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

Percentage Accurate: 85.1% → 91.5%

Time: 7.4s

Alternatives: 18

Speedup: 1.1×

• 50.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 91.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-174}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right) \cdot x - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* k j) 27.0 (* (* a t) 4.0))))
   (if (<= x -1e-87)
     (- (fma (fma (* 18.0 t) (* z y) (* -4.0 i)) x (* c b)) t_1)
     (if (<= x 2.8e-174)
       (-
        (-
         (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
         (* (* x 4.0) i))
        (* j (* k 27.0)))
       (fma c b (- (* (fma (* (* z y) t) 18.0 (* -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 = fma((k * j), 27.0, ((a * t) * 4.0));
	double tmp;
	if (x <= -1e-87) {
		tmp = fma(fma((18.0 * t), (z * y), (-4.0 * i)), x, (c * b)) - t_1;
	} else if (x <= 2.8e-174) {
		tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - (j * (k * 27.0));
	} else {
		tmp = fma(c, b, ((fma(((z * y) * t), 18.0, (-4.0 * i)) * x) - t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * j), 27.0, Float64(Float64(a * t) * 4.0))
	tmp = 0.0
	if (x <= -1e-87)
		tmp = Float64(fma(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)), x, Float64(c * b)) - t_1);
	elseif (x <= 2.8e-174)
		tmp = 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(j * Float64(k * 27.0)));
	else
		tmp = fma(c, b, Float64(Float64(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)) * x) - t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * 27.0 + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-87], N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 2.8e-174], 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[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.00000000000000002e-87

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 89.8%

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

   if -1.00000000000000002e-87 < x < 2.79999999999999999e-174

   1. Initial program 95.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

   if 2.79999999999999999e-174 < x

   1. Initial program 81.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 88.4%

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

   6. Applied rewrites 89.6%

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

Alternative 2: 90.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right) \cdot x - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot t, 18, \frac{c \cdot b}{z}\right) - \mathsf{fma}\left(\frac{\mathsf{fma}\left(i, x, a \cdot t\right)}{z}, 4, \frac{k \cdot j}{z} \cdot 27\right)\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 1e+81)
   (fma
    c
    b
    (-
     (* (fma (* (* z y) t) 18.0 (* -4.0 i)) x)
     (fma (* k j) 27.0 (* (* a t) 4.0))))
   (*
    (-
     (fma (* (* y x) t) 18.0 (/ (* c b) z))
     (fma (/ (fma i x (* a t)) z) 4.0 (* (/ (* k j) z) 27.0)))
    z)))

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 (z <= 1e+81) {
		tmp = fma(c, b, ((fma(((z * y) * t), 18.0, (-4.0 * i)) * x) - fma((k * j), 27.0, ((a * t) * 4.0))));
	} else {
		tmp = (fma(((y * x) * t), 18.0, ((c * b) / z)) - fma((fma(i, x, (a * t)) / z), 4.0, (((k * j) / z) * 27.0))) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 1e+81)
		tmp = fma(c, b, Float64(Float64(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)) * x) - fma(Float64(k * j), 27.0, Float64(Float64(a * t) * 4.0))));
	else
		tmp = Float64(Float64(fma(Float64(Float64(y * x) * t), 18.0, Float64(Float64(c * b) / z)) - fma(Float64(fma(i, x, Float64(a * t)) / z), 4.0, Float64(Float64(Float64(k * j) / z) * 27.0))) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 1e+81], N[(c * b + N[(N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0 + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(y * x), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(N[(c * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * 4.0 + N[(N[(N[(k * j), $MachinePrecision] / z), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.99999999999999921e80

   1. Initial program 85.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 89.6%

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

   6. Applied rewrites 90.7%

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

   if 9.99999999999999921e80 < z

   1. Initial program 82.1%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   7. Applied rewrites 88.9%

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

Alternative 3: 90.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.0%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 93.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 37.0%

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

   5. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 63.2

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

   7. Applied rewrites 63.2%

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

   8. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 63.9

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

   10. Applied rewrites 63.9%

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

Alternative 4: 88.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.1%

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

2. Taylor expanded in x around 0

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

   1. lower--.f64 N/A

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

4. Applied rewrites 87.7%

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

6. Applied rewrites 88.9%

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

Alternative 5: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x - t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+84)
     (- (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x) t_1)
     (if (<= t_1 1e+160)
       (fma (* 18.0 t) (* (* z y) x) (- (* c b) (* 4.0 (fma a t (* i x)))))
       (- (fma c b (* -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 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+84) {
		tmp = (fma((18.0 * t), (z * y), (-4.0 * i)) * x) - t_1;
	} else if (t_1 <= 1e+160) {
		tmp = fma((18.0 * t), ((z * y) * x), ((c * b) - (4.0 * fma(a, t, (i * x)))));
	} else {
		tmp = fma(c, b, (-4.0 * (a * t))) - t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+84)
		tmp = Float64(Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x) - t_1);
	elseif (t_1 <= 1e+160)
		tmp = fma(Float64(18.0 * t), Float64(Float64(z * y) * x), Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))));
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * Float64(a * t))) - t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+84], N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+160], N[(N[(18.0 * t), $MachinePrecision] * N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000012e84

   1. Initial program 82.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.9

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

   4. Applied rewrites 73.9%

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

   if -2.00000000000000012e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000001e160

   1. Initial program 87.1%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 82.1

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

   4. Applied rewrites 82.1%

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

   if 1.00000000000000001e160 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.9%

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

   2. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 73.9

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

   4. Applied rewrites 73.9%

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

Alternative 6: 76.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x - t\_1\\ \mathbf{elif}\;x \leq 0.00085:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -1.65e-46)
     (- (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x) t_1)
     (if (<= x 0.00085)
       (- (fma c b (* -4.0 (* a t))) t_1)
       (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* c b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -1.65e-46) {
		tmp = (fma((18.0 * t), (z * y), (-4.0 * i)) * x) - t_1;
	} else if (x <= 0.00085) {
		tmp = fma(c, b, (-4.0 * (a * t))) - t_1;
	} else {
		tmp = fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (c * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -1.65e-46)
		tmp = Float64(Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x) - t_1);
	elseif (x <= 0.00085)
		tmp = Float64(fma(c, b, Float64(-4.0 * Float64(a * t))) - t_1);
	else
		tmp = fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -1.65e-46], N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 0.00085], N[(N[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65000000000000007e-46

   1. Initial program 78.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.2

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

   4. Applied rewrites 73.2%

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

   if -1.65000000000000007e-46 < x < 8.49999999999999953e-4

   1. Initial program 94.6%

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

   2. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 79.1

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

   4. Applied rewrites 79.1%

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

   if 8.49999999999999953e-4 < x

   1. Initial program 75.3%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 71.5

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

   4. Applied rewrites 71.5%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

   7. Applied rewrites 75.3%

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

Alternative 7: 76.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.00085:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* c b))))
   (if (<= x -8.2e+40)
     t_1
     (if (<= x 0.00085) (- (fma c b (* -4.0 (* a t))) (* (* j 27.0) 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(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (c * b));
	double tmp;
	if (x <= -8.2e+40) {
		tmp = t_1;
	} else if (x <= 0.00085) {
		tmp = fma(c, b, (-4.0 * (a * t))) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b))
	tmp = 0.0
	if (x <= -8.2e+40)
		tmp = t_1;
	elseif (x <= 0.00085)
		tmp = Float64(fma(c, b, Float64(-4.0 * Float64(a * t))) - Float64(Float64(j * 27.0) * 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[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+40], t$95$1, If[LessEqual[x, 0.00085], N[(N[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2000000000000003e40 or 8.49999999999999953e-4 < x

   1. Initial program 75.0%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 72.5

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

   7. Applied rewrites 75.8%

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

   if -8.2000000000000003e40 < x < 8.49999999999999953e-4

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 77.4

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

   4. Applied rewrites 77.4%

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

Alternative 8: 72.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)))
   (if (<= x -6.8e+69)
     t_1
     (if (<= x 8.5e+56) (- (fma c b (* -4.0 (* a t))) (* (* j 27.0) 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((18.0 * t), (z * y), (-4.0 * i)) * x;
	double tmp;
	if (x <= -6.8e+69) {
		tmp = t_1;
	} else if (x <= 8.5e+56) {
		tmp = fma(c, b, (-4.0 * (a * t))) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x)
	tmp = 0.0
	if (x <= -6.8e+69)
		tmp = t_1;
	elseif (x <= 8.5e+56)
		tmp = Float64(fma(c, b, Float64(-4.0 * Float64(a * t))) - Float64(Float64(j * 27.0) * 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[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6.8e+69], t$95$1, If[LessEqual[x, 8.5e+56], N[(N[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.79999999999999973e69 or 8.4999999999999998e56 < x

   1. Initial program 73.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 68.8

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

   4. Applied rewrites 68.8%

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

   if -6.79999999999999973e69 < x < 8.4999999999999998e56

   1. Initial program 93.2%

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

   2. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 74.8

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

   4. Applied rewrites 74.8%

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

Alternative 9: 68.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+145}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+83)
     (- (* (* -4.0 i) x) t_1)
     (if (<= t_1 5e+145)
       (fma c b (* (fma i x (* a t)) -4.0))
       (- (* c b) (* j (* k 27.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+83) {
		tmp = ((-4.0 * i) * x) - t_1;
	} else if (t_1 <= 5e+145) {
		tmp = fma(c, b, (fma(i, x, (a * t)) * -4.0));
	} else {
		tmp = (c * b) - (j * (k * 27.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+83)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - t_1);
	elseif (t_1 <= 5e+145)
		tmp = fma(c, b, Float64(fma(i, x, Float64(a * t)) * -4.0));
	else
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+83], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 5e+145], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000006e83

   1. Initial program 82.6%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 64.3

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

   4. Applied rewrites 64.3%

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

   if -2.00000000000000006e83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999967e145

   1. Initial program 87.0%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 82.5

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

   4. Applied rewrites 82.5%

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

   5. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 69.6

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

   7. Applied rewrites 69.6%

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

   if 4.99999999999999967e145 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 67.9

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

   4. Applied rewrites 67.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 68.1

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

   6. Applied rewrites 68.1%

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

Alternative 10: 55.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(-4 \cdot a\right) \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* -4.0 a) t))))
   (if (<= (* b c) -4e+76)
     t_1
     (if (<= (* b c) 5e+72) (- (* (* -4.0 i) x) (* (* j 27.0) 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(c, b, ((-4.0 * a) * t));
	double tmp;
	if ((b * c) <= -4e+76) {
		tmp = t_1;
	} else if ((b * c) <= 5e+72) {
		tmp = ((-4.0 * i) * x) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(-4.0 * a) * t))
	tmp = 0.0
	if (Float64(b * c) <= -4e+76)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e+72)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - Float64(Float64(j * 27.0) * 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[(c * b + N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4e+76], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e+72], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.0000000000000002e76 or 4.99999999999999992e72 < (*.f64 b c)

   1. Initial program 82.1%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 85.4%

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

   6. Applied rewrites 88.4%

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

   7. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 61.1

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

   9. Applied rewrites 61.1%

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

   if -4.0000000000000002e76 < (*.f64 b c) < 4.99999999999999992e72

   1. Initial program 87.0%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 50.6

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

   4. Applied rewrites 50.6%

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

Alternative 11: 55.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot a\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+23)
     (fma c b (* (* k j) -27.0))
     (if (<= t_1 5e+137)
       (fma c b (* (* -4.0 a) t))
       (- (* c b) (* j (* k 27.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = fma(c, b, ((k * j) * -27.0));
	} else if (t_1 <= 5e+137) {
		tmp = fma(c, b, ((-4.0 * a) * t));
	} else {
		tmp = (c * b) - (j * (k * 27.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -1e+23)
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	elseif (t_1 <= 5e+137)
		tmp = fma(c, b, Float64(Float64(-4.0 * a) * t));
	else
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+23], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+137], N[(c * b + N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999992e22

   1. Initial program 83.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 85.5%

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 61.3

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

   9. Applied rewrites 61.3%

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

   if -9.9999999999999992e22 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e137

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 89.7%

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

   6. Applied rewrites 90.4%

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

   7. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 49.6

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

   9. Applied rewrites 49.6%

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

   if 5.0000000000000002e137 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 67.0

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

   4. Applied rewrites 67.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 67.3

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

   6. Applied rewrites 67.3%

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

Alternative 12: 54.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot a\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* k j) -27.0))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -1e+23)
     t_1
     (if (<= t_2 5e+137) (fma c b (* (* -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 = fma(c, b, ((k * j) * -27.0));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -1e+23) {
		tmp = t_1;
	} else if (t_2 <= 5e+137) {
		tmp = fma(c, b, ((-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 = fma(c, b, Float64(Float64(k * j) * -27.0))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -1e+23)
		tmp = t_1;
	elseif (t_2 <= 5e+137)
		tmp = fma(c, b, Float64(Float64(-4.0 * a) * t));
	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[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+23], t$95$1, If[LessEqual[t$95$2, 5e+137], N[(c * b + N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999992e22 or 5.0000000000000002e137 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.1%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 84.5%

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

   6. Applied rewrites 86.4%

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

   7. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 64.2

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

   9. Applied rewrites 64.2%

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

   if -9.9999999999999992e22 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e137

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 89.7%

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

   6. Applied rewrites 90.4%

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

   7. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 49.6

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

   9. Applied rewrites 49.6%

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

Alternative 13: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(-4 \cdot a\right) \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* -4.0 a) t))))
   (if (<= (* b c) -5e+61)
     t_1
     (if (<= (* b c) 5e+133) (* (fma i x (* a t)) -4.0) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((-4.0 * a) * t));
	double tmp;
	if ((b * c) <= -5e+61) {
		tmp = t_1;
	} else if ((b * c) <= 5e+133) {
		tmp = fma(i, x, (a * t)) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(-4.0 * a) * t))
	tmp = 0.0
	if (Float64(b * c) <= -5e+61)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e+133)
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+61], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e+133], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.00000000000000018e61 or 4.99999999999999961e133 < (*.f64 b c)

   1. Initial program 81.3%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 85.0%

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

   6. Applied rewrites 88.2%

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

   7. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 62.5

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

   9. Applied rewrites 62.5%

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

   if -5.00000000000000018e61 < (*.f64 b c) < 4.99999999999999961e133

   1. Initial program 87.2%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 66.5

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

   4. Applied rewrites 66.5%

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

   5. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 50.4

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

   7. Applied rewrites 50.4%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 45.4

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

   10. Applied rewrites 45.4%

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

Alternative 14: 51.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* a t) -4.0 (* c b))))
   (if (<= (* b c) -5e+61)
     t_1
     (if (<= (* b c) 5e+133) (* (fma i x (* a t)) -4.0) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((a * t), -4.0, (c * b));
	double tmp;
	if ((b * c) <= -5e+61) {
		tmp = t_1;
	} else if ((b * c) <= 5e+133) {
		tmp = fma(i, x, (a * t)) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(a * t), -4.0, Float64(c * b))
	tmp = 0.0
	if (Float64(b * c) <= -5e+61)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e+133)
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+61], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e+133], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.00000000000000018e61 or 4.99999999999999961e133 < (*.f64 b c)

   1. Initial program 81.3%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 75.3

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

   4. Applied rewrites 75.3%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 61.5

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

   7. Applied rewrites 61.5%

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

   if -5.00000000000000018e61 < (*.f64 b c) < 4.99999999999999961e133

   1. Initial program 87.2%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 66.5

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

   4. Applied rewrites 66.5%

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

   5. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 50.4

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

   7. Applied rewrites 50.4%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 45.4

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

   10. Applied rewrites 45.4%

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

Alternative 15: 48.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+61}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+61)
   (* c b)
   (if (<= (* b c) 5e+181) (* (fma i x (* a t)) -4.0) (* c b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+61) {
		tmp = c * b;
	} else if ((b * c) <= 5e+181) {
		tmp = fma(i, x, (a * t)) * -4.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e+61)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 5e+181)
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e+61], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+181], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.00000000000000018e61 or 5.0000000000000003e181 < (*.f64 b c)

   1. Initial program 80.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 54.6

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

   4. Applied rewrites 54.6%

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

   if -5.00000000000000018e61 < (*.f64 b c) < 5.0000000000000003e181

   1. Initial program 87.1%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 66.8

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

   4. Applied rewrites 66.8%

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

   5. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 50.8

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

   7. Applied rewrites 50.8%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 45.0

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

   10. Applied rewrites 45.0%

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

Alternative 16: 37.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+76}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 10^{+170}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+76)
   (* c b)
   (if (<= (* b c) 1e+170) (* (* -27.0 k) j) (* c b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+76) {
		tmp = c * b;
	} else if ((b * c) <= 1e+170) {
		tmp = (-27.0 * k) * j;
	} else {
		tmp = c * b;
	}
	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) :: tmp
    if ((b * c) <= (-4d+76)) then
        tmp = c * b
    else if ((b * c) <= 1d+170) then
        tmp = ((-27.0d0) * k) * j
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+76) {
		tmp = c * b;
	} else if ((b * c) <= 1e+170) {
		tmp = (-27.0 * k) * j;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4e+76:
		tmp = c * b
	elif (b * c) <= 1e+170:
		tmp = (-27.0 * k) * j
	else:
		tmp = c * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4e+76)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 1e+170)
		tmp = Float64(Float64(-27.0 * k) * j);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -4e+76)
		tmp = c * b;
	elseif ((b * c) <= 1e+170)
		tmp = (-27.0 * k) * j;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4e+76], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+170], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.0000000000000002e76 or 1.00000000000000003e170 < (*.f64 b c)

   1. Initial program 80.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 55.4

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

   4. Applied rewrites 55.4%

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

   if -4.0000000000000002e76 < (*.f64 b c) < 1.00000000000000003e170

   1. Initial program 87.2%

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

   2. 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. *-commutative N/A

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

      3. lower-*.f64 28.6

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

   4. Applied rewrites 28.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 28.6

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

   6. Applied rewrites 28.6%

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

Alternative 17: 37.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+76}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 10^{+170}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+76)
   (* c b)
   (if (<= (* b c) 1e+170) (* -27.0 (* k j)) (* c b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+76) {
		tmp = c * b;
	} else if ((b * c) <= 1e+170) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	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) :: tmp
    if ((b * c) <= (-4d+76)) then
        tmp = c * b
    else if ((b * c) <= 1d+170) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+76) {
		tmp = c * b;
	} else if ((b * c) <= 1e+170) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4e+76:
		tmp = c * b
	elif (b * c) <= 1e+170:
		tmp = -27.0 * (k * j)
	else:
		tmp = c * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4e+76)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 1e+170)
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -4e+76)
		tmp = c * b;
	elseif ((b * c) <= 1e+170)
		tmp = -27.0 * (k * j);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4e+76], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+170], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.0000000000000002e76 or 1.00000000000000003e170 < (*.f64 b c)

   1. Initial program 80.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 55.4

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

   4. Applied rewrites 55.4%

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

   if -4.0000000000000002e76 < (*.f64 b c) < 1.00000000000000003e170

   1. Initial program 87.2%

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

   2. 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. *-commutative N/A

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

      3. lower-*.f64 28.6

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

   4. Applied rewrites 28.6%

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

Alternative 18: 22.9% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ c \cdot b \end{array} \]

FPCore

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

C

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

Fortran

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 = c * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

1. Initial program 85.1%

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

2. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 22.9

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

4. Applied rewrites 22.9%

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

Reproduce

herbie shell --seed 2025120 
(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)))