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

Percentage Accurate: 85.1% → 90.2%

Time: 33.1s

Alternatives: 21

Speedup: 1.0×

• 51.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% 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: 90.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 4\right) \cdot i\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - t\_1\right) - t\_2 \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot t\_3\right) - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\frac{\mathsf{fma}\left(t, t\_3, \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)}{i} + x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 4.0) i))
        (t_2 (* (* j 27.0) k))
        (t_3 (fma -4.0 a (* 18.0 (* z (* x y))))))
   (if (<=
        (-
         (- (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c)) t_1)
         t_2)
        INFINITY)
     (- (- (+ (* b c) (* t t_3)) t_1) t_2)
     (* i (+ (/ (fma t t_3 (fma b c (* j (* k -27.0)))) i) (* x -4.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = fma(-4.0, a, (18.0 * (z * (x * y))));
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - t_1) - t_2) <= ((double) INFINITY)) {
		tmp = (((b * c) + (t * t_3)) - t_1) - t_2;
	} else {
		tmp = i * ((fma(t, t_3, fma(b, c, (j * (k * -27.0)))) / i) + (x * -4.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y))))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - t_1) - t_2) <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * t_3)) - t_1) - t_2);
	else
		tmp = Float64(i * Float64(Float64(fma(t, t_3, fma(b, c, Float64(j * Float64(k * -27.0)))) / i) + Float64(x * -4.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(i * N[(N[(N[(t * t$95$3 + N[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision] + N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

      5. lower-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 96.4

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

   5. Applied rewrites 96.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{i} - -4 \cdot x\right)\right)} \]

   5. Applied rewrites 68.4%

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

4. Final simplification 94.3%

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

Alternative 2: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+236}:\\ \;\;\;\;\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), \mathsf{fma}\left(b, c, -4 \cdot \mathsf{fma}\left(t, a, x \cdot i\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right), b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 -5e+236)
     (fma 18.0 (* t (* x (* y z))) (fma b c (* -4.0 (fma t a (* x i)))))
     (if (<= t_1 5e+187)
       (fma b c (fma -4.0 (fma a t (* x i)) (* j (* k -27.0))))
       (if (<= t_1 INFINITY)
         (fma -4.0 (* x i) (fma t (fma -4.0 a (* 18.0 (* z (* x y)))) (* b c)))
         (fma
          (* j k)
          -27.0
          (fma x (fma -4.0 i (* z (* t (* 18.0 y)))) (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -5e+236) {
		tmp = fma(18.0, (t * (x * (y * z))), fma(b, c, (-4.0 * fma(t, a, (x * i)))));
	} else if (t_1 <= 5e+187) {
		tmp = fma(b, c, fma(-4.0, fma(a, t, (x * i)), (j * (k * -27.0))));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma(-4.0, (x * i), fma(t, fma(-4.0, a, (18.0 * (z * (x * y)))), (b * c)));
	} else {
		tmp = fma((j * k), -27.0, fma(x, fma(-4.0, i, (z * (t * (18.0 * y)))), (b * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= -5e+236)
		tmp = fma(18.0, Float64(t * Float64(x * Float64(y * z))), fma(b, c, Float64(-4.0 * fma(t, a, Float64(x * i)))));
	elseif (t_1 <= 5e+187)
		tmp = fma(b, c, fma(-4.0, fma(a, t, Float64(x * i)), Float64(j * Float64(k * -27.0))));
	elseif (t_1 <= Inf)
		tmp = fma(-4.0, Float64(x * i), fma(t, fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))), Float64(b * c)));
	else
		tmp = fma(Float64(j * k), -27.0, fma(x, fma(-4.0, i, Float64(z * Float64(t * Float64(18.0 * y)))), Float64(b * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+236], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(-4.0 * N[(t * a + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+187], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(-4.0 * N[(x * i), $MachinePrecision] + N[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(x * N[(-4.0 * i + N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -4.9999999999999997e236

   1. Initial program 88.8%

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

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(-1 \cdot \frac{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{i} - -4 \cdot x\right)\right)} \]

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. sub-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. distribute-lft-out N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 87.7

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

   8. Applied rewrites 87.7%

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

   if -4.9999999999999997e236 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 5.0000000000000001e187

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 90.7

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

   5. Applied rewrites 90.7%

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

   if 5.0000000000000001e187 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < +inf.0

   1. Initial program 88.7%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Applied rewrites 86.7%

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

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

   1. Initial program 0.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 0.0

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 57.4%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*l* N/A

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

      7. associate-+r+ N/A

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

      8. associate-*r* N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

   7. Applied rewrites 65.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -5 \cdot 10^{+236}:\\ \;\;\;\;\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), \mathsf{fma}\left(b, c, -4 \cdot \mathsf{fma}\left(t, a, x \cdot i\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right), b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Developer Target 1: 88.9% 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 2024228 
(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)))