Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 71.3% → 99.5%

Time: 16.1s

Alternatives: 5

Speedup: N/A×

• 45.8% 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: 71.3% 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: 99.5% accurate, N/A× speedup

Math

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

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	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(Float64(t_0 + Float64(2.0 * x2)) + Float64(-1.0 * x1)) / t_3)
	t_5 = Float64(t_0 * t_4)
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) + Float64(-1.0 * x1)) / t_3))
	t_7 = Float64(Float64(Float64(2.0 * x1) * t_4) * Float64(t_4 + Float64(-1.0 * 3.0)))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_7 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))) * t_3) + t_5) + t_1) + x1) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_7 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(fma(2.0, x2, Float64(3.0 * Float64(x1 * x1))) - x1) / t_3)) - 6.0))) * t_3) + t_5) + t_1) + x1) + t_6));
	else
		tmp = Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(9.0 + fma(-1.0, Float64(Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_2)))) / x1), Float64(4.0 * t_2))) / x1)) / x1))));
	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] * 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[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$0 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 + N[(-1.0 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(t$95$7 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision] + t$95$1), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(N[(N[(N[(N[(t$95$7 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(2.0 * x2 + N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision] + t$95$1), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(N[(3.0 - N[(N[(9.0 + N[(-1.0 * N[(N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $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 x2 around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. pow2 N/A

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

      5. lift-*.f64 99.4

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

   5. Applied rewrites 99.4%

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

   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 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1} + -1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1} + -1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(2, x2, 3 \cdot \left(x1 \cdot x1\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + {x1}^{4} \cdot \left(6 - \frac{3 - \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}, 4 \cdot \left(2 \cdot x2 - 3\right)\right)}{x1}}{x1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left(x1 \cdot x1\right) - x1\\ t_3 := 1 + x1 \cdot x1\\ t_4 := \frac{x1 \cdot x1}{t\_3}\\ t_5 := 3 \cdot t\_4 - \left(3 + \frac{x1}{t\_3}\right)\\ t_6 := 2 \cdot x2 - 3\\ t_7 := \left(3 \cdot x1\right) \cdot x1\\ t_8 := \frac{\left(t\_7 + 2 \cdot x2\right) + -1 \cdot x1}{t\_1}\\ t_9 := \frac{t\_2}{t\_3}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_8\right) \cdot \left(t\_8 + -1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_8 - 6\right)\right) \cdot t\_1 + t\_7 \cdot t\_8\right) + t\_0\right) + x1\right) + 3 \cdot \frac{\left(t\_7 - 2 \cdot x2\right) + -1 \cdot x1}{t\_1}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(2, x1, \mathsf{fma}\left(3, \frac{\left(x1 \cdot x1\right) \cdot t\_2}{t\_3}, \mathsf{fma}\left(3, t\_9, \mathsf{fma}\left(x2, \mathsf{fma}\left(6, t\_4, \mathsf{fma}\left(8, \frac{x1 \cdot x2}{t\_3}, t\_3 \cdot \mathsf{fma}\left(2, \frac{x1 \cdot \mathsf{fma}\left(2, t\_5, 2 \cdot t\_9\right)}{t\_3}, 8 \cdot t\_4\right)\right)\right) - 6 \cdot {t\_3}^{-1}, \mathsf{fma}\left(t\_3, \mathsf{fma}\left(2, \frac{x1 \cdot \left(t\_5 \cdot t\_2\right)}{t\_3}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_9 - 6\right)\right), t\_0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + {x1}^{4} \cdot \left(6 - \frac{3 - \frac{9 + \mathsf{fma}\left(-1, \frac{2 + -2 \cdot \left(1 + 3 \cdot t\_6\right)}{x1}, 4 \cdot t\_6\right)}{x1}}{x1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- (* 3.0 (* x1 x1)) x1))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4 (/ (* x1 x1) t_3))
        (t_5 (- (* 3.0 t_4) (+ 3.0 (/ x1 t_3))))
        (t_6 (- (* 2.0 x2) 3.0))
        (t_7 (* (* 3.0 x1) x1))
        (t_8 (/ (+ (+ t_7 (* 2.0 x2)) (* -1.0 x1)) t_1))
        (t_9 (/ t_2 t_3)))
   (if (<=
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2.0 x1) t_8) (+ t_8 (* -1.0 3.0)))
               (* (* x1 x1) (- (* 4.0 t_8) 6.0)))
              t_1)
             (* t_7 t_8))
            t_0)
           x1)
          (* 3.0 (/ (+ (- t_7 (* 2.0 x2)) (* -1.0 x1)) t_1))))
        INFINITY)
     (fma
      2.0
      x1
      (fma
       3.0
       (/ (* (* x1 x1) t_2) t_3)
       (fma
        3.0
        t_9
        (fma
         x2
         (-
          (fma
           6.0
           t_4
           (fma
            8.0
            (/ (* x1 x2) t_3)
            (*
             t_3
             (fma 2.0 (/ (* x1 (fma 2.0 t_5 (* 2.0 t_9))) t_3) (* 8.0 t_4)))))
          (* 6.0 (pow t_3 -1.0)))
         (fma
          t_3
          (fma
           2.0
           (/ (* x1 (* t_5 t_2)) t_3)
           (* (* x1 x1) (- (* 4.0 t_9) 6.0)))
          t_0)))))
     (+
      x1
      (*
       (pow x1 4.0)
       (-
        6.0
        (/
         (-
          3.0
          (/
           (+
            9.0
            (fma -1.0 (/ (+ 2.0 (* -2.0 (+ 1.0 (* 3.0 t_6)))) x1) (* 4.0 t_6)))
           x1))
         x1)))))))

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)) - x1;
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = (x1 * x1) / t_3;
	double t_5 = (3.0 * t_4) - (3.0 + (x1 / t_3));
	double t_6 = (2.0 * x2) - 3.0;
	double t_7 = (3.0 * x1) * x1;
	double t_8 = ((t_7 + (2.0 * x2)) + (-1.0 * x1)) / t_1;
	double t_9 = t_2 / t_3;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_8) * (t_8 + (-1.0 * 3.0))) + ((x1 * x1) * ((4.0 * t_8) - 6.0))) * t_1) + (t_7 * t_8)) + t_0) + x1) + (3.0 * (((t_7 - (2.0 * x2)) + (-1.0 * x1)) / t_1)))) <= ((double) INFINITY)) {
		tmp = fma(2.0, x1, fma(3.0, (((x1 * x1) * t_2) / t_3), fma(3.0, t_9, fma(x2, (fma(6.0, t_4, fma(8.0, ((x1 * x2) / t_3), (t_3 * fma(2.0, ((x1 * fma(2.0, t_5, (2.0 * t_9))) / t_3), (8.0 * t_4))))) - (6.0 * pow(t_3, -1.0))), fma(t_3, fma(2.0, ((x1 * (t_5 * t_2)) / t_3), ((x1 * x1) * ((4.0 * t_9) - 6.0))), t_0)))));
	} else {
		tmp = x1 + (pow(x1, 4.0) * (6.0 - ((3.0 - ((9.0 + fma(-1.0, ((2.0 + (-2.0 * (1.0 + (3.0 * t_6)))) / x1), (4.0 * t_6))) / x1)) / x1)));
	}
	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 * Float64(x1 * x1)) - x1)
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(Float64(x1 * x1) / t_3)
	t_5 = Float64(Float64(3.0 * t_4) - Float64(3.0 + Float64(x1 / t_3)))
	t_6 = Float64(Float64(2.0 * x2) - 3.0)
	t_7 = Float64(Float64(3.0 * x1) * x1)
	t_8 = Float64(Float64(Float64(t_7 + Float64(2.0 * x2)) + Float64(-1.0 * x1)) / t_1)
	t_9 = Float64(t_2 / t_3)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_8) * Float64(t_8 + Float64(-1.0 * 3.0))) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_8) - 6.0))) * t_1) + Float64(t_7 * t_8)) + t_0) + x1) + Float64(3.0 * Float64(Float64(Float64(t_7 - Float64(2.0 * x2)) + Float64(-1.0 * x1)) / t_1)))) <= Inf)
		tmp = fma(2.0, x1, fma(3.0, Float64(Float64(Float64(x1 * x1) * t_2) / t_3), fma(3.0, t_9, fma(x2, Float64(fma(6.0, t_4, fma(8.0, Float64(Float64(x1 * x2) / t_3), Float64(t_3 * fma(2.0, Float64(Float64(x1 * fma(2.0, t_5, Float64(2.0 * t_9))) / t_3), Float64(8.0 * t_4))))) - Float64(6.0 * (t_3 ^ -1.0))), fma(t_3, fma(2.0, Float64(Float64(x1 * Float64(t_5 * t_2)) / t_3), Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_9) - 6.0))), t_0)))));
	else
		tmp = Float64(x1 + Float64((x1 ^ 4.0) * Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(9.0 + fma(-1.0, Float64(Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_6)))) / x1), Float64(4.0 * t_6))) / x1)) / x1))));
	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 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(3.0 * t$95$4), $MachinePrecision] - N[(3.0 + N[(x1 / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$7 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$8 = N[(N[(N[(t$95$7 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$2 / t$95$3), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$8), $MachinePrecision] * N[(t$95$8 + N[(-1.0 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$8), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$7 * t$95$8), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$7 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(3.0 * t$95$9 + N[(x2 * N[(N[(6.0 * t$95$4 + N[(8.0 * N[(N[(x1 * x2), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(t$95$3 * N[(2.0 * N[(N[(x1 * N[(2.0 * t$95$5 + N[(2.0 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(8.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.0 * N[Power[t$95$3, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(2.0 * N[(N[(x1 * N[(t$95$5 * t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$9), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(N[(3.0 - N[(N[(9.0 + N[(-1.0 * N[(N[(2.0 + N[(-2.0 * N[(1.0 + N[(3.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision] + N[(4.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $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 x2 around 0

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

   5. Applied rewrites 99.0%

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

   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 -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 100.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;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) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1} + -1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot 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) + -1 \cdot 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) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(2, x1, \mathsf{fma}\left(3, \frac{\left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x1 \cdot x1\right) - x1\right)}{1 + x1 \cdot x1}, \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - x1}{1 + x1 \cdot x1}, \mathsf{fma}\left(x2, \mathsf{fma}\left(6, \frac{x1 \cdot x1}{1 + x1 \cdot x1}, \mathsf{fma}\left(8, \frac{x1 \cdot x2}{1 + x1 \cdot x1}, \left(1 + x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, \frac{x1 \cdot \mathsf{fma}\left(2, 3 \cdot \frac{x1 \cdot x1}{1 + x1 \cdot x1} - \left(3 + \frac{x1}{1 + x1 \cdot x1}\right), 2 \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - x1}{1 + x1 \cdot x1}\right)}{1 + x1 \cdot x1}, 8 \cdot \frac{x1 \cdot x1}{1 + x1 \cdot x1}\right)\right)\right) - 6 \cdot {\left(1 + x1 \cdot x1\right)}^{-1}, \mathsf{fma}\left(1 + x1 \cdot x1, \mathsf{fma}\left(2, \frac{x1 \cdot \left(\left(3 \cdot \frac{x1 \cdot x1}{1 + x1 \cdot x1} - \left(3 + \frac{x1}{1 + x1 \cdot x1}\right)\right) \cdot \left(3 \cdot \left(x1 \cdot x1\right) - x1\right)\right)}{1 + x1 \cdot x1}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - x1}{1 + x1 \cdot x1} - 6\right)\right), \left(x1 \cdot x1\right) \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + {x1}^{4} \cdot \left(6 - \frac{3 - \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)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left(x1 \cdot x1\right) - x1\\ t_3 := 1 + x1 \cdot x1\\ t_4 := \left(3 \cdot x1\right) \cdot x1\\ t_5 := \frac{\left(t\_4 + 2 \cdot x2\right) + -1 \cdot x1}{t\_1}\\ t_6 := \frac{t\_2}{t\_3}\\ t_7 := \frac{x1 \cdot x1}{t\_3}\\ t_8 := 3 \cdot t\_7 - \left(3 + \frac{x1}{t\_3}\right)\\ t_9 := 2 \cdot x2 - 3\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_5\right) \cdot \left(t\_5 + -1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_5 - 6\right)\right) \cdot t\_1 + t\_4 \cdot t\_5\right) + t\_0\right) + x1\right) + 3 \cdot \frac{\left(t\_4 - 2 \cdot x2\right) + -1 \cdot x1}{t\_1}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(2, x1, \mathsf{fma}\left(3, \frac{\left(x1 \cdot x1\right) \cdot t\_2}{t\_3}, \mathsf{fma}\left(3, t\_6, \mathsf{fma}\left(x2, \mathsf{fma}\left(6, t\_7, \mathsf{fma}\left(8, \frac{x1 \cdot x2}{t\_3}, t\_3 \cdot \mathsf{fma}\left(2, \frac{x1 \cdot \mathsf{fma}\left(2, t\_8, 2 \cdot t\_6\right)}{t\_3}, 8 \cdot t\_7\right)\right)\right) - 6 \cdot {t\_3}^{-1}, \mathsf{fma}\left(t\_3, \mathsf{fma}\left(2, \frac{x1 \cdot \left(t\_8 \cdot t\_2\right)}{t\_3}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_6 - 6\right)\right), t\_0\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot t\_9, x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot t\_9\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (- (* 3.0 (* x1 x1)) x1))
        (t_3 (+ 1.0 (* x1 x1)))
        (t_4 (* (* 3.0 x1) x1))
        (t_5 (/ (+ (+ t_4 (* 2.0 x2)) (* -1.0 x1)) t_1))
        (t_6 (/ t_2 t_3))
        (t_7 (/ (* x1 x1) t_3))
        (t_8 (- (* 3.0 t_7) (+ 3.0 (/ x1 t_3))))
        (t_9 (- (* 2.0 x2) 3.0)))
   (if (<=
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2.0 x1) t_5) (+ t_5 (* -1.0 3.0)))
               (* (* x1 x1) (- (* 4.0 t_5) 6.0)))
              t_1)
             (* t_4 t_5))
            t_0)
           x1)
          (* 3.0 (/ (+ (- t_4 (* 2.0 x2)) (* -1.0 x1)) t_1))))
        INFINITY)
     (fma
      2.0
      x1
      (fma
       3.0
       (/ (* (* x1 x1) t_2) t_3)
       (fma
        3.0
        t_6
        (fma
         x2
         (-
          (fma
           6.0
           t_7
           (fma
            8.0
            (/ (* x1 x2) t_3)
            (*
             t_3
             (fma 2.0 (/ (* x1 (fma 2.0 t_8 (* 2.0 t_6))) t_3) (* 8.0 t_7)))))
          (* 6.0 (pow t_3 -1.0)))
         (fma
          t_3
          (fma
           2.0
           (/ (* x1 (* t_8 t_2)) t_3)
           (* (* x1 x1) (- (* 4.0 t_6) 6.0)))
          t_0)))))
     (fma
      -6.0
      x2
      (*
       x1
       (-
        (fma
         4.0
         (* x2 t_9)
         (*
          x1
          (-
           (fma
            2.0
            (fma -2.0 x2 (* -1.0 t_9))
            (fma 3.0 (- 3.0 (* -2.0 x2)) (fma 6.0 x2 (* 8.0 x2))))
           6.0)))
        1.0))))))

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)) - x1;
	double t_3 = 1.0 + (x1 * x1);
	double t_4 = (3.0 * x1) * x1;
	double t_5 = ((t_4 + (2.0 * x2)) + (-1.0 * x1)) / t_1;
	double t_6 = t_2 / t_3;
	double t_7 = (x1 * x1) / t_3;
	double t_8 = (3.0 * t_7) - (3.0 + (x1 / t_3));
	double t_9 = (2.0 * x2) - 3.0;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_5) * (t_5 + (-1.0 * 3.0))) + ((x1 * x1) * ((4.0 * t_5) - 6.0))) * t_1) + (t_4 * t_5)) + t_0) + x1) + (3.0 * (((t_4 - (2.0 * x2)) + (-1.0 * x1)) / t_1)))) <= ((double) INFINITY)) {
		tmp = fma(2.0, x1, fma(3.0, (((x1 * x1) * t_2) / t_3), fma(3.0, t_6, fma(x2, (fma(6.0, t_7, fma(8.0, ((x1 * x2) / t_3), (t_3 * fma(2.0, ((x1 * fma(2.0, t_8, (2.0 * t_6))) / t_3), (8.0 * t_7))))) - (6.0 * pow(t_3, -1.0))), fma(t_3, fma(2.0, ((x1 * (t_8 * t_2)) / t_3), ((x1 * x1) * ((4.0 * t_6) - 6.0))), t_0)))));
	} else {
		tmp = fma(-6.0, x2, (x1 * (fma(4.0, (x2 * t_9), (x1 * (fma(2.0, fma(-2.0, x2, (-1.0 * t_9)), fma(3.0, (3.0 - (-2.0 * x2)), fma(6.0, x2, (8.0 * x2)))) - 6.0))) - 1.0)));
	}
	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 * Float64(x1 * x1)) - x1)
	t_3 = Float64(1.0 + Float64(x1 * x1))
	t_4 = Float64(Float64(3.0 * x1) * x1)
	t_5 = Float64(Float64(Float64(t_4 + Float64(2.0 * x2)) + Float64(-1.0 * x1)) / t_1)
	t_6 = Float64(t_2 / t_3)
	t_7 = Float64(Float64(x1 * x1) / t_3)
	t_8 = Float64(Float64(3.0 * t_7) - Float64(3.0 + Float64(x1 / t_3)))
	t_9 = 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_5) * Float64(t_5 + Float64(-1.0 * 3.0))) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_5) - 6.0))) * t_1) + Float64(t_4 * t_5)) + t_0) + x1) + Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(2.0 * x2)) + Float64(-1.0 * x1)) / t_1)))) <= Inf)
		tmp = fma(2.0, x1, fma(3.0, Float64(Float64(Float64(x1 * x1) * t_2) / t_3), fma(3.0, t_6, fma(x2, Float64(fma(6.0, t_7, fma(8.0, Float64(Float64(x1 * x2) / t_3), Float64(t_3 * fma(2.0, Float64(Float64(x1 * fma(2.0, t_8, Float64(2.0 * t_6))) / t_3), Float64(8.0 * t_7))))) - Float64(6.0 * (t_3 ^ -1.0))), fma(t_3, fma(2.0, Float64(Float64(x1 * Float64(t_8 * t_2)) / t_3), Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_6) - 6.0))), t_0)))));
	else
		tmp = fma(-6.0, x2, Float64(x1 * Float64(fma(4.0, Float64(x2 * t_9), Float64(x1 * Float64(fma(2.0, fma(-2.0, x2, Float64(-1.0 * t_9)), fma(3.0, Float64(3.0 - Float64(-2.0 * x2)), fma(6.0, x2, Float64(8.0 * x2)))) - 6.0))) - 1.0)));
	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 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(x1 * x1), $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] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 / t$95$3), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$8 = N[(N[(3.0 * t$95$7), $MachinePrecision] - N[(3.0 + N[(x1 / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = 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$5), $MachinePrecision] * N[(t$95$5 + N[(-1.0 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$5), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$4 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$4 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * x1 + N[(3.0 * N[(N[(N[(x1 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(3.0 * t$95$6 + N[(x2 * N[(N[(6.0 * t$95$7 + N[(8.0 * N[(N[(x1 * x2), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(t$95$3 * N[(2.0 * N[(N[(x1 * N[(2.0 * t$95$8 + N[(2.0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(8.0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.0 * N[Power[t$95$3, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(2.0 * N[(N[(x1 * N[(t$95$8 * t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$6), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * x2 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$9), $MachinePrecision] + N[(x1 * N[(N[(2.0 * N[(-2.0 * x2 + N[(-1.0 * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(6.0 * x2 + N[(8.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $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 x2 around 0

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

   5. Applied rewrites 99.0%

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

   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

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

      1. lower-fma.f64 N/A

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

   5. Applied rewrites 67.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;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) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1} + -1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot 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) + -1 \cdot 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) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(2, x1, \mathsf{fma}\left(3, \frac{\left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x1 \cdot x1\right) - x1\right)}{1 + x1 \cdot x1}, \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - x1}{1 + x1 \cdot x1}, \mathsf{fma}\left(x2, \mathsf{fma}\left(6, \frac{x1 \cdot x1}{1 + x1 \cdot x1}, \mathsf{fma}\left(8, \frac{x1 \cdot x2}{1 + x1 \cdot x1}, \left(1 + x1 \cdot x1\right) \cdot \mathsf{fma}\left(2, \frac{x1 \cdot \mathsf{fma}\left(2, 3 \cdot \frac{x1 \cdot x1}{1 + x1 \cdot x1} - \left(3 + \frac{x1}{1 + x1 \cdot x1}\right), 2 \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - x1}{1 + x1 \cdot x1}\right)}{1 + x1 \cdot x1}, 8 \cdot \frac{x1 \cdot x1}{1 + x1 \cdot x1}\right)\right)\right) - 6 \cdot {\left(1 + x1 \cdot x1\right)}^{-1}, \mathsf{fma}\left(1 + x1 \cdot x1, \mathsf{fma}\left(2, \frac{x1 \cdot \left(\left(3 \cdot \frac{x1 \cdot x1}{1 + x1 \cdot x1} - \left(3 + \frac{x1}{1 + x1 \cdot x1}\right)\right) \cdot \left(3 \cdot \left(x1 \cdot x1\right) - x1\right)\right)}{1 + x1 \cdot x1}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{3 \cdot \left(x1 \cdot x1\right) - x1}{1 + x1 \cdot x1} - 6\right)\right), \left(x1 \cdot x1\right) \cdot x1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\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, 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, N/A× speedup

Math

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

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)) (* -1.0 x1)) t_1))
        (t_3 (- (* 2.0 x2) 3.0)))
   (if (<=
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2.0 x1) t_2) (+ t_2 (* -1.0 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)) (* -1.0 x1)) t_1))))
        INFINITY)
     (fma
      -6.0
      x2
      (fma
       x1
       (- (* 9.0 x1) 1.0)
       (* x2 (fma 8.0 (* x1 x2) (* x1 (- (* 12.0 x1) 12.0))))))
     (fma
      -6.0
      x2
      (*
       x1
       (-
        (fma
         4.0
         (* x2 t_3)
         (*
          x1
          (-
           (fma
            2.0
            (fma -2.0 x2 (* -1.0 t_3))
            (fma 3.0 (- 3.0 (* -2.0 x2)) (fma 6.0 x2 (* 8.0 x2))))
           6.0)))
        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)) + (-1.0 * x1)) / t_1;
	double t_3 = (2.0 * x2) - 3.0;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 + (-1.0 * 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)) + (-1.0 * x1)) / t_1)))) <= ((double) INFINITY)) {
		tmp = fma(-6.0, x2, fma(x1, ((9.0 * x1) - 1.0), (x2 * fma(8.0, (x1 * x2), (x1 * ((12.0 * x1) - 12.0))))));
	} else {
		tmp = fma(-6.0, x2, (x1 * (fma(4.0, (x2 * t_3), (x1 * (fma(2.0, fma(-2.0, x2, (-1.0 * t_3)), fma(3.0, (3.0 - (-2.0 * x2)), fma(6.0, x2, (8.0 * x2)))) - 6.0))) - 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)) + Float64(-1.0 * x1)) / t_1)
	t_3 = 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_2) * Float64(t_2 + Float64(-1.0 * 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)) + Float64(-1.0 * x1)) / t_1)))) <= Inf)
		tmp = fma(-6.0, x2, fma(x1, Float64(Float64(9.0 * x1) - 1.0), Float64(x2 * fma(8.0, Float64(x1 * x2), Float64(x1 * Float64(Float64(12.0 * x1) - 12.0))))));
	else
		tmp = fma(-6.0, x2, Float64(x1 * Float64(fma(4.0, Float64(x2 * t_3), Float64(x1 * Float64(fma(2.0, fma(-2.0, x2, Float64(-1.0 * t_3)), fma(3.0, Float64(3.0 - Float64(-2.0 * x2)), fma(6.0, x2, Float64(8.0 * x2)))) - 6.0))) - 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] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = 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$2), $MachinePrecision] * N[(t$95$2 + N[(-1.0 * 3.0), $MachinePrecision]), $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] + N[(-1.0 * x1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(-6.0 * x2 + N[(x1 * N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] + N[(x2 * N[(8.0 * N[(x1 * x2), $MachinePrecision] + N[(x1 * N[(N[(12.0 * x1), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * x2 + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$3), $MachinePrecision] + N[(x1 * N[(N[(2.0 * N[(-2.0 * x2 + N[(-1.0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(3.0 - N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] + N[(6.0 * x2 + N[(8.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $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

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

      1. lower-fma.f64 N/A

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

   5. Applied rewrites 68.4%

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

   6. Taylor expanded in x2 around 0

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 79.2

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

   8. Applied rewrites 79.2%

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

   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

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

      1. lower-fma.f64 N/A

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

   5. Applied rewrites 67.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1} + -1 \cdot 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) + -1 \cdot x1}{x1 \cdot x1 + 1}\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, \mathsf{fma}\left(x1, 9 \cdot x1 - 1, x2 \cdot \mathsf{fma}\left(8, x1 \cdot x2, x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-6, x2, x1 \cdot \left(\mathsf{fma}\left(4, x2 \cdot \left(2 \cdot x2 - 3\right), x1 \cdot \left(\mathsf{fma}\left(2, \mathsf{fma}\left(-2, x2, -1 \cdot \left(2 \cdot x2 - 3\right)\right), \mathsf{fma}\left(3, 3 - -2 \cdot x2, \mathsf{fma}\left(6, x2, 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.8% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-6, x2, \mathsf{fma}\left(x1, 9 \cdot x1 - 1, x2 \cdot \mathsf{fma}\left(8, x1 \cdot x2, x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right)\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (fma
  -6.0
  x2
  (fma
   x1
   (- (* 9.0 x1) 1.0)
   (* x2 (fma 8.0 (* x1 x2) (* x1 (- (* 12.0 x1) 12.0)))))))

C

double code(double x1, double x2) {
	return fma(-6.0, x2, fma(x1, ((9.0 * x1) - 1.0), (x2 * fma(8.0, (x1 * x2), (x1 * ((12.0 * x1) - 12.0))))));
}

Julia

function code(x1, x2)
	return fma(-6.0, x2, fma(x1, Float64(Float64(9.0 * x1) - 1.0), Float64(x2 * fma(8.0, Float64(x1 * x2), Float64(x1 * Float64(Float64(12.0 * x1) - 12.0))))))
end

Wolfram

code[x1_, x2_] := N[(-6.0 * x2 + N[(x1 * N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] + N[(x2 * N[(8.0 * N[(x1 * x2), $MachinePrecision] + N[(x1 * N[(N[(12.0 * x1), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in x1 around 0

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

   1. lower-fma.f64 N/A

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

5. Applied rewrites 68.3%

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

6. Taylor expanded in x2 around 0

   \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \left(9 \cdot x1 - 1\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
7. Step-by-step derivation

   1. lower-fma.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-fma.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower--.f64 N/A

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

   9. lower-*.f64 67.5

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

8. Applied rewrites 67.5%

   \[\leadsto \mathsf{fma}\left(-6, x2, \mathsf{fma}\left(x1, 9 \cdot x1 - 1, x2 \cdot \mathsf{fma}\left(8, x1 \cdot x2, x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right)\right) \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025065 
(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))))))