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

Percentage Accurate: 85.9% → 92.3%

Time: 6.6s

Alternatives: 20

Speedup: 0.8×

• 50.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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: 85.9% accurate, 1.0× speedup

Math

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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: 92.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-190}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-57}:\\ \;\;\;\;\left(\left(-x \cdot \left(i \cdot 4 - \left(\left(y \cdot 18\right) \cdot t\right) \cdot z\right)\right) + \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right) - \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(t \cdot \left(\mathsf{fma}\left(-18, x \cdot \left(y \cdot z\right), -1 \cdot \frac{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\right)}{t}\right) - -4 \cdot a\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -4.3e-190)
   (fma
    (* -27.0 (fmax j k))
    (fmin j k)
    (fma (* i x) -4.0 (fma (fma -4.0 a (* z (* y (* 18.0 x)))) t (* c b))))
   (if (<= t 3.1e-57)
     (-
      (+
       (- (* x (- (* i 4.0) (* (* (* y 18.0) t) z))))
       (fma (* a t) -4.0 (* c b)))
      (* (* (fmin j k) 27.0) (fmax j k)))
     (*
      -1.0
      (*
       t
       (-
        (fma
         -18.0
         (* x (* y z))
         (*
          -1.0
          (/
           (- (* b c) (fma 4.0 (* i x) (* 27.0 (* (fmin j k) (fmax j k)))))
           t)))
        (* -4.0 a)))))))

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 <= -4.3e-190) {
		tmp = fma((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -4.0, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, (c * b))));
	} else if (t <= 3.1e-57) {
		tmp = (-(x * ((i * 4.0) - (((y * 18.0) * t) * z))) + fma((a * t), -4.0, (c * b))) - ((fmin(j, k) * 27.0) * fmax(j, k));
	} else {
		tmp = -1.0 * (t * (fma(-18.0, (x * (y * z)), (-1.0 * (((b * c) - fma(4.0, (i * x), (27.0 * (fmin(j, k) * fmax(j, k))))) / t))) - (-4.0 * a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -4.3e-190)
		tmp = fma(Float64(-27.0 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -4.0, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, Float64(c * b))));
	elseif (t <= 3.1e-57)
		tmp = Float64(Float64(Float64(-Float64(x * Float64(Float64(i * 4.0) - Float64(Float64(Float64(y * 18.0) * t) * z)))) + fma(Float64(a * t), -4.0, Float64(c * b))) - Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k)));
	else
		tmp = Float64(-1.0 * Float64(t * Float64(fma(-18.0, Float64(x * Float64(y * z)), Float64(-1.0 * Float64(Float64(Float64(b * c) - fma(4.0, Float64(i * x), Float64(27.0 * Float64(fmin(j, k) * fmax(j, k))))) / t))) - Float64(-4.0 * a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -4.3e-190], N[(N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-57], N[(N[((-N[(x * N[(N[(i * 4.0), $MachinePrecision] - N[(N[(N[(y * 18.0), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(t * N[(N[(-18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision] + N[(27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3e-190

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   if -4.3e-190 < t < 3.09999999999999976e-57

   1. Initial program 85.9%

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

   3. Applied rewrites 87.8%

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

   if 3.09999999999999976e-57 < t

   1. Initial program 85.9%

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

   2. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 77.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\mathsf{fma}\left(-18, x \cdot \left(y \cdot z\right), -1 \cdot \frac{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)}{t}\right) - -4 \cdot a\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 92.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-50}:\\ \;\;\;\;\left(\left(-x \cdot \left(i \cdot 4 - \left(\left(y \cdot 18\right) \cdot t\right) \cdot z\right)\right) + \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right) - \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -27.0 (fmax j k))
          (fmin j k)
          (fma
           (* i x)
           -4.0
           (fma (fma -4.0 a (* z (* y (* 18.0 x)))) t (* c b))))))
   (if (<= t -4.3e-190)
     t_1
     (if (<= t 5e-50)
       (-
        (+
         (- (* x (- (* i 4.0) (* (* (* y 18.0) t) z))))
         (fma (* a t) -4.0 (* c b)))
        (* (* (fmin j k) 27.0) (fmax 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((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -4.0, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, (c * b))));
	double tmp;
	if (t <= -4.3e-190) {
		tmp = t_1;
	} else if (t <= 5e-50) {
		tmp = (-(x * ((i * 4.0) - (((y * 18.0) * t) * z))) + fma((a * t), -4.0, (c * b))) - ((fmin(j, k) * 27.0) * fmax(j, k));
	} 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 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -4.0, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, Float64(c * b))))
	tmp = 0.0
	if (t <= -4.3e-190)
		tmp = t_1;
	elseif (t <= 5e-50)
		tmp = Float64(Float64(Float64(-Float64(x * Float64(Float64(i * 4.0) - Float64(Float64(Float64(y * 18.0) * t) * z)))) + fma(Float64(a * t), -4.0, Float64(c * b))) - Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k)));
	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 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e-190], t$95$1, If[LessEqual[t, 5e-50], N[(N[((-N[(x * N[(N[(i * 4.0), $MachinePrecision] - N[(N[(N[(y * 18.0), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3e-190 or 4.99999999999999968e-50 < t

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   if -4.3e-190 < t < 4.99999999999999968e-50

   1. Initial program 85.9%

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

   3. Applied rewrites 87.8%

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

Alternative 3: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := -27 \cdot \mathsf{max}\left(j, k\right)\\ t_2 := \mathsf{fma}\left(t\_1, \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{-188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-208}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (fmax j k)))
        (t_2
         (fma
          t_1
          (fmin j k)
          (fma
           (* i x)
           -4.0
           (fma (fma -4.0 a (* z (* y (* 18.0 x)))) t (* c b))))))
   (if (<= t -5.2e-188)
     t_2
     (if (<= t 6e-208) (fma t_1 (fmin j k) (fma (* i x) -4.0 (* b c))) 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 = -27.0 * fmax(j, k);
	double t_2 = fma(t_1, fmin(j, k), fma((i * x), -4.0, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, (c * b))));
	double tmp;
	if (t <= -5.2e-188) {
		tmp = t_2;
	} else if (t <= 6e-208) {
		tmp = fma(t_1, fmin(j, k), fma((i * x), -4.0, (b * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * fmax(j, k))
	t_2 = fma(t_1, fmin(j, k), fma(Float64(i * x), -4.0, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, Float64(c * b))))
	tmp = 0.0
	if (t <= -5.2e-188)
		tmp = t_2;
	elseif (t <= 6e-208)
		tmp = fma(t_1, fmin(j, k), fma(Float64(i * x), -4.0, Float64(b * c)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e-188], t$95$2, If[LessEqual[t, 6e-208], N[(t$95$1 * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2000000000000001e-188 or 5.99999999999999972e-208 < t

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   if -5.2000000000000001e-188 < t < 5.99999999999999972e-208

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in t around 0

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

      1. lower-*.f64 62.0%

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

   6. Applied rewrites 62.0%

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

Alternative 4: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{-80}:\\ \;\;\;\;\mathsf{fma}\left(-27, t\_1, \mathsf{fma}\left(b, c, t \cdot \mathsf{fma}\left(-4, a, 18 \cdot t\_2\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-197}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(18, t \cdot t\_2, b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, -4, \left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fmin j k) (fmax j k))) (t_2 (* x (* y z))))
   (if (<= t -1.16e-80)
     (fma -27.0 t_1 (fma b c (* t (fma -4.0 a (* 18.0 t_2)))))
     (if (<= t 9.5e-197)
       (fma (* -27.0 (fmax j k)) (fmin j k) (fma (* i x) -4.0 (* b c)))
       (if (<= t 3e+192)
         (- (fma 18.0 (* t t_2) (* b c)) (fma 4.0 (* i x) (* 27.0 t_1)))
         (* (fma a -4.0 (* (* (* 18.0 x) y) z)) 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 t_1 = fmin(j, k) * fmax(j, k);
	double t_2 = x * (y * z);
	double tmp;
	if (t <= -1.16e-80) {
		tmp = fma(-27.0, t_1, fma(b, c, (t * fma(-4.0, a, (18.0 * t_2)))));
	} else if (t <= 9.5e-197) {
		tmp = fma((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -4.0, (b * c)));
	} else if (t <= 3e+192) {
		tmp = fma(18.0, (t * t_2), (b * c)) - fma(4.0, (i * x), (27.0 * t_1));
	} else {
		tmp = fma(a, -4.0, (((18.0 * x) * y) * z)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fmin(j, k) * fmax(j, k))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (t <= -1.16e-80)
		tmp = fma(-27.0, t_1, fma(b, c, Float64(t * fma(-4.0, a, Float64(18.0 * t_2)))));
	elseif (t <= 9.5e-197)
		tmp = fma(Float64(-27.0 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -4.0, Float64(b * c)));
	elseif (t <= 3e+192)
		tmp = Float64(fma(18.0, Float64(t * t_2), Float64(b * c)) - fma(4.0, Float64(i * x), Float64(27.0 * t_1)));
	else
		tmp = Float64(fma(a, -4.0, Float64(Float64(Float64(18.0 * x) * y) * z)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.16e-80], N[(-27.0 * t$95$1 + N[(b * c + N[(t * N[(-4.0 * a + N[(18.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-197], N[(N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+192], N[(N[(18.0 * N[(t * t$95$2), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision] + N[(27.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * -4.0 + N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15999999999999996e-80

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in i around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 76.4%

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

   6. Applied rewrites 76.4%

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

   if -1.15999999999999996e-80 < t < 9.5000000000000003e-197

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in t around 0

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

      1. lower-*.f64 62.0%

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

   6. Applied rewrites 62.0%

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

   if 9.5000000000000003e-197 < t < 3e192

   1. Initial program 85.9%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.5%

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

   4. Applied rewrites 73.5%

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

   if 3e192 < t

   1. Initial program 85.9%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4} \cdot a\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      7. lower-*.f64 41.8%

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

   6. Applied rewrites 42.5%

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

Alternative 5: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\\ t_2 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{-80}:\\ \;\;\;\;\mathsf{fma}\left(-27, t\_1, \mathsf{fma}\left(b, c, t\_2\right)\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, t\_1, t\_2\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fmin j k) (fmax j k)))
        (t_2 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -1.16e-80)
     (fma -27.0 t_1 (fma b c t_2))
     (if (<= t 2.05e+180)
       (fma (* -27.0 (fmax j k)) (fmin j k) (fma (* i x) -4.0 (* b c)))
       (fma -27.0 t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fmin(j, k) * fmax(j, k);
	double t_2 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -1.16e-80) {
		tmp = fma(-27.0, t_1, fma(b, c, t_2));
	} else if (t <= 2.05e+180) {
		tmp = fma((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -4.0, (b * c)));
	} else {
		tmp = fma(-27.0, t_1, t_2);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fmin(j, k) * fmax(j, k))
	t_2 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.16e-80)
		tmp = fma(-27.0, t_1, fma(b, c, t_2));
	elseif (t <= 2.05e+180)
		tmp = fma(Float64(-27.0 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -4.0, Float64(b * c)));
	else
		tmp = fma(-27.0, t_1, t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.16e-80], N[(-27.0 * t$95$1 + N[(b * c + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+180], N[(N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15999999999999996e-80

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in i around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 76.4%

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

   6. Applied rewrites 76.4%

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

   if -1.15999999999999996e-80 < t < 2.05e180

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in t around 0

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

      1. lower-*.f64 62.0%

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

   6. Applied rewrites 62.0%

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

   if 2.05e180 < t

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in i around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 76.4%

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

   6. Applied rewrites 76.4%

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

   7. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 58.4%

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

   9. Applied rewrites 58.4%

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

Alternative 6: 71.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, -4, \left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, b \cdot c - \left(27 \cdot \mathsf{min}\left(j, k\right)\right) \cdot \mathsf{max}\left(j, k\right)\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma a -4.0 (* (* (* 18.0 x) y) z)) t)))
   (if (<= t -7.2e+207)
     t_1
     (if (<= t -8.5e+90)
       (fma (* t -4.0) a (- (* b c) (* (* 27.0 (fmin j k)) (fmax j k))))
       (if (<= t 3e+192)
         (fma (* -27.0 (fmax j k)) (fmin j k) (fma (* i x) -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(a, -4.0, (((18.0 * x) * y) * z)) * t;
	double tmp;
	if (t <= -7.2e+207) {
		tmp = t_1;
	} else if (t <= -8.5e+90) {
		tmp = fma((t * -4.0), a, ((b * c) - ((27.0 * fmin(j, k)) * fmax(j, k))));
	} else if (t <= 3e+192) {
		tmp = fma((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -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(a, -4.0, Float64(Float64(Float64(18.0 * x) * y) * z)) * t)
	tmp = 0.0
	if (t <= -7.2e+207)
		tmp = t_1;
	elseif (t <= -8.5e+90)
		tmp = fma(Float64(t * -4.0), a, Float64(Float64(b * c) - Float64(Float64(27.0 * fmin(j, k)) * fmax(j, k))));
	elseif (t <= 3e+192)
		tmp = fma(Float64(-27.0 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -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[(a * -4.0 + N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -7.2e+207], t$95$1, If[LessEqual[t, -8.5e+90], N[(N[(t * -4.0), $MachinePrecision] * a + N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[Min[j, k], $MachinePrecision]), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+192], N[(N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.20000000000000028e207 or 3e192 < t

   1. Initial program 85.9%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4} \cdot a\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      7. lower-*.f64 41.8%

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

   6. Applied rewrites 42.5%

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

   if -7.20000000000000028e207 < t < -8.5000000000000002e90

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate--r+ N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate--l+ N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower-*.f64 N/A

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

      20. lower--.f64 60.8%

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

   6. Applied rewrites 60.8%

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

   if -8.5000000000000002e90 < t < 3e192

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in t around 0

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

      1. lower-*.f64 62.0%

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

   6. Applied rewrites 62.0%

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

Alternative 7: 70.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, -4, \left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;b \cdot c - \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(\mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right)\right)\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma a -4.0 (* (* (* 18.0 x) y) z)) t)))
   (if (<= t -7.2e+207)
     t_1
     (if (<= t -8.5e+90)
       (- (* b c) (fma 4.0 (* a t) (* 27.0 (* (fmin j k) (fmax j k)))))
       (if (<= t 3e+192)
         (fma (* -27.0 (fmax j k)) (fmin j k) (fma (* i x) -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(a, -4.0, (((18.0 * x) * y) * z)) * t;
	double tmp;
	if (t <= -7.2e+207) {
		tmp = t_1;
	} else if (t <= -8.5e+90) {
		tmp = (b * c) - fma(4.0, (a * t), (27.0 * (fmin(j, k) * fmax(j, k))));
	} else if (t <= 3e+192) {
		tmp = fma((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -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(a, -4.0, Float64(Float64(Float64(18.0 * x) * y) * z)) * t)
	tmp = 0.0
	if (t <= -7.2e+207)
		tmp = t_1;
	elseif (t <= -8.5e+90)
		tmp = Float64(Float64(b * c) - fma(4.0, Float64(a * t), Float64(27.0 * Float64(fmin(j, k) * fmax(j, k)))));
	elseif (t <= 3e+192)
		tmp = fma(Float64(-27.0 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -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[(a * -4.0 + N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -7.2e+207], t$95$1, If[LessEqual[t, -8.5e+90], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision] + N[(27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+192], N[(N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.20000000000000028e207 or 3e192 < t

   1. Initial program 85.9%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4} \cdot a\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      7. lower-*.f64 41.8%

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

   6. Applied rewrites 42.5%

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

   if -7.20000000000000028e207 < t < -8.5000000000000002e90

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   if -8.5000000000000002e90 < t < 3e192

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in t around 0

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

      1. lower-*.f64 62.0%

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

   6. Applied rewrites 62.0%

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

Alternative 8: 70.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-27, \mathsf{min}\left(j, k\right) \cdot \mathsf{max}\left(j, k\right), t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          -27.0
          (* (fmin j k) (fmax j k))
          (* t (fma -4.0 a (* 18.0 (* x (* y z))))))))
   (if (<= t -2.7e+131)
     t_1
     (if (<= t 2.05e+180)
       (fma (* -27.0 (fmax j k)) (fmin j k) (fma (* i x) -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, (fmin(j, k) * fmax(j, k)), (t * fma(-4.0, a, (18.0 * (x * (y * z))))));
	double tmp;
	if (t <= -2.7e+131) {
		tmp = t_1;
	} else if (t <= 2.05e+180) {
		tmp = fma((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -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(-27.0, Float64(fmin(j, k) * fmax(j, k)), Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z))))))
	tmp = 0.0
	if (t <= -2.7e+131)
		tmp = t_1;
	elseif (t <= 2.05e+180)
		tmp = fma(Float64(-27.0 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -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[(-27.0 * N[(N[Min[j, k], $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+131], t$95$1, If[LessEqual[t, 2.05e+180], N[(N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000004e131 or 2.05e180 < t

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in i around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 76.4%

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

   6. Applied rewrites 76.4%

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

   7. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 58.4%

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

   9. Applied rewrites 58.4%

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

   if -2.70000000000000004e131 < t < 2.05e180

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in t around 0

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

      1. lower-*.f64 62.0%

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

   6. Applied rewrites 62.0%

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

Alternative 9: 69.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, -4, \left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot \mathsf{max}\left(j, k\right), \mathsf{min}\left(j, k\right), \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma a -4.0 (* (* (* 18.0 x) y) z)) t)))
   (if (<= t -1.65e+192)
     t_1
     (if (<= t 3e+192)
       (fma (* -27.0 (fmax j k)) (fmin j k) (fma (* i x) -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(a, -4.0, (((18.0 * x) * y) * z)) * t;
	double tmp;
	if (t <= -1.65e+192) {
		tmp = t_1;
	} else if (t <= 3e+192) {
		tmp = fma((-27.0 * fmax(j, k)), fmin(j, k), fma((i * x), -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(a, -4.0, Float64(Float64(Float64(18.0 * x) * y) * z)) * t)
	tmp = 0.0
	if (t <= -1.65e+192)
		tmp = t_1;
	elseif (t <= 3e+192)
		tmp = fma(Float64(-27.0 * fmax(j, k)), fmin(j, k), fma(Float64(i * x), -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[(a * -4.0 + N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.65e+192], t$95$1, If[LessEqual[t, 3e+192], N[(N[(-27.0 * N[Max[j, k], $MachinePrecision]), $MachinePrecision] * N[Min[j, k], $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65000000000000005e192 or 3e192 < t

   1. Initial program 85.9%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4} \cdot a\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      7. lower-*.f64 41.8%

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

   6. Applied rewrites 42.5%

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

   if -1.65000000000000005e192 < t < 3e192

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in t around 0

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

      1. lower-*.f64 62.0%

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

   6. Applied rewrites 62.0%

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

Alternative 10: 59.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-127}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k))))
        (t_2 (* x (fma -4.0 i (* 18.0 (* t (* y z)))))))
   (if (<= x -1.85e-75)
     t_2
     (if (<= x 3.9e-274)
       t_1
       (if (<= x 9e-127)
         (fma (* a -4.0) t (* b c))
         (if (<= x 1.5e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -1.85e-75) {
		tmp = t_2;
	} else if (x <= 3.9e-274) {
		tmp = t_1;
	} else if (x <= 9e-127) {
		tmp = fma((a * -4.0), t, (b * c));
	} else if (x <= 1.5e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -1.85e-75)
		tmp = t_2;
	elseif (x <= 3.9e-274)
		tmp = t_1;
	elseif (x <= 9e-127)
		tmp = fma(Float64(a * -4.0), t, Float64(b * c));
	elseif (x <= 1.5e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e-75], t$95$2, If[LessEqual[x, 3.9e-274], t$95$1, If[LessEqual[x, 9e-127], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85000000000000012e-75 or 1.5e14 < x

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.7%

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

   6. Applied rewrites 42.7%

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

   if -1.85000000000000012e-75 < x < 3.89999999999999985e-274 or 8.9999999999999998e-127 < x < 1.5e14

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 44.1%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 44.1%

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

   if 3.89999999999999985e-274 < x < 8.9999999999999998e-127

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 41.6%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 41.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(a \cdot t\right) \]

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      8. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      9. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

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

Alternative 11: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+82}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+131)
     t_1
     (if (<= t_2 -1e+82)
       (* 18.0 (* t (* x (* y z))))
       (if (<= t_2 2e+61) (fma (* a -4.0) 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 = (b * c) - (27.0 * (j * k));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+131) {
		tmp = t_1;
	} else if (t_2 <= -1e+82) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t_2 <= 2e+61) {
		tmp = fma((a * -4.0), 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(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+131)
		tmp = t_1;
	elseif (t_2 <= -1e+82)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t_2 <= 2e+61)
		tmp = fma(Float64(a * -4.0), 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[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+131], t$95$1, If[LessEqual[t$95$2, -1e+82], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+61], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999995e131 or 1.9999999999999999e61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 44.1%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 44.1%

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

   if -4.99999999999999995e131 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999996e81

   1. Initial program 85.9%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4} \cdot a\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      7. lower-*.f64 41.8%

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 20.6%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 20.6%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 25.8%

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

   10. Applied rewrites 25.8%

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

   if -9.9999999999999996e81 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e61

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 41.6%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 41.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(a \cdot t\right) \]

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      8. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      9. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

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

Alternative 12: 54.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{if}\;b \cdot c \leq -3.6 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* a -4.0) t (* b c))))
   (if (<= (* b c) -3.6e+107)
     t_1
     (if (<= (* b c) 9.6e+187) (fma (* t a) -4.0 (* (* 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((a * -4.0), t, (b * c));
	double tmp;
	if ((b * c) <= -3.6e+107) {
		tmp = t_1;
	} else if ((b * c) <= 9.6e+187) {
		tmp = fma((t * a), -4.0, ((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(a * -4.0), t, Float64(b * c))
	tmp = 0.0
	if (Float64(b * c) <= -3.6e+107)
		tmp = t_1;
	elseif (Float64(b * c) <= 9.6e+187)
		tmp = fma(Float64(t * a), -4.0, 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[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.6e+107], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9.6e+187], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.5999999999999998e107 or 9.59999999999999942e187 < (*.f64 b c)

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 41.6%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 41.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(a \cdot t\right) \]

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      8. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      9. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

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

   if -3.5999999999999998e107 < (*.f64 b c) < 9.59999999999999942e187

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in b around 0

      \[\leadsto -1 \cdot \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(a \cdot t\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot \color{blue}{t}, 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 40.5%

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

   7. Applied rewrites 40.5%

      \[\leadsto -1 \cdot \color{blue}{\mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -1 \cdot \mathsf{fma}\left(4, \color{blue}{a \cdot t}, 27 \cdot \left(j \cdot k\right)\right) \]

      2. lift-fma.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(\color{blue}{j} \cdot k\right)\right) \]

      4. distribute-rgt-in N/A

         \[\leadsto \left(4 \cdot \left(a \cdot t\right)\right) \cdot -1 + \left(27 \cdot \left(j \cdot k\right)\right) \cdot \color{blue}{-1} \]

      5. *-commutative N/A

         \[\leadsto \left(4 \cdot \left(a \cdot t\right)\right) \cdot -1 + -1 \cdot \left(27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(4 \cdot \left(a \cdot t\right)\right) \cdot -1 + -1 \cdot \left(27 \cdot \left(j \cdot \color{blue}{k}\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(4 \cdot \left(a \cdot t\right)\right) \cdot -1 + \left(-1 \cdot 27\right) \cdot \left(j \cdot \color{blue}{k}\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(4 \cdot \left(a \cdot t\right)\right) \cdot -1 + -27 \cdot \left(j \cdot k\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(4 \cdot \left(a \cdot t\right)\right) \cdot -1 + -27 \cdot \left(j \cdot k\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(a \cdot t\right) \cdot 4\right) \cdot -1 + -27 \cdot \left(j \cdot k\right) \]

      11. associate-*l* N/A

          \[\leadsto \left(a \cdot t\right) \cdot \left(4 \cdot -1\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      12. metadata-eval N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 40.5%

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

   9. Applied rewrites 40.5%

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

Alternative 13: 53.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+125)
     t_1
     (if (<= t_2 2e+61) (fma (* a -4.0) 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 = (b * c) - (27.0 * (j * k));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+125) {
		tmp = t_1;
	} else if (t_2 <= 2e+61) {
		tmp = fma((a * -4.0), 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(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+125)
		tmp = t_1;
	elseif (t_2 <= 2e+61)
		tmp = fma(Float64(a * -4.0), 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[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+125], t$95$1, If[LessEqual[t$95$2, 2e+61], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999998e125 or 1.9999999999999999e61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 44.1%

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 44.1%

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

   if -1.9999999999999998e125 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e61

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 41.6%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 41.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(a \cdot t\right) \]

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      8. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      9. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

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

Alternative 14: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ t_2 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* (fmax j k) -27.0) (fmin j k)))
        (t_2 (* (* (fmin j k) 27.0) (fmax j k))))
   (if (<= t_2 -2e+232)
     t_1
     (if (<= t_2 5e+153) (fma (* a -4.0) 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 = (fmax(j, k) * -27.0) * fmin(j, k);
	double t_2 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_2 <= -2e+232) {
		tmp = t_1;
	} else if (t_2 <= 5e+153) {
		tmp = fma((a * -4.0), 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(Float64(fmax(j, k) * -27.0) * fmin(j, k))
	t_2 = Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k))
	tmp = 0.0
	if (t_2 <= -2e+232)
		tmp = t_1;
	elseif (t_2 <= 5e+153)
		tmp = fma(Float64(a * -4.0), 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[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+232], t$95$1, If[LessEqual[t$95$2, 5e+153], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000011e232 or 5.00000000000000018e153 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.3%

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

   4. Applied rewrites 23.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

      6. lower-*.f64 23.3%

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

      7. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

      8. *-commutative N/A

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

      9. lower-*.f64 23.3%

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

   6. Applied rewrites 23.3%

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

   if -2.00000000000000011e232 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000018e153

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3%

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in j around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 41.6%

         \[\leadsto b \cdot c - 4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 41.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(a \cdot t\right) \]

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      8. lift-*.f64 N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot c \]

      9. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 41.9%

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

   9. Applied rewrites 41.9%

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

Alternative 15: 36.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := -1 \cdot \left(-1 \cdot \left(b \cdot c\right)\right)\\ \mathbf{if}\;b \cdot c \leq -3.6 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{+187}:\\ \;\;\;\;\left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -1.0 (* -1.0 (* b c)))))
   (if (<= (* b c) -3.6e+107)
     t_1
     (if (<= (* b c) 9.6e+187) (* (* (fmax j k) -27.0) (fmin 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 = -1.0 * (-1.0 * (b * c));
	double tmp;
	if ((b * c) <= -3.6e+107) {
		tmp = t_1;
	} else if ((b * c) <= 9.6e+187) {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-1.0d0) * ((-1.0d0) * (b * c))
    if ((b * c) <= (-3.6d+107)) then
        tmp = t_1
    else if ((b * c) <= 9.6d+187) then
        tmp = (fmax(j, k) * (-27.0d0)) * fmin(j, k)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -1.0 * (-1.0 * (b * c));
	double tmp;
	if ((b * c) <= -3.6e+107) {
		tmp = t_1;
	} else if ((b * c) <= 9.6e+187) {
		tmp = (fmax(j, k) * -27.0) * fmin(j, k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -1.0 * (-1.0 * (b * c))
	tmp = 0
	if (b * c) <= -3.6e+107:
		tmp = t_1
	elif (b * c) <= 9.6e+187:
		tmp = (fmax(j, k) * -27.0) * fmin(j, k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-1.0 * Float64(-1.0 * Float64(b * c)))
	tmp = 0.0
	if (Float64(b * c) <= -3.6e+107)
		tmp = t_1;
	elseif (Float64(b * c) <= 9.6e+187)
		tmp = Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -1.0 * (-1.0 * (b * c));
	tmp = 0.0;
	if ((b * c) <= -3.6e+107)
		tmp = t_1;
	elseif ((b * c) <= 9.6e+187)
		tmp = (max(j, k) * -27.0) * min(j, k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-1.0 * N[(-1.0 * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.6e+107], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9.6e+187], N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.5999999999999998e107 or 9.59999999999999942e187 < (*.f64 b c)

   1. Initial program 85.9%

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

   3. Applied rewrites 89.3%

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

   4. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 74.9%

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

   7. Taylor expanded in b around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{\left(b \cdot c\right)}\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(-1 \cdot \left(b \cdot \color{blue}{c}\right)\right) \]

      2. lower-*.f64 24.3%

         \[\leadsto -1 \cdot \left(-1 \cdot \left(b \cdot c\right)\right) \]

   9. Applied rewrites 24.3%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{\left(b \cdot c\right)}\right) \]

   if -3.5999999999999998e107 < (*.f64 b c) < 9.59999999999999942e187

   1. Initial program 85.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.3%

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

   4. Applied rewrites 23.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

      6. lower-*.f64 23.3%

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

      7. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

      8. *-commutative N/A

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

      9. lower-*.f64 23.3%

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

   6. Applied rewrites 23.3%

      \[\leadsto \left(k \cdot -27\right) \cdot \color{blue}{j} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 35.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{max}\left(j, k\right) \cdot -27\right) \cdot \mathsf{min}\left(j, k\right)\\ t_2 := \left(\mathsf{min}\left(j, k\right) \cdot 27\right) \cdot \mathsf{max}\left(j, k\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+68}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* (fmax j k) -27.0) (fmin j k)))
        (t_2 (* (* (fmin j k) 27.0) (fmax j k))))
   (if (<= t_2 -5e+130) t_1 (if (<= t_2 1e+68) (* -4.0 (* i x)) 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 = (fmax(j, k) * -27.0) * fmin(j, k);
	double t_2 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_2 <= -5e+130) {
		tmp = t_1;
	} else if (t_2 <= 1e+68) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (fmax(j, k) * (-27.0d0)) * fmin(j, k)
    t_2 = (fmin(j, k) * 27.0d0) * fmax(j, k)
    if (t_2 <= (-5d+130)) then
        tmp = t_1
    else if (t_2 <= 1d+68) then
        tmp = (-4.0d0) * (i * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (fmax(j, k) * -27.0) * fmin(j, k);
	double t_2 = (fmin(j, k) * 27.0) * fmax(j, k);
	double tmp;
	if (t_2 <= -5e+130) {
		tmp = t_1;
	} else if (t_2 <= 1e+68) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (fmax(j, k) * -27.0) * fmin(j, k)
	t_2 = (fmin(j, k) * 27.0) * fmax(j, k)
	tmp = 0
	if t_2 <= -5e+130:
		tmp = t_1
	elif t_2 <= 1e+68:
		tmp = -4.0 * (i * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(fmax(j, k) * -27.0) * fmin(j, k))
	t_2 = Float64(Float64(fmin(j, k) * 27.0) * fmax(j, k))
	tmp = 0.0
	if (t_2 <= -5e+130)
		tmp = t_1;
	elseif (t_2 <= 1e+68)
		tmp = Float64(-4.0 * Float64(i * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (max(j, k) * -27.0) * min(j, k);
	t_2 = (min(j, k) * 27.0) * max(j, k);
	tmp = 0.0;
	if (t_2 <= -5e+130)
		tmp = t_1;
	elseif (t_2 <= 1e+68)
		tmp = -4.0 * (i * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[Max[j, k], $MachinePrecision] * -27.0), $MachinePrecision] * N[Min[j, k], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Min[j, k], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[j, k], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+130], t$95$1, If[LessEqual[t$95$2, 1e+68], N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999996e130 or 9.99999999999999953e67 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.3%

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

   4. Applied rewrites 23.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

      6. lower-*.f64 23.3%

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

      7. lift-*.f64 N/A

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

      8. *-commutative N/A

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

      9. lower-*.f64 23.3%

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

   6. Applied rewrites 23.3%

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

   if -4.9999999999999996e130 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999953e67

   1. Initial program 85.9%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 22.0%

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

   4. Applied rewrites 22.0%

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

Alternative 17: 35.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+130}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k\\ \mathbf{elif}\;t\_1 \leq 10^{+68}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+130)
     (* (* j -27.0) k)
     (if (<= t_1 1e+68) (* -4.0 (* i x)) (* -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 <= -5e+130) {
		tmp = (j * -27.0) * k;
	} else if (t_1 <= 1e+68) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 <= (-5d+130)) then
        tmp = (j * (-27.0d0)) * k
    else if (t_1 <= 1d+68) then
        tmp = (-4.0d0) * (i * x)
    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 <= -5e+130) {
		tmp = (j * -27.0) * k;
	} else if (t_1 <= 1e+68) {
		tmp = -4.0 * (i * x);
	} 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 <= -5e+130:
		tmp = (j * -27.0) * k
	elif t_1 <= 1e+68:
		tmp = -4.0 * (i * x)
	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 <= -5e+130)
		tmp = Float64(Float64(j * -27.0) * k);
	elseif (t_1 <= 1e+68)
		tmp = Float64(-4.0 * Float64(i * x));
	else
		tmp = Float64(-27.0 * Float64(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 <= -5e+130)
		tmp = (j * -27.0) * k;
	elseif (t_1 <= 1e+68)
		tmp = -4.0 * (i * x);
	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, -5e+130], N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t$95$1, 1e+68], N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999996e130

   1. Initial program 85.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.3%

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

   4. Applied rewrites 23.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

         \[\leadsto \left(j \cdot -27\right) \cdot k \]

      6. lower-*.f64 23.3%

         \[\leadsto \left(j \cdot -27\right) \cdot k \]

   6. Applied rewrites 23.3%

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

   if -4.9999999999999996e130 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999953e67

   1. Initial program 85.9%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 22.0%

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

   4. Applied rewrites 22.0%

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

   if 9.99999999999999953e67 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.3%

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

   4. Applied rewrites 23.3%

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

Alternative 18: 35.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+68}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+130) t_1 (if (<= t_2 1e+68) (* -4.0 (* i x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+130) {
		tmp = t_1;
	} else if (t_2 <= 1e+68) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+130)) then
        tmp = t_1
    else if (t_2 <= 1d+68) then
        tmp = (-4.0d0) * (i * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+130) {
		tmp = t_1;
	} else if (t_2 <= 1e+68) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+130:
		tmp = t_1
	elif t_2 <= 1e+68:
		tmp = -4.0 * (i * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+130)
		tmp = t_1;
	elseif (t_2 <= 1e+68)
		tmp = Float64(-4.0 * Float64(i * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+130)
		tmp = t_1;
	elseif (t_2 <= 1e+68)
		tmp = -4.0 * (i * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+130], t$95$1, If[LessEqual[t$95$2, 1e+68], N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999996e130 or 9.99999999999999953e67 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.3%

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

   4. Applied rewrites 23.3%

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

   if -4.9999999999999996e130 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999953e67

   1. Initial program 85.9%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 22.0%

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

   4. Applied rewrites 22.0%

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

Alternative 19: 34.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+61}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+125) t_1 (if (<= t_2 2e+61) (* -4.0 (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+125) {
		tmp = t_1;
	} else if (t_2 <= 2e+61) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+125)) then
        tmp = t_1
    else if (t_2 <= 2d+61) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+125) {
		tmp = t_1;
	} else if (t_2 <= 2e+61) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+125:
		tmp = t_1
	elif t_2 <= 2e+61:
		tmp = -4.0 * (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+125)
		tmp = t_1;
	elseif (t_2 <= 2e+61)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+125)
		tmp = t_1;
	elseif (t_2 <= 2e+61)
		tmp = -4.0 * (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+125], t$95$1, If[LessEqual[t$95$2, 2e+61], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999998e125 or 1.9999999999999999e61 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.3%

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

   4. Applied rewrites 23.3%

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

   if -1.9999999999999998e125 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e61

   1. Initial program 85.9%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4} \cdot a\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      7. lower-*.f64 41.8%

         \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{a}\right)\right) \]

   4. Applied rewrites 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 20.6%

         \[\leadsto -4 \cdot \left(a \cdot t\right) \]

   7. Applied rewrites 20.6%

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 20.6% accurate, 6.4× speedup

Math

\[-4 \cdot \left(a \cdot t\right) \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = (-4.0d0) * (a * t)
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 -4.0 * (a * t);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.9%

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

2. Taylor expanded in t around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)}\right) \]

   3. lower--.f64 N/A

      \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4 \cdot a}\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{-4} \cdot a\right)\right) \]

   5. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

   6. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

   7. lower-*.f64 41.8%

      \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot \color{blue}{a}\right)\right) \]

4. Applied rewrites 41.8%

   \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]

5. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 20.6%

      \[\leadsto -4 \cdot \left(a \cdot t\right) \]

7. Applied rewrites 20.6%

   \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025188 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))