Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.8% → 99.4%

Time: 9.5s

Alternatives: 17

Speedup: 6.6×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (+
    x1
    (+
     (+
      (+
       (+
        (*
         (+
          (* (* (* 2.0 x1) t_2) (- t_2 3.0))
          (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
         t_1)
        (* t_0 t_2))
       (* (* x1 x1) x1))
      x1)
     (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

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(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    code = x1 + (((((((((2.0d0 * x1) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)))
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Python

def code(x1, x2):
	t_0 = (3.0 * x1) * x1
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	return Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
end

MATLAB

function tmp = code(x1, x2)
	t_0 = (3.0 * x1) * x1;
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Initial Program: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (+
    x1
    (+
     (+
      (+
       (+
        (*
         (+
          (* (* (* 2.0 x1) t_2) (- t_2 3.0))
          (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
         t_1)
        (* t_0 t_2))
       (* (* x1 x1) x1))
      x1)
     (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

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(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    code = x1 + (((((((((2.0d0 * x1) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)))
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Python

def code(x1, x2):
	t_0 = (3.0 * x1) * x1
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	return Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
end

MATLAB

function tmp = code(x1, x2)
	t_0 = (3.0 * x1) * x1;
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Alternative 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right)\\ t_1 := \left(x1 \cdot x1\right) \cdot x1\\ t_2 := 2 \cdot x2 - 3\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{t\_0 - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_5 := \left(3 \cdot x1\right) \cdot x1\\ t_6 := \frac{\left(t\_5 + 2 \cdot x2\right) - x1}{t\_3}\\ t_7 := 3 \cdot \frac{\left(t\_5 - 2 \cdot x2\right) - x1}{t\_3}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_6\right) \cdot \left(t\_6 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_6 - 6\right)\right) \cdot t\_3 + t\_5 \cdot t\_6\right) + t\_1\right) + x1\right) + t\_7\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot t\_4, t\_4 - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{t\_0}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_5 \cdot t\_4\right) + t\_1\right) + x1\right) + t\_7\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_2\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_2, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma (* 3.0 x1) x1 (* 2.0 x2)))
        (t_1 (* (* x1 x1) x1))
        (t_2 (- (* 2.0 x2) 3.0))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- t_0 x1) (fma x1 x1 1.0)))
        (t_5 (* (* 3.0 x1) x1))
        (t_6 (/ (- (+ t_5 (* 2.0 x2)) x1) t_3))
        (t_7 (* 3.0 (/ (- (- t_5 (* 2.0 x2)) x1) t_3))))
   (if (<=
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2.0 x1) t_6) (- t_6 3.0))
               (* (* x1 x1) (- (* 4.0 t_6) 6.0)))
              t_3)
             (* t_5 t_6))
            t_1)
           x1)
          t_7))
        INFINITY)
     (+
      x1
      (+
       (+
        (+
         (fma
          (fma
           (* (* 2.0 x1) t_4)
           (- t_4 3.0)
           (*
            (* x1 x1)
            (-
             (* 4.0 (- (/ t_0 (fma x1 x1 1.0)) (/ x1 (fma x1 x1 1.0))))
             6.0)))
          (fma x1 x1 1.0)
          (* t_5 t_4))
         t_1)
        x1)
       t_7))
     (+
      x1
      (*
       x1
       (fma
        -1.0
        (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_2))))
        (* x1 (+ 9.0 (fma 4.0 t_2 (* x1 (- (* 6.0 x1) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = fma((3.0 * x1), x1, (2.0 * x2));
	double t_1 = (x1 * x1) * x1;
	double t_2 = (2.0 * x2) - 3.0;
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = (t_0 - x1) / fma(x1, x1, 1.0);
	double t_5 = (3.0 * x1) * x1;
	double t_6 = ((t_5 + (2.0 * x2)) - x1) / t_3;
	double t_7 = 3.0 * (((t_5 - (2.0 * x2)) - x1) / t_3);
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_6) * (t_6 - 3.0)) + ((x1 * x1) * ((4.0 * t_6) - 6.0))) * t_3) + (t_5 * t_6)) + t_1) + x1) + t_7)) <= ((double) INFINITY)) {
		tmp = x1 + (((fma(fma(((2.0 * x1) * t_4), (t_4 - 3.0), ((x1 * x1) * ((4.0 * ((t_0 / fma(x1, x1, 1.0)) - (x1 / fma(x1, x1, 1.0)))) - 6.0))), fma(x1, x1, 1.0), (t_5 * t_4)) + t_1) + x1) + t_7);
	} else {
		tmp = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_2)))), (x1 * (9.0 + fma(4.0, t_2, (x1 * ((6.0 * x1) - 3.0)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = fma(Float64(3.0 * x1), x1, Float64(2.0 * x2))
	t_1 = Float64(Float64(x1 * x1) * x1)
	t_2 = Float64(Float64(2.0 * x2) - 3.0)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(t_0 - x1) / fma(x1, x1, 1.0))
	t_5 = Float64(Float64(3.0 * x1) * x1)
	t_6 = Float64(Float64(Float64(t_5 + Float64(2.0 * x2)) - x1) / t_3)
	t_7 = Float64(3.0 * Float64(Float64(Float64(t_5 - Float64(2.0 * x2)) - x1) / t_3))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_6) * Float64(t_6 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_6) - 6.0))) * t_3) + Float64(t_5 * t_6)) + t_1) + x1) + t_7)) <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(fma(fma(Float64(Float64(2.0 * x1) * t_4), Float64(t_4 - 3.0), Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(t_0 / fma(x1, x1, 1.0)) - Float64(x1 / fma(x1, x1, 1.0)))) - 6.0))), fma(x1, x1, 1.0), Float64(t_5 * t_4)) + t_1) + x1) + t_7));
	else
		tmp = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_2)))), Float64(x1 * Float64(9.0 + fma(4.0, t_2, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$0 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$5 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * N[(N[(N[(t$95$5 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(t$95$6 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$6), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] + N[(t$95$5 * t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + x1), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(t$95$0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$5 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + x1), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$2 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   4. Applied rewrites 99.4%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. lift--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\color{blue}{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(\color{blue}{3 \cdot x1}, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, \color{blue}{2 \cdot x2}\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. lift-fma.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\color{blue}{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right)} - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      6. lift-fma.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{\color{blue}{x1 \cdot x1 + 1}} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      7. div-sub N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(\frac{\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2}{x1 \cdot x1 + 1} - \frac{x1}{x1 \cdot x1 + 1}\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      8. lower--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(\frac{\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2}{x1 \cdot x1 + 1} - \frac{x1}{x1 \cdot x1 + 1}\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\color{blue}{\frac{\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2}{x1 \cdot x1 + 1}} - \frac{x1}{x1 \cdot x1 + 1}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      10. lift-fma.f64 N/A

          \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\color{blue}{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right)}}{x1 \cdot x1 + 1} - \frac{x1}{x1 \cdot x1 + 1}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(\color{blue}{3 \cdot x1}, x1, 2 \cdot x2\right)}{x1 \cdot x1 + 1} - \frac{x1}{x1 \cdot x1 + 1}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, \color{blue}{2 \cdot x2}\right)}{x1 \cdot x1 + 1} - \frac{x1}{x1 \cdot x1 + 1}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      13. lift-fma.f64 N/A

          \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right)}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}} - \frac{x1}{x1 \cdot x1 + 1}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      14. lower-/.f64 N/A

          \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \color{blue}{\frac{x1}{x1 \cdot x1 + 1}}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      15. lift-fma.f64 99.4

          \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\color{blue}{\mathsf{fma}\left(x1, x1, 1\right)}}\right) - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Applied rewrites 99.4%

      \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right)}{\mathsf{fma}\left(x1, x1, 1\right)} - \frac{x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 99.4%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 99.4%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := \left(x1 \cdot x1\right) \cdot x1\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_4 := \left(3 \cdot x1\right) \cdot x1\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) - x1}{t\_2}\\ t_6 := 3 \cdot \frac{\left(t\_4 - 2 \cdot x2\right) - x1}{t\_2}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_5\right) \cdot \left(t\_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_5 - 6\right)\right) \cdot t\_2 + t\_4 \cdot t\_5\right) + t\_1\right) + x1\right) + t\_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot t\_3, t\_3 - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_3 - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_4 \cdot t\_3\right) + t\_1\right) + x1\right) + t\_6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_0\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_0, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (* (* x1 x1) x1))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)))
        (t_4 (* (* 3.0 x1) x1))
        (t_5 (/ (- (+ t_4 (* 2.0 x2)) x1) t_2))
        (t_6 (* 3.0 (/ (- (- t_4 (* 2.0 x2)) x1) t_2))))
   (if (<=
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2.0 x1) t_5) (- t_5 3.0))
               (* (* x1 x1) (- (* 4.0 t_5) 6.0)))
              t_2)
             (* t_4 t_5))
            t_1)
           x1)
          t_6))
        INFINITY)
     (+
      x1
      (+
       (+
        (+
         (fma
          (fma
           (* (* 2.0 x1) t_3)
           (- t_3 3.0)
           (* (* x1 x1) (- (* 4.0 t_3) 6.0)))
          (fma x1 x1 1.0)
          (* t_4 t_3))
         t_1)
        x1)
       t_6))
     (+
      x1
      (*
       x1
       (fma
        -1.0
        (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_0))))
        (* x1 (+ 9.0 (fma 4.0 t_0 (* x1 (- (* 6.0 x1) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = (x1 * x1) * x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = (fma((3.0 * x1), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_4 = (3.0 * x1) * x1;
	double t_5 = ((t_4 + (2.0 * x2)) - x1) / t_2;
	double t_6 = 3.0 * (((t_4 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * ((4.0 * t_5) - 6.0))) * t_2) + (t_4 * t_5)) + t_1) + x1) + t_6)) <= ((double) INFINITY)) {
		tmp = x1 + (((fma(fma(((2.0 * x1) * t_3), (t_3 - 3.0), ((x1 * x1) * ((4.0 * t_3) - 6.0))), fma(x1, x1, 1.0), (t_4 * t_3)) + t_1) + x1) + t_6);
	} else {
		tmp = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_0)))), (x1 * (9.0 + fma(4.0, t_0, (x1 * ((6.0 * x1) - 3.0)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(Float64(x1 * x1) * x1)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(fma(Float64(3.0 * x1), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_4 = Float64(Float64(3.0 * x1) * x1)
	t_5 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) - x1) / t_2)
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_5) - 6.0))) * t_2) + Float64(t_4 * t_5)) + t_1) + x1) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(fma(fma(Float64(Float64(2.0 * x1) * t_3), Float64(t_3 - 3.0), Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0))), fma(x1, x1, 1.0), Float64(t_4 * t_3)) + t_1) + x1) + t_6));
	else
		tmp = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_0)))), Float64(x1 * Float64(9.0 + fma(4.0, t_0, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$5), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(t$95$4 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$4 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$0 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   4. Applied rewrites 99.4%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 99.4%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 99.4%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 2 \cdot x2 - 3\\ t_3 := \left(3 \cdot x1\right) \cdot x1\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_1}\\ t_5 := t\_3 \cdot t\_4\\ t_6 := \left(\left(2 \cdot x1\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right)\\ t_7 := 3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(t\_6 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_4 - 6\right)\right) \cdot t\_1 + t\_5\right) + t\_0\right) + x1\right) + t\_7\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\left(t\_6 + \left(x1 \cdot x1\right) \cdot 6\right) \cdot t\_1 + t\_5\right) + t\_0\right) + x1\right) + t\_7\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_2\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_2, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- (* 2.0 x2) 3.0))
        (t_3 (* (* 3.0 x1) x1))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_1))
        (t_5 (* t_3 t_4))
        (t_6 (* (* (* 2.0 x1) t_4) (- t_4 3.0)))
        (t_7 (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_1))))
   (if (<=
        (+
         x1
         (+
          (+
           (+ (+ (* (+ t_6 (* (* x1 x1) (- (* 4.0 t_4) 6.0))) t_1) t_5) t_0)
           x1)
          t_7))
        INFINITY)
     (+ x1 (+ (+ (+ (+ (* (+ t_6 (* (* x1 x1) 6.0)) t_1) t_5) t_0) x1) t_7))
     (+
      x1
      (*
       x1
       (fma
        -1.0
        (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_2))))
        (* x1 (+ 9.0 (fma 4.0 t_2 (* x1 (- (* 6.0 x1) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (2.0 * x2) - 3.0;
	double t_3 = (3.0 * x1) * x1;
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_1;
	double t_5 = t_3 * t_4;
	double t_6 = ((2.0 * x1) * t_4) * (t_4 - 3.0);
	double t_7 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_1);
	double tmp;
	if ((x1 + ((((((t_6 + ((x1 * x1) * ((4.0 * t_4) - 6.0))) * t_1) + t_5) + t_0) + x1) + t_7)) <= ((double) INFINITY)) {
		tmp = x1 + ((((((t_6 + ((x1 * x1) * 6.0)) * t_1) + t_5) + t_0) + x1) + t_7);
	} else {
		tmp = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_2)))), (x1 * (9.0 + fma(4.0, t_2, (x1 * ((6.0 * x1) - 3.0)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(2.0 * x2) - 3.0)
	t_3 = Float64(Float64(3.0 * x1) * x1)
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_1)
	t_5 = Float64(t_3 * t_4)
	t_6 = Float64(Float64(Float64(2.0 * x1) * t_4) * Float64(t_4 - 3.0))
	t_7 = Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_6 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))) * t_1) + t_5) + t_0) + x1) + t_7)) <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_6 + Float64(Float64(x1 * x1) * 6.0)) * t_1) + t_5) + t_0) + x1) + t_7));
	else
		tmp = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_2)))), Float64(x1 * Float64(9.0 + fma(4.0, t_2, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(t$95$6 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + t$95$5), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(N[(N[(N[(N[(t$95$6 + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + t$95$5), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$2 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \color{blue}{6}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 95.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \color{blue}{6}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 99.4%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 99.4%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \left(3 \cdot x1\right) \cdot x1\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_1}\\ t_4 := 3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_1}\\ t_5 := \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_6 := 2 \cdot x2 - 3\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_3 - 6\right)\right) \cdot t\_1 + t\_2 \cdot t\_3\right) + t\_0\right) + x1\right) + t\_4\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(x1 \cdot \mathsf{fma}\left(-2, x1, 4 \cdot x2\right), t\_5 - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_5 - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_2 \cdot t\_5\right) + t\_0\right) + x1\right) + t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_6\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_6, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* (* 3.0 x1) x1))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_4 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1)))
        (t_5 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)))
        (t_6 (- (* 2.0 x2) 3.0)))
   (if (<=
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2.0 x1) t_3) (- t_3 3.0))
               (* (* x1 x1) (- (* 4.0 t_3) 6.0)))
              t_1)
             (* t_2 t_3))
            t_0)
           x1)
          t_4))
        INFINITY)
     (+
      x1
      (+
       (+
        (+
         (fma
          (fma
           (* x1 (fma -2.0 x1 (* 4.0 x2)))
           (- t_5 3.0)
           (* (* x1 x1) (- (* 4.0 t_5) 6.0)))
          (fma x1 x1 1.0)
          (* t_2 t_5))
         t_0)
        x1)
       t_4))
     (+
      x1
      (*
       x1
       (fma
        -1.0
        (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_6))))
        (* x1 (+ 9.0 (fma 4.0 t_6 (* x1 (- (* 6.0 x1) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (3.0 * x1) * x1;
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_4 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1);
	double t_5 = (fma((3.0 * x1), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_6 = (2.0 * x2) - 3.0;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_1) + (t_2 * t_3)) + t_0) + x1) + t_4)) <= ((double) INFINITY)) {
		tmp = x1 + (((fma(fma((x1 * fma(-2.0, x1, (4.0 * x2))), (t_5 - 3.0), ((x1 * x1) * ((4.0 * t_5) - 6.0))), fma(x1, x1, 1.0), (t_2 * t_5)) + t_0) + x1) + t_4);
	} else {
		tmp = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_6)))), (x1 * (9.0 + fma(4.0, t_6, (x1 * ((6.0 * x1) - 3.0)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(3.0 * x1) * x1)
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1))
	t_5 = Float64(Float64(fma(Float64(3.0 * x1), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_6 = Float64(Float64(2.0 * x2) - 3.0)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0))) * t_1) + Float64(t_2 * t_3)) + t_0) + x1) + t_4)) <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(fma(fma(Float64(x1 * fma(-2.0, x1, Float64(4.0 * x2))), Float64(t_5 - 3.0), Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_5) - 6.0))), fma(x1, x1, 1.0), Float64(t_2 * t_5)) + t_0) + x1) + t_4));
	else
		tmp = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_6)))), Float64(x1 * Float64(9.0 + fma(4.0, t_6, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(N[(N[(N[(N[(x1 * N[(-2.0 * x1 + N[(4.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$5), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$2 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$6 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   4. Applied rewrites 99.4%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around 0

      \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x1 \cdot \left(-2 \cdot x1 + 4 \cdot x2\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(x1 \cdot \color{blue}{\left(-2 \cdot x1 + 4 \cdot x2\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(x1 \cdot \mathsf{fma}\left(-2, \color{blue}{x1}, 4 \cdot x2\right), \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. lower-*.f64 93.8

         \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(x1 \cdot \mathsf{fma}\left(-2, x1, 4 \cdot x2\right), \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Applied rewrites 93.8%

      \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x1 \cdot \mathsf{fma}\left(-2, x1, 4 \cdot x2\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 99.4%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 99.4%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<=
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2.0 x1) t_2) (- t_2 3.0))
               (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
              t_1)
             (* t_0 t_2))
            (* (* x1 x1) x1))
           x1)
          (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))
        INFINITY)
     (fma -6.0 x2 (* x1 (- (* -12.0 x2) 1.0)))
     (fma -6.0 x2 (* x1 (- (* 9.0 x1) 1.0))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= ((double) INFINITY)) {
		tmp = fma(-6.0, x2, (x1 * ((-12.0 * x2) - 1.0)));
	} else {
		tmp = fma(-6.0, x2, (x1 * ((9.0 * x1) - 1.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= Inf)
		tmp = fma(-6.0, x2, Float64(x1 * Float64(Float64(-12.0 * x2) - 1.0)));
	else
		tmp = fma(-6.0, x2, Float64(x1 * Float64(Float64(9.0 * x1) - 1.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(-6.0 * x2 + N[(x1 * N[(N[(-12.0 * x2), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * x2 + N[(x1 * N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 57.9

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 57.9%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 54.7

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right) \]

   11. Applied rewrites 54.7%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right) \]

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 43.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 55.0

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 55.0%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       4. lower-*.f64 66.1

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   11. Applied rewrites 66.1%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   12. Taylor expanded in x2 around 0

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
   13. Step-by-step derivation

       1. lower-*.f64 86.8

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]

   14. Applied rewrites 86.8%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(9 + -19 \cdot x1\right) - 1\\ t_1 := \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_2 := x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot t\_1, t\_1 - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_1 - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot t\_1\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 9\right)\\ t_3 := 2 \cdot x2 - 3\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 \cdot t\_0\\ \mathbf{elif}\;x1 \leq -0.24:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x1 \leq 0.092:\\ \;\;\;\;\mathsf{fma}\left(x1, t\_0, x2 \cdot \left(\mathsf{fma}\left(x1, x2 \cdot \left(8 + -8 \cdot \left(x1 \cdot x1\right)\right), x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_3\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0))
        (t_1 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)))
        (t_2
         (+
          x1
          (+
           (+
            (+
             (fma
              (fma
               (* (* 2.0 x1) t_1)
               (- t_1 3.0)
               (* (* x1 x1) (- (* 4.0 t_1) 6.0)))
              (fma x1 x1 1.0)
              (* (* (* 3.0 x1) x1) t_1))
             (* (* x1 x1) x1))
            x1)
           9.0)))
        (t_3 (- (* 2.0 x2) 3.0)))
   (if (<= x1 -5.6e+102)
     (* x1 t_0)
     (if (<= x1 -0.24)
       t_2
       (if (<= x1 0.092)
         (fma
          x1
          t_0
          (*
           x2
           (-
            (fma
             x1
             (* x2 (+ 8.0 (* -8.0 (* x1 x1))))
             (* x1 (- (* x1 (+ 12.0 (* 24.0 x1))) 12.0)))
            6.0)))
         (if (<= x1 2e+94)
           t_2
           (+
            x1
            (*
             x1
             (fma
              -1.0
              (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_3))))
              (* x1 (+ 9.0 (fma 4.0 t_3 (* x1 (- (* 6.0 x1) 3.0))))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (9.0 + (-19.0 * x1))) - 1.0;
	double t_1 = (fma((3.0 * x1), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_2 = x1 + (((fma(fma(((2.0 * x1) * t_1), (t_1 - 3.0), ((x1 * x1) * ((4.0 * t_1) - 6.0))), fma(x1, x1, 1.0), (((3.0 * x1) * x1) * t_1)) + ((x1 * x1) * x1)) + x1) + 9.0);
	double t_3 = (2.0 * x2) - 3.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 * t_0;
	} else if (x1 <= -0.24) {
		tmp = t_2;
	} else if (x1 <= 0.092) {
		tmp = fma(x1, t_0, (x2 * (fma(x1, (x2 * (8.0 + (-8.0 * (x1 * x1)))), (x1 * ((x1 * (12.0 + (24.0 * x1))) - 12.0))) - 6.0)));
	} else if (x1 <= 2e+94) {
		tmp = t_2;
	} else {
		tmp = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_3)))), (x1 * (9.0 + fma(4.0, t_3, (x1 * ((6.0 * x1) - 3.0)))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0)
	t_1 = Float64(Float64(fma(Float64(3.0 * x1), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_2 = Float64(x1 + Float64(Float64(Float64(fma(fma(Float64(Float64(2.0 * x1) * t_1), Float64(t_1 - 3.0), Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_1) - 6.0))), fma(x1, x1, 1.0), Float64(Float64(Float64(3.0 * x1) * x1) * t_1)) + Float64(Float64(x1 * x1) * x1)) + x1) + 9.0))
	t_3 = Float64(Float64(2.0 * x2) - 3.0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 * t_0);
	elseif (x1 <= -0.24)
		tmp = t_2;
	elseif (x1 <= 0.092)
		tmp = fma(x1, t_0, Float64(x2 * Float64(fma(x1, Float64(x2 * Float64(8.0 + Float64(-8.0 * Float64(x1 * x1)))), Float64(x1 * Float64(Float64(x1 * Float64(12.0 + Float64(24.0 * x1))) - 12.0))) - 6.0)));
	elseif (x1 <= 2e+94)
		tmp = t_2;
	else
		tmp = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_3)))), Float64(x1 * Float64(9.0 + fma(4.0, t_3, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(3.0 * x1), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$1), $MachinePrecision] * N[(t$95$1 - 3.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$1), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 * t$95$0), $MachinePrecision], If[LessEqual[x1, -0.24], t$95$2, If[LessEqual[x1, 0.092], N[(x1 * t$95$0 + N[(x2 * N[(N[(x1 * N[(x2 * N[(8.0 + N[(-8.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(12.0 + N[(24.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+94], t$95$2, N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$3 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.9%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      5. lower-*.f64 99.1

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   8. Applied rewrites 99.1%

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]

   if -5.60000000000000037e102 < x1 < -0.23999999999999999 or 0.091999999999999998 < x1 < 2e94

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   4. Applied rewrites 99.3%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 98.2%

      \[\leadsto x1 + \left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(2 \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]

   if -0.23999999999999999 < x1 < 0.091999999999999998

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)} \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}, x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]

   8. Applied rewrites 99.4%

      \[\leadsto \mathsf{fma}\left(x1, \color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right) - 1}, x2 \cdot \left(\mathsf{fma}\left(x1, x2 \cdot \left(8 + -8 \cdot \left(x1 \cdot x1\right)\right), x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]

   if 2e94 < x1

   1. Initial program 27.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 99.6%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 99.6%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 96.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ \mathbf{if}\;x1 \leq -1:\\ \;\;\;\;x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_0\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_0, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - 1, x2 \cdot \left(\mathsf{fma}\left(x1, x2 \cdot \left(8 + -8 \cdot \left(x1 \cdot x1\right)\right), x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + {x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{18}{x1}, 4 \cdot t\_0\right)}{x1}}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0)))
   (if (<= x1 -1.0)
     (+
      x1
      (*
       x1
       (fma
        -1.0
        (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_0))))
        (* x1 (+ 9.0 (fma 4.0 t_0 (* x1 (- (* 6.0 x1) 3.0))))))))
     (if (<= x1 1.0)
       (fma
        x1
        (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0)
        (*
         x2
         (-
          (fma
           x1
           (* x2 (+ 8.0 (* -8.0 (* x1 x1))))
           (* x1 (- (* x1 (+ 12.0 (* 24.0 x1))) 12.0)))
          6.0)))
       (+
        x1
        (*
         (pow x1 4.0)
         (+
          6.0
          (*
           -1.0
           (/
            (+ 3.0 (* -1.0 (/ (+ 9.0 (fma -1.0 (/ 18.0 x1) (* 4.0 t_0))) x1)))
            x1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double tmp;
	if (x1 <= -1.0) {
		tmp = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_0)))), (x1 * (9.0 + fma(4.0, t_0, (x1 * ((6.0 * x1) - 3.0)))))));
	} else if (x1 <= 1.0) {
		tmp = fma(x1, ((x1 * (9.0 + (-19.0 * x1))) - 1.0), (x2 * (fma(x1, (x2 * (8.0 + (-8.0 * (x1 * x1)))), (x1 * ((x1 * (12.0 + (24.0 * x1))) - 12.0))) - 6.0)));
	} else {
		tmp = x1 + (pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + fma(-1.0, (18.0 / x1), (4.0 * t_0))) / x1))) / x1))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	tmp = 0.0
	if (x1 <= -1.0)
		tmp = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_0)))), Float64(x1 * Float64(9.0 + fma(4.0, t_0, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))));
	elseif (x1 <= 1.0)
		tmp = fma(x1, Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0), Float64(x2 * Float64(fma(x1, Float64(x2 * Float64(8.0 + Float64(-8.0 * Float64(x1 * x1)))), Float64(x1 * Float64(Float64(x1 * Float64(12.0 + Float64(24.0 * x1))) - 12.0))) - 6.0)));
	else
		tmp = Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-1.0 * Float64(Float64(3.0 + Float64(-1.0 * Float64(Float64(9.0 + fma(-1.0, Float64(18.0 / x1), Float64(4.0 * t_0))) / x1))) / x1)))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, If[LessEqual[x1, -1.0], N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$0 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.0], N[(x1 * N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(x2 * N[(8.0 + N[(-8.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(12.0 + N[(24.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 + N[(-1.0 * N[(N[(3.0 + N[(-1.0 * N[(N[(9.0 + N[(-1.0 * N[(18.0 / x1), $MachinePrecision] + N[(4.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1

   1. Initial program 32.9%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 93.1%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 93.1%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]

   if -1 < x1 < 1

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)} \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}, x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]

   8. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(x1, \color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right) - 1}, x2 \cdot \left(\mathsf{fma}\left(x1, x2 \cdot \left(8 + -8 \cdot \left(x1 \cdot x1\right)\right), x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]

   if 1 < x1

   1. Initial program 48.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 92.7%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 + {x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{18}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 92.7%

      \[\leadsto x1 + {x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{18}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 87.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(9 + -19 \cdot x1\right) - 1\\ \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;x1 \cdot t\_0\\ \mathbf{elif}\;x1 \leq -0.57:\\ \;\;\;\;8 \cdot \frac{x1 \cdot \left(x2 \cdot x2\right)}{1 + x1 \cdot x1}\\ \mathbf{elif}\;x1 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x1, t\_0, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(x2, 8 + -8 \cdot \left(x1 \cdot x1\right), x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0)))
   (if (<= x1 -3.5e+99)
     (* x1 t_0)
     (if (<= x1 -0.57)
       (* 8.0 (/ (* x1 (* x2 x2)) (+ 1.0 (* x1 x1))))
       (if (<= x1 1.0)
         (fma
          x1
          t_0
          (*
           x2
           (-
            (*
             x1
             (fma
              x2
              (+ 8.0 (* -8.0 (* x1 x1)))
              (- (* x1 (+ 12.0 (* 24.0 x1))) 12.0)))
            6.0)))
         (+
          x1
          (+
           (+ (+ (* 4.0 (* x1 (* x2 (- (* 2.0 x2) 3.0)))) (* (* x1 x1) x1)) x1)
           9.0)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * (9.0 + (-19.0 * x1))) - 1.0;
	double tmp;
	if (x1 <= -3.5e+99) {
		tmp = x1 * t_0;
	} else if (x1 <= -0.57) {
		tmp = 8.0 * ((x1 * (x2 * x2)) / (1.0 + (x1 * x1)));
	} else if (x1 <= 1.0) {
		tmp = fma(x1, t_0, (x2 * ((x1 * fma(x2, (8.0 + (-8.0 * (x1 * x1))), ((x1 * (12.0 + (24.0 * x1))) - 12.0))) - 6.0)));
	} else {
		tmp = x1 + ((((4.0 * (x1 * (x2 * ((2.0 * x2) - 3.0)))) + ((x1 * x1) * x1)) + x1) + 9.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0)
	tmp = 0.0
	if (x1 <= -3.5e+99)
		tmp = Float64(x1 * t_0);
	elseif (x1 <= -0.57)
		tmp = Float64(8.0 * Float64(Float64(x1 * Float64(x2 * x2)) / Float64(1.0 + Float64(x1 * x1))));
	elseif (x1 <= 1.0)
		tmp = fma(x1, t_0, Float64(x2 * Float64(Float64(x1 * fma(x2, Float64(8.0 + Float64(-8.0 * Float64(x1 * x1))), Float64(Float64(x1 * Float64(12.0 + Float64(24.0 * x1))) - 12.0))) - 6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))) + Float64(Float64(x1 * x1) * x1)) + x1) + 9.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]}, If[LessEqual[x1, -3.5e+99], N[(x1 * t$95$0), $MachinePrecision], If[LessEqual[x1, -0.57], N[(8.0 * N[(N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.0], N[(x1 * t$95$0 + N[(x2 * N[(N[(x1 * N[(x2 * N[(8.0 + N[(-8.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(12.0 + N[(24.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(N[(4.0 * N[(x1 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.4999999999999998e99

   1. Initial program 2.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      5. lower-*.f64 97.6

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   8. Applied rewrites 97.6%

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]

   if -3.4999999999999998e99 < x1 < -0.569999999999999951

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x2 around inf

      \[\leadsto \color{blue}{8 \cdot \frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 8 \cdot \color{blue}{\frac{x1 \cdot {x2}^{2}}{1 + {x1}^{2}}} \]

      2. lower-/.f64 N/A

         \[\leadsto 8 \cdot \frac{x1 \cdot {x2}^{2}}{\color{blue}{1 + {x1}^{2}}} \]

      3. lower-*.f64 N/A

         \[\leadsto 8 \cdot \frac{x1 \cdot {x2}^{2}}{\color{blue}{1} + {x1}^{2}} \]

      4. unpow2 N/A

         \[\leadsto 8 \cdot \frac{x1 \cdot \left(x2 \cdot x2\right)}{1 + {x1}^{2}} \]

      5. lower-*.f64 N/A

         \[\leadsto 8 \cdot \frac{x1 \cdot \left(x2 \cdot x2\right)}{1 + {x1}^{2}} \]

      6. lower-+.f64 N/A

         \[\leadsto 8 \cdot \frac{x1 \cdot \left(x2 \cdot x2\right)}{1 + \color{blue}{{x1}^{2}}} \]

      7. pow2 N/A

         \[\leadsto 8 \cdot \frac{x1 \cdot \left(x2 \cdot x2\right)}{1 + x1 \cdot \color{blue}{x1}} \]

      8. lift-*.f64 25.8

         \[\leadsto 8 \cdot \frac{x1 \cdot \left(x2 \cdot x2\right)}{1 + x1 \cdot \color{blue}{x1}} \]

   5. Applied rewrites 25.8%

      \[\leadsto \color{blue}{8 \cdot \frac{x1 \cdot \left(x2 \cdot x2\right)}{1 + x1 \cdot x1}} \]

   if -0.569999999999999951 < x1 < 1

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 74.7

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 74.7%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       4. lower-*.f64 74.4

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   11. Applied rewrites 74.4%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   12. Taylor expanded in x2 around 0

       \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)} \]
   13. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}, x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]

   14. Applied rewrites 99.3%

       \[\leadsto \mathsf{fma}\left(x1, \color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right) - 1}, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(x2, 8 + -8 \cdot \left(x1 \cdot x1\right), x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) - 6\right)\right) \]

   if 1 < x1

   1. Initial program 48.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto x1 + \left(\left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{\left(2 \cdot x2 - 3\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. lower--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - \color{blue}{3}\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. lift-*.f64 25.4

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Applied rewrites 25.4%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.7%

      \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 96.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_0\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_0, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - 1, x2 \cdot \left(\mathsf{fma}\left(x1, x2 \cdot \left(8 + -8 \cdot \left(x1 \cdot x1\right)\right), x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1
         (+
          x1
          (*
           x1
           (fma
            -1.0
            (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_0))))
            (* x1 (+ 9.0 (fma 4.0 t_0 (* x1 (- (* 6.0 x1) 3.0))))))))))
   (if (<= x1 -1.0)
     t_1
     (if (<= x1 1.0)
       (fma
        x1
        (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0)
        (*
         x2
         (-
          (fma
           x1
           (* x2 (+ 8.0 (* -8.0 (* x1 x1))))
           (* x1 (- (* x1 (+ 12.0 (* 24.0 x1))) 12.0)))
          6.0)))
       t_1))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_0)))), (x1 * (9.0 + fma(4.0, t_0, (x1 * ((6.0 * x1) - 3.0)))))));
	double tmp;
	if (x1 <= -1.0) {
		tmp = t_1;
	} else if (x1 <= 1.0) {
		tmp = fma(x1, ((x1 * (9.0 + (-19.0 * x1))) - 1.0), (x2 * (fma(x1, (x2 * (8.0 + (-8.0 * (x1 * x1)))), (x1 * ((x1 * (12.0 + (24.0 * x1))) - 12.0))) - 6.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_0)))), Float64(x1 * Float64(9.0 + fma(4.0, t_0, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))))
	tmp = 0.0
	if (x1 <= -1.0)
		tmp = t_1;
	elseif (x1 <= 1.0)
		tmp = fma(x1, Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0), Float64(x2 * Float64(fma(x1, Float64(x2 * Float64(8.0 + Float64(-8.0 * Float64(x1 * x1)))), Float64(x1 * Float64(Float64(x1 * Float64(12.0 + Float64(24.0 * x1))) - 12.0))) - 6.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$0 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.0], t$95$1, If[LessEqual[x1, 1.0], N[(x1 * N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(x2 * N[(8.0 + N[(-8.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(12.0 + N[(24.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1 or 1 < x1

   1. Initial program 40.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 92.9%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 92.9%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]

   if -1 < x1 < 1

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)} \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}, x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]

   8. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(x1, \color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right) - 1}, x2 \cdot \left(\mathsf{fma}\left(x1, x2 \cdot \left(8 + -8 \cdot \left(x1 \cdot x1\right)\right), x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 96.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot t\_0\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, t\_0, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - 1, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(x2, 8 + -8 \cdot \left(x1 \cdot x1\right), x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1
         (+
          x1
          (*
           x1
           (fma
            -1.0
            (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_0))))
            (* x1 (+ 9.0 (fma 4.0 t_0 (* x1 (- (* 6.0 x1) 3.0))))))))))
   (if (<= x1 -1.0)
     t_1
     (if (<= x1 1.0)
       (fma
        x1
        (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0)
        (*
         x2
         (-
          (*
           x1
           (fma
            x2
            (+ 8.0 (* -8.0 (* x1 x1)))
            (- (* x1 (+ 12.0 (* 24.0 x1))) 12.0)))
          6.0)))
       t_1))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 + (x1 * fma(-1.0, (2.0 + (-2.0 * (1.0 + (3.0 * t_0)))), (x1 * (9.0 + fma(4.0, t_0, (x1 * ((6.0 * x1) - 3.0)))))));
	double tmp;
	if (x1 <= -1.0) {
		tmp = t_1;
	} else if (x1 <= 1.0) {
		tmp = fma(x1, ((x1 * (9.0 + (-19.0 * x1))) - 1.0), (x2 * ((x1 * fma(x2, (8.0 + (-8.0 * (x1 * x1))), ((x1 * (12.0 + (24.0 * x1))) - 12.0))) - 6.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 + Float64(x1 * fma(-1.0, Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_0)))), Float64(x1 * Float64(9.0 + fma(4.0, t_0, Float64(x1 * Float64(Float64(6.0 * x1) - 3.0))))))))
	tmp = 0.0
	if (x1 <= -1.0)
		tmp = t_1;
	elseif (x1 <= 1.0)
		tmp = fma(x1, Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0), Float64(x2 * Float64(Float64(x1 * fma(x2, Float64(8.0 + Float64(-8.0 * Float64(x1 * x1))), Float64(Float64(x1 * Float64(12.0 + Float64(24.0 * x1))) - 12.0))) - 6.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 * N[(-1.0 * N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(9.0 + N[(4.0 * t$95$0 + N[(x1 * N[(N[(6.0 * x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.0], t$95$1, If[LessEqual[x1, 1.0], N[(x1 * N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * N[(x2 * N[(8.0 + N[(-8.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(12.0 + N[(24.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1 or 1 < x1

   1. Initial program 40.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around -inf

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + {x1}^{4} \cdot \color{blue}{\left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1} + 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   5. Applied rewrites 92.9%

      \[\leadsto x1 + \color{blue}{{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)} \]

   6. Taylor expanded in x1 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + x1 \cdot \left(-1 \cdot \left(2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \color{blue}{x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x1 + x1 \cdot \mathsf{fma}\left(-1, 2 + \color{blue}{-2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}, x1 \cdot \left(9 + \left(4 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right) \]

   8. Applied rewrites 92.9%

      \[\leadsto x1 + x1 \cdot \color{blue}{\mathsf{fma}\left(-1, 2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right), x1 \cdot \left(9 + \mathsf{fma}\left(4, 2 \cdot x2 - 3, x1 \cdot \left(6 \cdot x1 - 3\right)\right)\right)\right)} \]

   if -1 < x1 < 1

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 74.7

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 74.7%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       4. lower-*.f64 74.4

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   11. Applied rewrites 74.4%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   12. Taylor expanded in x2 around 0

       \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) + \color{blue}{x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)} \]
   13. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x1, x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}, x2 \cdot \left(\left(x1 \cdot \left(x2 \cdot \left(8 + -8 \cdot {x1}^{2}\right)\right) + x1 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 6\right)\right) \]

   14. Applied rewrites 99.3%

       \[\leadsto \mathsf{fma}\left(x1, \color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right) - 1}, x2 \cdot \left(x1 \cdot \mathsf{fma}\left(x2, 8 + -8 \cdot \left(x1 \cdot x1\right), x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right) - 6\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 80.9% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\\ \mathbf{elif}\;x1 \leq 0.185:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot t\_0 - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(\left(4 \cdot \left(x1 \cdot t\_0\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- (* 2.0 x2) 3.0))))
   (if (<= x1 -3.5e+99)
     (* x1 (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0))
     (if (<= x1 0.185)
       (fma -6.0 x2 (* x1 (- (* 4.0 t_0) 1.0)))
       (+ x1 (+ (+ (+ (* 4.0 (* x1 t_0)) (* (* x1 x1) x1)) x1) 9.0))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((2.0 * x2) - 3.0);
	double tmp;
	if (x1 <= -3.5e+99) {
		tmp = x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0);
	} else if (x1 <= 0.185) {
		tmp = fma(-6.0, x2, (x1 * ((4.0 * t_0) - 1.0)));
	} else {
		tmp = x1 + ((((4.0 * (x1 * t_0)) + ((x1 * x1) * x1)) + x1) + 9.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))
	tmp = 0.0
	if (x1 <= -3.5e+99)
		tmp = Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0));
	elseif (x1 <= 0.185)
		tmp = fma(-6.0, x2, Float64(x1 * Float64(Float64(4.0 * t_0) - 1.0)));
	else
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(4.0 * Float64(x1 * t_0)) + Float64(Float64(x1 * x1) * x1)) + x1) + 9.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.5e+99], N[(x1 * N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.185], N[(-6.0 * x2 + N[(x1 * N[(N[(4.0 * t$95$0), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + 9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.4999999999999998e99

   1. Initial program 2.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      5. lower-*.f64 97.6

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   8. Applied rewrites 97.6%

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]

   if -3.4999999999999998e99 < x1 < 0.185

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)} \]
   4. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{x2}, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right) \]

   5. Applied rewrites 78.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right)} \]

   if 0.185 < x1

   1. Initial program 48.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto x1 + \left(\left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \color{blue}{\left(2 \cdot x2 - 3\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. lower--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - \color{blue}{3}\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. lift-*.f64 25.4

         \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Applied rewrites 25.4%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.6%

      \[\leadsto x1 + \left(\left(\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{9}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 78.1% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.5e+99)
   (* x1 (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0))
   (if (<= x1 4.5e+153)
     (fma -6.0 x2 (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 1.0)))
     (fma -6.0 x2 (* x1 (- (* 9.0 x1) 1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.5e+99) {
		tmp = x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0);
	} else if (x1 <= 4.5e+153) {
		tmp = fma(-6.0, x2, (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0)));
	} else {
		tmp = fma(-6.0, x2, (x1 * ((9.0 * x1) - 1.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.5e+99)
		tmp = Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0));
	elseif (x1 <= 4.5e+153)
		tmp = fma(-6.0, x2, Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 1.0)));
	else
		tmp = fma(-6.0, x2, Float64(x1 * Float64(Float64(9.0 * x1) - 1.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.5e+99], N[(x1 * N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(-6.0 * x2 + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * x2 + N[(x1 * N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.4999999999999998e99

   1. Initial program 2.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      5. lower-*.f64 97.6

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   8. Applied rewrites 97.6%

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]

   if -3.4999999999999998e99 < x1 < 4.5000000000000001e153

   1. Initial program 99.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)} \]
   4. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{x2}, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right) \]

   5. Applied rewrites 69.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\right)} \]

   if 4.5000000000000001e153 < x1

   1. Initial program 0.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 49.6

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 49.6%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       4. lower-*.f64 73.7

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   11. Applied rewrites 73.7%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   12. Taylor expanded in x2 around 0

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
   13. Step-by-step derivation

       1. lower-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]

   14. Applied rewrites 100.0%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 67.9% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.5e+101)
   (* x1 (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0))
   (if (<= x1 1.4e+153)
     (fma -6.0 x2 (* x1 (- (* -12.0 x2) 1.0)))
     (fma -6.0 x2 (* x1 (- (* 9.0 x1) 1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+101) {
		tmp = x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0);
	} else if (x1 <= 1.4e+153) {
		tmp = fma(-6.0, x2, (x1 * ((-12.0 * x2) - 1.0)));
	} else {
		tmp = fma(-6.0, x2, (x1 * ((9.0 * x1) - 1.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.5e+101)
		tmp = Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0));
	elseif (x1 <= 1.4e+153)
		tmp = fma(-6.0, x2, Float64(x1 * Float64(Float64(-12.0 * x2) - 1.0)));
	else
		tmp = fma(-6.0, x2, Float64(x1 * Float64(Float64(9.0 * x1) - 1.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.5e+101], N[(x1 * N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.4e+153], N[(-6.0 * x2 + N[(x1 * N[(N[(-12.0 * x2), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * x2 + N[(x1 * N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.49999999999999994e101

   1. Initial program 1.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      5. lower-*.f64 98.6

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   8. Applied rewrites 98.6%

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]

   if -2.49999999999999994e101 < x1 < 1.39999999999999993e153

   1. Initial program 99.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 58.2

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 58.2%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 54.6

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right) \]

   11. Applied rewrites 54.6%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(-12 \cdot x2 - 1\right)\right) \]

   if 1.39999999999999993e153 < x1

   1. Initial program 0.6%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 49.6

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 49.6%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       4. lower-*.f64 73.6

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   11. Applied rewrites 73.6%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   12. Taylor expanded in x2 around 0

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
   13. Step-by-step derivation

       1. lower-*.f64 99.8

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]

   14. Applied rewrites 99.8%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 67.9% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot 9\right) - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -2.5e+101)
   (* x1 (- (* x1 (+ 9.0 (* -19.0 x1))) 1.0))
   (fma -6.0 x2 (* x1 (- (fma -12.0 x2 (* x1 9.0)) 1.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.5e+101) {
		tmp = x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0);
	} else {
		tmp = fma(-6.0, x2, (x1 * (fma(-12.0, x2, (x1 * 9.0)) - 1.0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.5e+101)
		tmp = Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0));
	else
		tmp = fma(-6.0, x2, Float64(x1 * Float64(fma(-12.0, x2, Float64(x1 * 9.0)) - 1.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -2.5e+101], N[(x1 * N[(N[(x1 * N[(9.0 + N[(-19.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * x2 + N[(x1 * N[(N[(-12.0 * x2 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.49999999999999994e101

   1. Initial program 1.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      5. lower-*.f64 98.6

         \[\leadsto x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   8. Applied rewrites 98.6%

      \[\leadsto x1 \cdot \color{blue}{\left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)} \]

   if -2.49999999999999994e101 < x1

   1. Initial program 84.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x1 around 0

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   5. Applied rewrites 46.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

      8. lower-*.f64 56.9

         \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. Applied rewrites 56.9%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   9. Taylor expanded in x1 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]
   10. Step-by-step derivation

       1. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

       4. lower-*.f64 60.6

          \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   11. Applied rewrites 60.6%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

   12. Taylor expanded in x2 around 0

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot 9\right) - 1\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 61.5%

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot 9\right) - 1\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 64.0% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (fma -6.0 x2 (* x1 (- (* 9.0 x1) 1.0))))

C

double code(double x1, double x2) {
	return fma(-6.0, x2, (x1 * ((9.0 * x1) - 1.0)));
}

Julia

function code(x1, x2)
	return fma(-6.0, x2, Float64(x1 * Float64(Float64(9.0 * x1) - 1.0)))
end

Wolfram

code[x1_, x2_] := N[(-6.0 * x2 + N[(x1 * N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.8%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x1 around 0

   \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) + x1 \cdot \left(\left(2 \cdot \left(-2 \cdot x2 + -1 \cdot \left(2 \cdot x2 - 3\right)\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(2 \cdot \left(\left(1 + \left(2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

5. Applied rewrites 50.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, \mathsf{fma}\left(8, x2, x1 \cdot \left(\mathsf{fma}\left(2, \left(1 + \mathsf{fma}\left(2, x2 \cdot \left(3 - 2 \cdot x2\right), 3 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 2 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right), 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)\right)} \]

6. Taylor expanded in x2 around 0

   \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(x1 \cdot \left(9 + -19 \cdot x1\right) + x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]
7. Step-by-step derivation

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   2. lower-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   3. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   5. lower--.f64 N/A

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   7. lower-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

   8. lower-*.f64 57.1

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

8. Applied rewrites 57.1%

   \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(x1, 9 + -19 \cdot x1, x2 \cdot \left(x1 \cdot \left(12 + 24 \cdot x1\right) - 12\right)\right) - 1\right)\right) \]

9. Taylor expanded in x1 around 0

   \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\left(-12 \cdot x2 + x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]
10. Step-by-step derivation

    1. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

    2. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

    3. lower-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

    4. lower-*.f64 60.6

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

11. Applied rewrites 60.6%

    \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(-12, x2, x1 \cdot \left(9 + 12 \cdot x2\right)\right) - 1\right)\right) \]

12. Taylor expanded in x2 around 0

    \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
13. Step-by-step derivation

    1. lower-*.f64 64.0

       \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]

14. Applied rewrites 64.0%

    \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right)\right) \]
15. Add Preprocessing

Alternative 16: 26.5% accurate, 33.1× speedup

Math

\[\begin{array}{l} \\ x1 + -6 \cdot x2 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* -6.0 x2)))

C

double code(double x1, double x2) {
	return x1 + (-6.0 * x2);
}

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(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + ((-6.0d0) * x2)
end function

Java

public static double code(double x1, double x2) {
	return x1 + (-6.0 * x2);
}

Python

def code(x1, x2):
	return x1 + (-6.0 * x2)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(-6.0 * x2))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (-6.0 * x2);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.8%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x1 around 0

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. lower-*.f64 26.5

      \[\leadsto x1 + -6 \cdot \color{blue}{x2} \]

5. Applied rewrites 26.5%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
6. Add Preprocessing

Alternative 17: 26.4% accurate, 49.7× speedup

Math

\[\begin{array}{l} \\ -6 \cdot x2 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* -6.0 x2))

C

double code(double x1, double x2) {
	return -6.0 * x2;
}

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(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (-6.0d0) * x2
end function

Java

public static double code(double x1, double x2) {
	return -6.0 * x2;
}

Python

def code(x1, x2):
	return -6.0 * x2

Julia

function code(x1, x2)
	return Float64(-6.0 * x2)
end

MATLAB

function tmp = code(x1, x2)
	tmp = -6.0 * x2;
end

Wolfram

code[x1_, x2_] := N[(-6.0 * x2), $MachinePrecision]

Derivation

1. Initial program 69.8%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x1 around 0

   \[\leadsto \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. lower-*.f64 26.4

      \[\leadsto -6 \cdot \color{blue}{x2} \]

5. Applied rewrites 26.4%

   \[\leadsto \color{blue}{-6 \cdot x2} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025088 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (+ (* x1 x1) 1.0)) (* (* (* 3.0 x1) x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (* (* x1 x1) x1)) x1) (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))