if (<= t 0.0028)
       (- (fma (* i x) -4.0 (* b c)) (* (* j 27.0) k))
       (* (fma (* (* y z) x) 18.0 (* a -4.0)) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6e+231) {
		tmp = fma(((x * y) * z), 18.0, (a * -4.0)) * t;
	} else if (t <= -3.35e-124) {
		tmp = fma((-4.0 * t), a, fma(b, c, ((-27.0 * k) * j)));
	} else if (t <= 0.0028) {
		tmp = fma((i * x), -4.0, (b * c)) - ((j * 27.0) * k);
	} else {
		tmp = fma(((y * z) * x), 18.0, (a * -4.0)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -6e+231)
		tmp = Float64(fma(Float64(Float64(x * y) * z), 18.0, Float64(a * -4.0)) * t);
	elseif (t <= -3.35e-124)
		tmp = fma(Float64(-4.0 * t), a, fma(b, c, Float64(Float64(-27.0 * k) * j)));
	elseif (t <= 0.0028)
		tmp = Float64(fma(Float64(i * x), -4.0, Float64(b * c)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -6e+231], N[(N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, -3.35e-124], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b * c + N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0028], N[(N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.0000000000000003e231

   1. Initial program 87.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 91.8

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

   8. Applied rewrites 91.8%

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

   if -6.0000000000000003e231 < t < -3.35e-124

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.1%

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

   7. Applied rewrites 89.4%

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

   8. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 67.2

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

   10. Applied rewrites 67.2%

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

   12. Applied rewrites 69.9%

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

   if -3.35e-124 < t < 0.00279999999999999997

   1. Initial program 80.5%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if 0.00279999999999999997 < t

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.9%

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

   7. Applied rewrites 85.9%

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

   8. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 74.1

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

   10. Applied rewrites 74.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+231}:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-124}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(b, c, \left(-27 \cdot k\right) \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 0.0028:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, b \cdot c\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;t \leq -23000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.00075:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 k) j (* (* a t) -4.0))))
   (if (<= t -1.7e+167)
     (* (fma -4.0 i (* (* (* y z) t) 18.0)) x)
     (if (<= t -23000.0)
       t_1
       (if (<= t 2.4e-204)
         (- (* b c) (* (* j 27.0) k))
         (if (<= t 0.00075) (fma (* j k) -27.0 (* (* i x) -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((-27.0 * k), j, ((a * t) * -4.0));
	double tmp;
	if (t <= -1.7e+167) {
		tmp = fma(-4.0, i, (((y * z) * t) * 18.0)) * x;
	} else if (t <= -23000.0) {
		tmp = t_1;
	} else if (t <= 2.4e-204) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 0.00075) {
		tmp = fma((j * k), -27.0, ((i * x) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0))
	tmp = 0.0
	if (t <= -1.7e+167)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(y * z) * t) * 18.0)) * x);
	elseif (t <= -23000.0)
		tmp = t_1;
	elseif (t <= 2.4e-204)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 0.00075)
		tmp = fma(Float64(j * k), -27.0, Float64(Float64(i * x) * -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[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+167], N[(N[(-4.0 * i + N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, -23000.0], t$95$1, If[LessEqual[t, 2.4e-204], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00075], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7e167

   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-sub-sign-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 67.4

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

   5. Applied rewrites 67.4%

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

   if -1.7e167 < t < -23000 or 7.5000000000000002e-4 < t

   1. Initial program 91.8%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 35.4

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

   5. Applied rewrites 35.4%

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

   6. Taylor expanded in b around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. associate-*r* N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

      13. distribute-lft-out N/A

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

      14. lower-*.f64 N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-*.f64 86.7

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

   8. Applied rewrites 86.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 58.8%

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

       1. lift--.f64 N/A

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

       2. sub-neg N/A

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

       3. lift-*.f64 N/A

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

       4. distribute-lft-neg-out N/A

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

       5. lift-*.f64 N/A

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

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

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

       7. metadata-eval N/A

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

       8. associate-*r* N/A

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lift-*.f64 N/A

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

   13. Applied rewrites 61.5%

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

   if -23000 < t < 2.4e-204

   1. Initial program 81.4%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 82.8

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

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 70.7%

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

   if 2.4e-204 < t < 7.5000000000000002e-4

   1. Initial program 82.2%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 55.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;t \leq -23000:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.00075:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2.15e+257)
   (* (fma (* (* x y) z) 18.0 (* a -4.0)) t)
   (if (<= t 1.08e+134)
     (fma (fma i x (* a t)) -4.0 (fma c b (* (* j k) -27.0)))
     (* (fma (* (* y z) x) 18.0 (* a -4.0)) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2.15e+257) {
		tmp = fma(((x * y) * z), 18.0, (a * -4.0)) * t;
	} else if (t <= 1.08e+134) {
		tmp = fma(fma(i, x, (a * t)), -4.0, fma(c, b, ((j * k) * -27.0)));
	} else {
		tmp = fma(((y * z) * x), 18.0, (a * -4.0)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -2.15e+257)
		tmp = Float64(fma(Float64(Float64(x * y) * z), 18.0, Float64(a * -4.0)) * t);
	elseif (t <= 1.08e+134)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	else
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -2.15e+257], N[(N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 1.08e+134], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1499999999999999e257

   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 x around 0

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 97.0

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

   8. Applied rewrites 97.0%

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

   if -2.1499999999999999e257 < t < 1.0800000000000001e134

   1. Initial program 83.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 87.7%

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

   7. Applied rewrites 89.1%

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

   8. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--r- N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 81.9%

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

   if 1.0800000000000001e134 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.5%

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

   7. Applied rewrites 88.5%

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

   8. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 83.0

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

   10. Applied rewrites 83.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8500:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -8500.0)
   (* (fma (* (* x y) z) 18.0 (* a -4.0)) t)
   (if (<= t 2.4e-204)
     (- (* b c) (* (* j 27.0) k))
     (if (<= t 0.001)
       (fma (* j k) -27.0 (* (* i x) -4.0))
       (* (fma (* (* y z) x) 18.0 (* a -4.0)) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -8500.0) {
		tmp = fma(((x * y) * z), 18.0, (a * -4.0)) * t;
	} else if (t <= 2.4e-204) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 0.001) {
		tmp = fma((j * k), -27.0, ((i * x) * -4.0));
	} else {
		tmp = fma(((y * z) * x), 18.0, (a * -4.0)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -8500.0)
		tmp = Float64(fma(Float64(Float64(x * y) * z), 18.0, Float64(a * -4.0)) * t);
	elseif (t <= 2.4e-204)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 0.001)
		tmp = fma(Float64(j * k), -27.0, Float64(Float64(i * x) * -4.0));
	else
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -8500.0], N[(N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 2.4e-204], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.001], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8500

   1. Initial program 87.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.1%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 67.8

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

   8. Applied rewrites 67.8%

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

   if -8500 < t < 2.4e-204

   1. Initial program 81.4%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 82.8

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

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 70.7%

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

   if 2.4e-204 < t < 1e-3

   1. Initial program 82.2%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 55.5%

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

   if 1e-3 < t

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.9%

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

   7. Applied rewrites 85.9%

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

   8. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 74.1

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

   10. Applied rewrites 74.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8500:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{if}\;t \leq -8500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* (* x y) z) 18.0 (* a -4.0)) t)))
   (if (<= t -8500.0)
     t_1
     (if (<= t 2.4e-204)
       (- (* b c) (* (* j 27.0) k))
       (if (<= t 0.001) (fma (* j k) -27.0 (* (* i x) -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(((x * y) * z), 18.0, (a * -4.0)) * t;
	double tmp;
	if (t <= -8500.0) {
		tmp = t_1;
	} else if (t <= 2.4e-204) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 0.001) {
		tmp = fma((j * k), -27.0, ((i * x) * -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(Float64(Float64(x * y) * z), 18.0, Float64(a * -4.0)) * t)
	tmp = 0.0
	if (t <= -8500.0)
		tmp = t_1;
	elseif (t <= 2.4e-204)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 0.001)
		tmp = fma(Float64(j * k), -27.0, Float64(Float64(i * x) * -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[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -8500.0], t$95$1, If[LessEqual[t, 2.4e-204], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.001], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8500 or 1e-3 < t

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.9%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 70.7

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

   8. Applied rewrites 70.7%

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

   if -8500 < t < 2.4e-204

   1. Initial program 81.4%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 82.8

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

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 70.7%

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

   if 2.4e-204 < t < 1e-3

   1. Initial program 82.2%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 55.5%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8500:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.001:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(x \cdot y\right) \cdot z, 18, a \cdot -4\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+83}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+83)
     (* (* j k) -27.0)
     (if (<= t_1 5e+152) (* (* i x) -4.0) (* (* -27.0 j) k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+83) {
		tmp = (j * k) * -27.0;
	} else if (t_1 <= 5e+152) {
		tmp = (i * x) * -4.0;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-1d+83)) then
        tmp = (j * k) * (-27.0d0)
    else if (t_1 <= 5d+152) then
        tmp = (i * x) * (-4.0d0)
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+83) {
		tmp = (j * k) * -27.0;
	} else if (t_1 <= 5e+152) {
		tmp = (i * x) * -4.0;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+83:
		tmp = (j * k) * -27.0
	elif t_1 <= 5e+152:
		tmp = (i * x) * -4.0
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -1e+83)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (t_1 <= 5e+152)
		tmp = Float64(Float64(i * x) * -4.0);
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+83)
		tmp = (j * k) * -27.0;
	elseif (t_1 <= 5e+152)
		tmp = (i * x) * -4.0;
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+83], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+152], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000003e83

   1. Initial program 81.6%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

   if -1.00000000000000003e83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5e152

   1. Initial program 85.8%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 24.5

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

   5. Applied rewrites 24.5%

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

   if 5e152 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.6%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 72.3

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

   5. Applied rewrites 72.3%

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

   7. Applied rewrites 74.7%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+83}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{if}\;t \leq -23000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.00075:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 k) j (* (* a t) -4.0))))
   (if (<= t -23000.0)
     t_1
     (if (<= t 2.4e-204)
       (- (* b c) (* (* j 27.0) k))
       (if (<= t 0.00075) (fma (* j k) -27.0 (* (* i x) -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((-27.0 * k), j, ((a * t) * -4.0));
	double tmp;
	if (t <= -23000.0) {
		tmp = t_1;
	} else if (t <= 2.4e-204) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 0.00075) {
		tmp = fma((j * k), -27.0, ((i * x) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0))
	tmp = 0.0
	if (t <= -23000.0)
		tmp = t_1;
	elseif (t <= 2.4e-204)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 0.00075)
		tmp = fma(Float64(j * k), -27.0, Float64(Float64(i * x) * -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[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -23000.0], t$95$1, If[LessEqual[t, 2.4e-204], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00075], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -23000 or 7.5000000000000002e-4 < t

   1. Initial program 89.4%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 36.9

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

   5. Applied rewrites 36.9%

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

   6. Taylor expanded in b around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. associate-*r* N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

      13. distribute-lft-out N/A

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

      14. lower-*.f64 N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-*.f64 86.8

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

   8. Applied rewrites 86.8%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 56.1%

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

       1. lift--.f64 N/A

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

       2. sub-neg N/A

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

       3. lift-*.f64 N/A

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

       4. distribute-lft-neg-out N/A

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

       5. lift-*.f64 N/A

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

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

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

       7. metadata-eval N/A

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

       8. associate-*r* N/A

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lift-*.f64 N/A

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

   13. Applied rewrites 57.1%

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

   if -23000 < t < 2.4e-204

   1. Initial program 81.4%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 82.8

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

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 70.7%

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

   if 2.4e-204 < t < 7.5000000000000002e-4

   1. Initial program 82.2%

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

   3. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. +-commutative N/A

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

   10. Applied rewrites 55.5%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23000:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 0.00075:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 71.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 i (* (* (* y z) t) 18.0)) x)))
   (if (<= x -2.8e+46)
     t_1
     (if (<= x 1.2e+39) (fma (* -27.0 k) j (fma (* a t) -4.0 (* b c))) 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, (((y * z) * t) * 18.0)) * x;
	double tmp;
	if (x <= -2.8e+46) {
		tmp = t_1;
	} else if (x <= 1.2e+39) {
		tmp = fma((-27.0 * k), j, fma((a * t), -4.0, (b * c)));
	} 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(y * z) * t) * 18.0)) * x)
	tmp = 0.0
	if (x <= -2.8e+46)
		tmp = t_1;
	elseif (x <= 1.2e+39)
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(a * t), -4.0, Float64(b * c)));
	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[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.8e+46], t$95$1, If[LessEqual[x, 1.2e+39], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000018e46 or 1.2e39 < x

   1. Initial program 73.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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-sub-sign-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 63.6

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

   5. Applied rewrites 63.6%

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

   if -2.80000000000000018e46 < x < 1.2e39

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.4%

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

   7. Applied rewrites 86.1%

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

   8. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 79.4

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

   10. Applied rewrites 79.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 i (* (* (* y z) t) 18.0)) x)))
   (if (<= x -2.8e+46)
     t_1
     (if (<= x 1.2e+39) (fma -27.0 (* j k) (fma -4.0 (* a t) (* b c))) 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, (((y * z) * t) * 18.0)) * x;
	double tmp;
	if (x <= -2.8e+46) {
		tmp = t_1;
	} else if (x <= 1.2e+39) {
		tmp = fma(-27.0, (j * k), fma(-4.0, (a * t), (b * c)));
	} 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(y * z) * t) * 18.0)) * x)
	tmp = 0.0
	if (x <= -2.8e+46)
		tmp = t_1;
	elseif (x <= 1.2e+39)
		tmp = fma(-27.0, Float64(j * k), fma(-4.0, Float64(a * t), Float64(b * c)));
	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[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.8e+46], t$95$1, If[LessEqual[x, 1.2e+39], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000018e46 or 1.2e39 < x

   1. Initial program 73.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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-sub-sign-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 63.6

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

   5. Applied rewrites 63.6%

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

   if -2.80000000000000018e46 < x < 1.2e39

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.4%

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

   6. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 78.1

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

   8. Applied rewrites 78.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(y \cdot z\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{if}\;t \leq -23000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.0038:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 k) j (* (* a t) -4.0))))
   (if (<= t -23000.0)
     t_1
     (if (<= t 0.0038) (fma (* -27.0 k) j (* b c)) 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((-27.0 * k), j, ((a * t) * -4.0));
	double tmp;
	if (t <= -23000.0) {
		tmp = t_1;
	} else if (t <= 0.0038) {
		tmp = fma((-27.0 * k), j, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0))
	tmp = 0.0
	if (t <= -23000.0)
		tmp = t_1;
	elseif (t <= 0.0038)
		tmp = fma(Float64(-27.0 * k), j, Float64(b * c));
	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[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -23000.0], t$95$1, If[LessEqual[t, 0.0038], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -23000 or 0.00379999999999999999 < 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 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 37.2

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

   5. Applied rewrites 37.2%

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

   6. Taylor expanded in b around 0

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

      1. distribute-lft-out N/A

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

      2. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      3. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      4. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. distribute-lft-out N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(18 \cdot t, x \cdot \left(y \cdot z\right), -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{18 \cdot t}, x \cdot \left(y \cdot z\right), -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(x \cdot y\right) \cdot z}, -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(x \cdot y\right) \cdot z}, -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(y \cdot x\right)} \cdot z, -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(y \cdot x\right)} \cdot z, -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(18 \cdot t, \left(y \cdot x\right) \cdot z, \color{blue}{-4 \cdot \left(i \cdot x\right) + -4 \cdot \left(a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      13. distribute-lft-out N/A

          \[\leadsto \mathsf{fma}\left(18 \cdot t, \left(y \cdot x\right) \cdot z, \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(18 \cdot t, \left(y \cdot x\right) \cdot z, \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(18 \cdot t, \left(y \cdot x\right) \cdot z, -4 \cdot \color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      16. lower-*.f64 86.7

          \[\leadsto \mathsf{fma}\left(18 \cdot t, \left(y \cdot x\right) \cdot z, -4 \cdot \mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   8. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18 \cdot t, \left(y \cdot x\right) \cdot z, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   9. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   10. Step-by-step derivation

   11. Applied rewrites 56.6%

       \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{-4} - \left(j \cdot 27\right) \cdot k \]
   12. Step-by-step derivation

       1. lift--.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4 - \left(j \cdot 27\right) \cdot k} \]

       2. sub-neg N/A

          \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4 + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

       3. lift-*.f64 N/A

          \[\leadsto \left(a \cdot t\right) \cdot -4 + \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) \]

       4. distribute-lft-neg-out N/A

          \[\leadsto \left(a \cdot t\right) \cdot -4 + \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} \]

       5. lift-*.f64 N/A

          \[\leadsto \left(a \cdot t\right) \cdot -4 + \left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right)\right) \cdot k \]

       6. distribute-rgt-neg-in N/A

          \[\leadsto \left(a \cdot t\right) \cdot -4 + \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)} \cdot k \]

       7. metadata-eval N/A

          \[\leadsto \left(a \cdot t\right) \cdot -4 + \left(j \cdot \color{blue}{-27}\right) \cdot k \]

       8. associate-*r* N/A

          \[\leadsto \left(a \cdot t\right) \cdot -4 + \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

       9. lift-*.f64 N/A

          \[\leadsto \left(a \cdot t\right) \cdot -4 + j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

       10. *-commutative N/A

           \[\leadsto \left(a \cdot t\right) \cdot -4 + \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

       11. lift-*.f64 N/A

           \[\leadsto \left(a \cdot t\right) \cdot -4 + \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   13. Applied rewrites 57.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \left(t \cdot a\right) \cdot -4\right)} \]

   if -23000 < t < 0.00379999999999999999

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27, k \cdot j, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 89.7%

      \[\leadsto \mathsf{fma}\left(-27, k \cdot j, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\right)\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   9. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

      6. metadata-eval N/A

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) + \color{blue}{-27} \cdot \left(j \cdot k\right) \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} \]

      8. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) \]

      9. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right) + b \cdot c\right)} \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right) + b \cdot c\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\left(a \cdot t\right) \cdot -4} + b \cdot c\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\color{blue}{a \cdot t}, -4, b \cdot c\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right)\right) \]

      16. lower-*.f64 67.3

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right)\right) \]

   10. Applied rewrites 67.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right)} \]

   11. Taylor expanded in t around 0

       \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 61.6%

       \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23000:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;t \leq 0.0038:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot x\right) \cdot -4\\ \mathbf{if}\;i \leq -3.8 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* i x) -4.0)))
   (if (<= i -3.8e+111)
     t_1
     (if (<= i 1.65e+261) (fma (* -27.0 k) j (* b c)) 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 = (i * x) * -4.0;
	double tmp;
	if (i <= -3.8e+111) {
		tmp = t_1;
	} else if (i <= 1.65e+261) {
		tmp = fma((-27.0 * k), j, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(i * x) * -4.0)
	tmp = 0.0
	if (i <= -3.8e+111)
		tmp = t_1;
	elseif (i <= 1.65e+261)
		tmp = fma(Float64(-27.0 * k), j, Float64(b * c));
	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[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[i, -3.8e+111], t$95$1, If[LessEqual[i, 1.65e+261], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -3.79999999999999976e111 or 1.65e261 < i

   1. Initial program 84.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      3. lower-*.f64 61.9

         \[\leadsto \color{blue}{\left(i \cdot x\right)} \cdot -4 \]

   5. Applied rewrites 61.9%

      \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

   if -3.79999999999999976e111 < i < 1.65e261

   1. Initial program 85.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Applied rewrites 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27, k \cdot j, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 88.3%

      \[\leadsto \mathsf{fma}\left(-27, k \cdot j, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\right)\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   9. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

      6. metadata-eval N/A

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) + \color{blue}{-27} \cdot \left(j \cdot k\right) \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} \]

      8. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) \]

      9. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right) + b \cdot c\right)} \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right) + b \cdot c\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\left(a \cdot t\right) \cdot -4} + b \cdot c\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)}\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\color{blue}{a \cdot t}, -4, b \cdot c\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right)\right) \]

      16. lower-*.f64 68.5

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right)\right) \]

   10. Applied rewrites 68.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right)} \]

   11. Taylor expanded in t around 0

       \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 51.4%

       \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, b \cdot c\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 23.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \left(-27 \cdot k\right) \cdot j \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* (* -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) {
	return (-27.0 * k) * j;
}

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 = ((-27.0d0) * k) * j
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 (-27.0 * k) * j;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (-27.0 * k) * j

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(-27.0 * k) * j)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (-27.0 * k) * j;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]

Derivation

1. Initial program 84.8%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in j around inf

   \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   2. *-commutative N/A

      \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   3. lower-*.f64 27.7

      \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

5. Applied rewrites 27.7%

   \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
6. Step-by-step derivation

7. Applied rewrites 27.7%

   \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]
8. Add Preprocessing

Alternative 21: 23.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \left(-27 \cdot j\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* (* -27.0 j) 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 (-27.0 * j) * 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 = ((-27.0d0) * j) * 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 (-27.0 * j) * k;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (-27.0 * j) * k

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(-27.0 * j) * k)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (-27.0 * j) * k;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]

Derivation

1. Initial program 84.8%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in j around inf

   \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   2. *-commutative N/A

      \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   3. lower-*.f64 27.7

      \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

5. Applied rewrites 27.7%

   \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
6. Step-by-step derivation

7. Applied rewrites 28.1%

   \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]
8. Add Preprocessing

Alternative 22: 23.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \left(j \cdot k\right) \cdot -27 \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* (* j k) -27.0))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (j * k) * -27.0;
}

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 = (j * k) * (-27.0d0)
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 (j * k) * -27.0;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (j * k) * -27.0

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(j * k) * -27.0)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (j * k) * -27.0;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]

Derivation

1. Initial program 84.8%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in j around inf

   \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   2. *-commutative N/A

      \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   3. lower-*.f64 27.7

      \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

5. Applied rewrites 27.7%

   \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

6. Final simplification 27.7%

   \[\leadsto \left(j \cdot k\right) \cdot -27 \]
7. Add Preprocessing

Developer Target 1: 88.8% 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 2024298 
(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)))