Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.2% → 99.4%

Time: 15.7s

Alternatives: 23

Speedup: 7.8×

• 47.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) * x1)
	t_1 = Float64(Float64(3.0 * x1) * x1)
	t_2 = Float64(fma(x2, 2.0, t_1) - x1)
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(t_1 * t_4)
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_3))
	t_7 = Float64(t_2 / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))) * t_3) + t_5) + t_0) + x1) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(Float64(fma(Float64(Float64(Float64(Float64(4.0 * t_2) / fma(x1, x1, 1.0)) - 6.0) * x1), x1, Float64(Float64(t_7 - 3.0) * Float64(t_7 * Float64(2.0 * x1)))) * t_3) + t_5) + t_0) + x1) + t_6));
	else
		tmp = Float64(fma(Float64(fma(Float64(fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * Float64(Float64(x1 * x1) * Float64(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[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x2 * 2.0 + t$95$1), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$1 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$2 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + 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$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(4.0 * t$95$2), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision] * x1), $MachinePrecision] * x1 + N[(N[(t$95$7 - 3.0), $MachinePrecision] * N[(t$95$7 * N[(2.0 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 3.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 6.0), $MachinePrecision] * N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $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 99.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

   4. Applied rewrites 99.5%

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

   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

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

   5. Applied rewrites 98.6%

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

   7. Applied rewrites 98.6%

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

Alternative 2: 61.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right)\\ t_4 := \left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+213}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;t\_3 \leq 10^{-57}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+216}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;x1 + \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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))
        (t_3
         (+
          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)))))
        (t_4 (* (- (* 9.0 x1) 1.0) x1)))
   (if (<= t_3 -1e+213)
     (* (* (* x2 x2) 8.0) x1)
     (if (<= t_3 -1e+38)
       (* -6.0 x2)
       (if (<= t_3 1e-57)
         t_4
         (if (<= t_3 2e+216)
           (* -6.0 x2)
           (if (<= t_3 INFINITY) (+ x1 (* (* (* x2 x2) x1) 8.0)) t_4)))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double t_4 = ((9.0 * x1) - 1.0) * x1;
	double tmp;
	if (t_3 <= -1e+213) {
		tmp = ((x2 * x2) * 8.0) * x1;
	} else if (t_3 <= -1e+38) {
		tmp = -6.0 * x2;
	} else if (t_3 <= 1e-57) {
		tmp = t_4;
	} else if (t_3 <= 2e+216) {
		tmp = -6.0 * x2;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = x1 + (((x2 * x2) * x1) * 8.0);
	} else {
		tmp = t_4;
	}
	return tmp;
}

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;
	double t_3 = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double t_4 = ((9.0 * x1) - 1.0) * x1;
	double tmp;
	if (t_3 <= -1e+213) {
		tmp = ((x2 * x2) * 8.0) * x1;
	} else if (t_3 <= -1e+38) {
		tmp = -6.0 * x2;
	} else if (t_3 <= 1e-57) {
		tmp = t_4;
	} else if (t_3 <= 2e+216) {
		tmp = -6.0 * x2;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = x1 + (((x2 * x2) * x1) * 8.0);
	} else {
		tmp = t_4;
	}
	return tmp;
}

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
	t_3 = 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)))
	t_4 = ((9.0 * x1) - 1.0) * x1
	tmp = 0
	if t_3 <= -1e+213:
		tmp = ((x2 * x2) * 8.0) * x1
	elif t_3 <= -1e+38:
		tmp = -6.0 * x2
	elif t_3 <= 1e-57:
		tmp = t_4
	elif t_3 <= 2e+216:
		tmp = -6.0 * x2
	elif t_3 <= math.inf:
		tmp = x1 + (((x2 * x2) * x1) * 8.0)
	else:
		tmp = t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = 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))))
	t_4 = Float64(Float64(Float64(9.0 * x1) - 1.0) * x1)
	tmp = 0.0
	if (t_3 <= -1e+213)
		tmp = Float64(Float64(Float64(x2 * x2) * 8.0) * x1);
	elseif (t_3 <= -1e+38)
		tmp = Float64(-6.0 * x2);
	elseif (t_3 <= 1e-57)
		tmp = t_4;
	elseif (t_3 <= 2e+216)
		tmp = Float64(-6.0 * x2);
	elseif (t_3 <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * x2) * x1) * 8.0));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = 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;
	t_3 = 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)));
	t_4 = ((9.0 * x1) - 1.0) * x1;
	tmp = 0.0;
	if (t_3 <= -1e+213)
		tmp = ((x2 * x2) * 8.0) * x1;
	elseif (t_3 <= -1e+38)
		tmp = -6.0 * x2;
	elseif (t_3 <= 1e-57)
		tmp = t_4;
	elseif (t_3 <= 2e+216)
		tmp = -6.0 * x2;
	elseif (t_3 <= Inf)
		tmp = x1 + (((x2 * x2) * x1) * 8.0);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = 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]}, Block[{t$95$4 = N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+213], N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision], If[LessEqual[t$95$3, -1e+38], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[t$95$3, 1e-57], t$95$4, If[LessEqual[t$95$3, 2e+216], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(x1 + N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 4 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)))))) < -9.99999999999999984e212

   1. Initial program 100.0%

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

   3. Taylor expanded in x2 around inf

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in x1 around 0

      \[\leadsto 8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 80.4%

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

   if -9.99999999999999984e212 < (+.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)))))) < -9.99999999999999977e37 or 9.99999999999999955e-58 < (+.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)))))) < 2e216

   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

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

   5. Applied rewrites 59.0%

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

   if -9.99999999999999977e37 < (+.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)))))) < 9.99999999999999955e-58 or +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 39.6%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 78.7%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 81.7%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 77.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 69.4%

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

   if 2e216 < (+.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 100.0%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 44.1%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 41.0%

      \[\leadsto x1 + \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot \color{blue}{8} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 60.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \left(9 \cdot x1 - 1\right) \cdot x1\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_2}\\ t_4 := x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_3 - 6\right)\right) \cdot t\_2 + t\_0 \cdot t\_3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_2}\right)\\ t_5 := \left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{+213}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;t\_4 \leq 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+216}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (* (- (* 9.0 x1) 1.0) x1))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_4
         (+
          x1
          (+
           (+
            (+
             (+
              (*
               (+
                (* (* (* 2.0 x1) t_3) (- t_3 3.0))
                (* (* x1 x1) (- (* 4.0 t_3) 6.0)))
               t_2)
              (* t_0 t_3))
             (* (* x1 x1) x1))
            x1)
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))))
        (t_5 (* (* (* x2 x2) 8.0) x1)))
   (if (<= t_4 -1e+213)
     t_5
     (if (<= t_4 -1e+38)
       (* -6.0 x2)
       (if (<= t_4 1e-57)
         t_1
         (if (<= t_4 2e+216) (* -6.0 x2) (if (<= t_4 INFINITY) t_5 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = ((9.0 * x1) - 1.0) * x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_2) + (t_0 * t_3)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double t_5 = ((x2 * x2) * 8.0) * x1;
	double tmp;
	if (t_4 <= -1e+213) {
		tmp = t_5;
	} else if (t_4 <= -1e+38) {
		tmp = -6.0 * x2;
	} else if (t_4 <= 1e-57) {
		tmp = t_1;
	} else if (t_4 <= 2e+216) {
		tmp = -6.0 * x2;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = ((9.0 * x1) - 1.0) * x1;
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_2) + (t_0 * t_3)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	double t_5 = ((x2 * x2) * 8.0) * x1;
	double tmp;
	if (t_4 <= -1e+213) {
		tmp = t_5;
	} else if (t_4 <= -1e+38) {
		tmp = -6.0 * x2;
	} else if (t_4 <= 1e-57) {
		tmp = t_1;
	} else if (t_4 <= 2e+216) {
		tmp = -6.0 * x2;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (3.0 * x1) * x1
	t_1 = ((9.0 * x1) - 1.0) * x1
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_4 = x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_2) + (t_0 * t_3)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)))
	t_5 = ((x2 * x2) * 8.0) * x1
	tmp = 0
	if t_4 <= -1e+213:
		tmp = t_5
	elif t_4 <= -1e+38:
		tmp = -6.0 * x2
	elif t_4 <= 1e-57:
		tmp = t_1
	elif t_4 <= 2e+216:
		tmp = -6.0 * x2
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(Float64(9.0 * x1) - 1.0) * x1)
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0))) * t_2) + Float64(t_0 * t_3)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))))
	t_5 = Float64(Float64(Float64(x2 * x2) * 8.0) * x1)
	tmp = 0.0
	if (t_4 <= -1e+213)
		tmp = t_5;
	elseif (t_4 <= -1e+38)
		tmp = Float64(-6.0 * x2);
	elseif (t_4 <= 1e-57)
		tmp = t_1;
	elseif (t_4 <= 2e+216)
		tmp = Float64(-6.0 * x2);
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (3.0 * x1) * x1;
	t_1 = ((9.0 * x1) - 1.0) * x1;
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_4 = x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_2) + (t_0 * t_3)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)));
	t_5 = ((x2 * x2) * 8.0) * x1;
	tmp = 0.0;
	if (t_4 <= -1e+213)
		tmp = t_5;
	elseif (t_4 <= -1e+38)
		tmp = -6.0 * x2;
	elseif (t_4 <= 1e-57)
		tmp = t_1;
	elseif (t_4 <= 2e+216)
		tmp = -6.0 * x2;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(t$95$0 * t$95$3), $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$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision]}, If[LessEqual[t$95$4, -1e+213], t$95$5, If[LessEqual[t$95$4, -1e+38], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[t$95$4, 1e-57], t$95$1, If[LessEqual[t$95$4, 2e+216], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 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)))))) < -9.99999999999999984e212 or 2e216 < (+.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 100.0%

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

   3. Taylor expanded in x2 around inf

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

   5. Applied rewrites 50.8%

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

   6. Taylor expanded in x1 around 0

      \[\leadsto 8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.1%

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

   if -9.99999999999999984e212 < (+.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)))))) < -9.99999999999999977e37 or 9.99999999999999955e-58 < (+.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)))))) < 2e216

   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

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

   5. Applied rewrites 59.0%

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

   if -9.99999999999999977e37 < (+.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)))))) < 9.99999999999999955e-58 or +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 39.6%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 78.7%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 81.7%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 77.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 69.4%

       \[\leadsto \left(9 \cdot x1 - 1\right) \cdot \color{blue}{x1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right)\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+213}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+221} \lor \neg \left(t\_3 \leq \infty\right):\\ \;\;\;\;\mathsf{fma}\left(9 \cdot x1 - 1, x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \end{array} \end{array} \]

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))
        (t_3
         (+
          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))))))
   (if (<= t_3 -1e+213)
     (* (* (* x2 x2) 8.0) x1)
     (if (or (<= t_3 5e+221) (not (<= t_3 INFINITY)))
       (fma (- (* 9.0 x1) 1.0) x1 (* -6.0 x2))
       (+ x1 (* (* (* x2 x2) x1) 8.0))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double tmp;
	if (t_3 <= -1e+213) {
		tmp = ((x2 * x2) * 8.0) * x1;
	} else if ((t_3 <= 5e+221) || !(t_3 <= ((double) INFINITY))) {
		tmp = fma(((9.0 * x1) - 1.0), x1, (-6.0 * x2));
	} else {
		tmp = x1 + (((x2 * x2) * x1) * 8.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = 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))))
	tmp = 0.0
	if (t_3 <= -1e+213)
		tmp = Float64(Float64(Float64(x2 * x2) * 8.0) * x1);
	elseif ((t_3 <= 5e+221) || !(t_3 <= Inf))
		tmp = fma(Float64(Float64(9.0 * x1) - 1.0), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * x2) * x1) * 8.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = 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]}, If[LessEqual[t$95$3, -1e+213], N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision], If[Or[LessEqual[t$95$3, 5e+221], N[Not[LessEqual[t$95$3, Infinity]], $MachinePrecision]], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 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)))))) < -9.99999999999999984e212

   1. Initial program 100.0%

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

   3. Taylor expanded in x2 around inf

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in x1 around 0

      \[\leadsto 8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 80.4%

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

   if -9.99999999999999984e212 < (+.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)))))) < 5.0000000000000002e221 or +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 61.4%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 72.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 74.2%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 71.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 78.4%

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

   if 5.0000000000000002e221 < (+.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 100.0%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 47.2%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 43.9%

      \[\leadsto x1 + \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot \color{blue}{8} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.1%

   \[\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) - 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) \leq -1 \cdot 10^{+213}:\\ \;\;\;\;\left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1\\ \mathbf{elif}\;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) \leq 5 \cdot 10^{+221} \lor \neg \left(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) \leq \infty\right):\\ \;\;\;\;\mathsf{fma}\left(9 \cdot x1 - 1, x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* x1 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* (* 3.0 x1) x1))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_4 (* t_2 t_3))
        (t_5 (* (* (* 2.0 x1) t_3) (- t_3 3.0)))
        (t_6 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1))))
   (if (<=
        (+
         x1
         (+
          (+
           (+ (+ (* (+ t_5 (* (* x1 x1) (- (* 4.0 t_3) 6.0))) t_1) t_4) t_0)
           x1)
          t_6))
        INFINITY)
     (+ x1 (+ (+ (+ (+ (* (+ t_5 (* (* x1 x1) 6.0)) t_1) t_4) t_0) x1) t_6))
     (*
      (fma
       (/ (fma (/ (fma (fma 2.0 x2 -3.0) 4.0 9.0) x1) -1.0 3.0) x1)
       -1.0
       6.0)
      (* (* x1 x1) (* 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;
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_4 = t_2 * t_3;
	double t_5 = ((2.0 * x1) * t_3) * (t_3 - 3.0);
	double t_6 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1);
	double tmp;
	if ((x1 + ((((((t_5 + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_1) + t_4) + t_0) + x1) + t_6)) <= ((double) INFINITY)) {
		tmp = x1 + ((((((t_5 + ((x1 * x1) * 6.0)) * t_1) + t_4) + t_0) + x1) + t_6);
	} else {
		tmp = fma((fma((fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * ((x1 * x1) * (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 * x1) * x1)
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	t_4 = Float64(t_2 * t_3)
	t_5 = Float64(Float64(Float64(2.0 * x1) * t_3) * Float64(t_3 - 3.0))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0))) * t_1) + t_4) + t_0) + x1) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(t_5 + Float64(Float64(x1 * x1) * 6.0)) * t_1) + t_4) + t_0) + x1) + t_6));
	else
		tmp = Float64(fma(Float64(fma(Float64(fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * Float64(Float64(x1 * x1) * Float64(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 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(N[(N[(N[(N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 3.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 6.0), $MachinePrecision] * N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $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 99.5%

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

   3. Taylor expanded in x1 around inf

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

   5. Applied rewrites 95.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 98.6%

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

   7. Applied rewrites 98.6%

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

Alternative 6: 99.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \mathsf{fma}\left(x2, 2, t\_0\right) - x1\\ t_2 := \frac{t\_1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_3 := x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\left(t\_2 - 3\right) \cdot t\_2, 2 \cdot x1, \left(\frac{4 \cdot t\_1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right) \cdot \left(x1 \cdot x1\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_2 \cdot t\_0\right) + \mathsf{fma}\left(3, 3, x1\right)\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;\left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{elif}\;x1 \leq -0.004:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 0.0095:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (- (fma x2 2.0 t_0) x1))
        (t_2 (/ t_1 (fma x1 x1 1.0)))
        (t_3
         (+
          x1
          (fma
           (* x1 x1)
           x1
           (+
            (fma
             (fma
              (* (- t_2 3.0) t_2)
              (* 2.0 x1)
              (* (- (/ (* 4.0 t_1) (fma x1 x1 1.0)) 6.0) (* x1 x1)))
             (fma x1 x1 1.0)
             (* t_2 t_0))
            (fma 3.0 3.0 x1))))))
   (if (<= x1 -1e+154)
     (* (- (* 9.0 x1) 1.0) x1)
     (if (<= x1 -0.004)
       t_3
       (if (<= x1 0.0095)
         (+
          x1
          (fma
           x2
           -6.0
           (fma
            (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
            x2
            (* (fma 9.0 x1 -2.0) x1))))
         (if (<= x1 5e+74)
           t_3
           (*
            (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0)
            (* x1 x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = fma(x2, 2.0, t_0) - x1;
	double t_2 = t_1 / fma(x1, x1, 1.0);
	double t_3 = x1 + fma((x1 * x1), x1, (fma(fma(((t_2 - 3.0) * t_2), (2.0 * x1), ((((4.0 * t_1) / fma(x1, x1, 1.0)) - 6.0) * (x1 * x1))), fma(x1, x1, 1.0), (t_2 * t_0)) + fma(3.0, 3.0, x1)));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = ((9.0 * x1) - 1.0) * x1;
	} else if (x1 <= -0.004) {
		tmp = t_3;
	} else if (x1 <= 0.0095) {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	} else if (x1 <= 5e+74) {
		tmp = t_3;
	} else {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(fma(x2, 2.0, t_0) - x1)
	t_2 = Float64(t_1 / fma(x1, x1, 1.0))
	t_3 = Float64(x1 + fma(Float64(x1 * x1), x1, Float64(fma(fma(Float64(Float64(t_2 - 3.0) * t_2), Float64(2.0 * x1), Float64(Float64(Float64(Float64(4.0 * t_1) / fma(x1, x1, 1.0)) - 6.0) * Float64(x1 * x1))), fma(x1, x1, 1.0), Float64(t_2 * t_0)) + fma(3.0, 3.0, x1))))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = Float64(Float64(Float64(9.0 * x1) - 1.0) * x1);
	elseif (x1 <= -0.004)
		tmp = t_3;
	elseif (x1 <= 0.0095)
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	elseif (x1 <= 5e+74)
		tmp = t_3;
	else
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(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[(x2 * 2.0 + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(N[(N[(N[(N[(t$95$2 - 3.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(2.0 * x1), $MachinePrecision] + N[(N[(N[(N[(4.0 * t$95$1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$2 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * 3.0 + x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1), $MachinePrecision], If[LessEqual[x1, -0.004], t$95$3, If[LessEqual[x1, 0.0095], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+74], t$95$3, N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000004e154

   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

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

   5. Applied rewrites 83.3%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.3%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 76.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 100.0%

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

   if -1.00000000000000004e154 < x1 < -0.0040000000000000001 or 0.00949999999999999976 < x1 < 4.99999999999999963e74

   1. Initial program 67.7%

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 96.8%

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

   if -0.0040000000000000001 < x1 < 0.00949999999999999976

   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

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

   5. Applied rewrites 88.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 88.5%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 99.7%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]

   if 4.99999999999999963e74 < x1

   1. Initial program 44.6%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 10.7%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 100.0%

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

Alternative 7: 99.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \mathsf{fma}\left(x2, 2, t\_0\right) - x1\\ t_2 := \frac{t\_1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_3 := \mathsf{fma}\left(\mathsf{fma}\left(\left(t\_2 - 3\right) \cdot t\_2, 2 \cdot x1, \left(\frac{4 \cdot t\_1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right) \cdot \left(x1 \cdot x1\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_2 \cdot t\_0\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;\left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{elif}\;x1 \leq -0.012:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1 \cdot x1, x1, t\_3 + -6 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 0.0095:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+74}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1 \cdot x1, x1, t\_3 + x1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (- (fma x2 2.0 t_0) x1))
        (t_2 (/ t_1 (fma x1 x1 1.0)))
        (t_3
         (fma
          (fma
           (* (- t_2 3.0) t_2)
           (* 2.0 x1)
           (* (- (/ (* 4.0 t_1) (fma x1 x1 1.0)) 6.0) (* x1 x1)))
          (fma x1 x1 1.0)
          (* t_2 t_0))))
   (if (<= x1 -1e+154)
     (* (- (* 9.0 x1) 1.0) x1)
     (if (<= x1 -0.012)
       (+ x1 (fma (* x1 x1) x1 (+ t_3 (* -6.0 x2))))
       (if (<= x1 0.0095)
         (+
          x1
          (fma
           x2
           -6.0
           (fma
            (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
            x2
            (* (fma 9.0 x1 -2.0) x1))))
         (if (<= x1 5e+74)
           (+ x1 (fma (* x1 x1) x1 (+ t_3 x1)))
           (*
            (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0)
            (* x1 x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = fma(x2, 2.0, t_0) - x1;
	double t_2 = t_1 / fma(x1, x1, 1.0);
	double t_3 = fma(fma(((t_2 - 3.0) * t_2), (2.0 * x1), ((((4.0 * t_1) / fma(x1, x1, 1.0)) - 6.0) * (x1 * x1))), fma(x1, x1, 1.0), (t_2 * t_0));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = ((9.0 * x1) - 1.0) * x1;
	} else if (x1 <= -0.012) {
		tmp = x1 + fma((x1 * x1), x1, (t_3 + (-6.0 * x2)));
	} else if (x1 <= 0.0095) {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	} else if (x1 <= 5e+74) {
		tmp = x1 + fma((x1 * x1), x1, (t_3 + x1));
	} else {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(fma(x2, 2.0, t_0) - x1)
	t_2 = Float64(t_1 / fma(x1, x1, 1.0))
	t_3 = fma(fma(Float64(Float64(t_2 - 3.0) * t_2), Float64(2.0 * x1), Float64(Float64(Float64(Float64(4.0 * t_1) / fma(x1, x1, 1.0)) - 6.0) * Float64(x1 * x1))), fma(x1, x1, 1.0), Float64(t_2 * t_0))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = Float64(Float64(Float64(9.0 * x1) - 1.0) * x1);
	elseif (x1 <= -0.012)
		tmp = Float64(x1 + fma(Float64(x1 * x1), x1, Float64(t_3 + Float64(-6.0 * x2))));
	elseif (x1 <= 0.0095)
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	elseif (x1 <= 5e+74)
		tmp = Float64(x1 + fma(Float64(x1 * x1), x1, Float64(t_3 + x1)));
	else
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(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[(x2 * 2.0 + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(t$95$2 - 3.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(2.0 * x1), $MachinePrecision] + N[(N[(N[(N[(4.0 * t$95$1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$2 * t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1), $MachinePrecision], If[LessEqual[x1, -0.012], N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(t$95$3 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0095], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+74], N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(t$95$3 + x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.00000000000000004e154

   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

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

   5. Applied rewrites 83.3%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.3%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 76.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 100.0%

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

   if -1.00000000000000004e154 < x1 < -0.012

   1. Initial program 51.4%

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

   4. Applied rewrites 96.8%

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

   5. Taylor expanded in x1 around 0

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

   7. Applied rewrites 95.1%

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

   if -0.012 < x1 < 0.00949999999999999976

   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

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

   5. Applied rewrites 88.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 88.5%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 99.7%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]

   if 0.00949999999999999976 < x1 < 4.99999999999999963e74

   1. Initial program 99.3%

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 98.3%

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

   if 4.99999999999999963e74 < x1

   1. Initial program 44.6%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 10.7%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 100.0%

       \[\leadsto \left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \color{blue}{\left(x1 \cdot x1\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 99.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := \mathsf{fma}\left(x2, 2, t\_0\right) - x1\\ t_2 := \frac{t\_1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_3 := x1 + \mathsf{fma}\left(x1 \cdot x1, x1, \mathsf{fma}\left(\mathsf{fma}\left(\left(t\_2 - 3\right) \cdot t\_2, 2 \cdot x1, \left(\frac{4 \cdot t\_1}{\mathsf{fma}\left(x1, x1, 1\right)} - 6\right) \cdot \left(x1 \cdot x1\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_2 \cdot t\_0\right) + x1\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;\left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{elif}\;x1 \leq -0.012:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x1 \leq 0.0095:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (- (fma x2 2.0 t_0) x1))
        (t_2 (/ t_1 (fma x1 x1 1.0)))
        (t_3
         (+
          x1
          (fma
           (* x1 x1)
           x1
           (+
            (fma
             (fma
              (* (- t_2 3.0) t_2)
              (* 2.0 x1)
              (* (- (/ (* 4.0 t_1) (fma x1 x1 1.0)) 6.0) (* x1 x1)))
             (fma x1 x1 1.0)
             (* t_2 t_0))
            x1)))))
   (if (<= x1 -1e+154)
     (* (- (* 9.0 x1) 1.0) x1)
     (if (<= x1 -0.012)
       t_3
       (if (<= x1 0.0095)
         (+
          x1
          (fma
           x2
           -6.0
           (fma
            (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
            x2
            (* (fma 9.0 x1 -2.0) x1))))
         (if (<= x1 5e+74)
           t_3
           (*
            (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0)
            (* x1 x1))))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = fma(x2, 2.0, t_0) - x1;
	double t_2 = t_1 / fma(x1, x1, 1.0);
	double t_3 = x1 + fma((x1 * x1), x1, (fma(fma(((t_2 - 3.0) * t_2), (2.0 * x1), ((((4.0 * t_1) / fma(x1, x1, 1.0)) - 6.0) * (x1 * x1))), fma(x1, x1, 1.0), (t_2 * t_0)) + x1));
	double tmp;
	if (x1 <= -1e+154) {
		tmp = ((9.0 * x1) - 1.0) * x1;
	} else if (x1 <= -0.012) {
		tmp = t_3;
	} else if (x1 <= 0.0095) {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	} else if (x1 <= 5e+74) {
		tmp = t_3;
	} else {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(fma(x2, 2.0, t_0) - x1)
	t_2 = Float64(t_1 / fma(x1, x1, 1.0))
	t_3 = Float64(x1 + fma(Float64(x1 * x1), x1, Float64(fma(fma(Float64(Float64(t_2 - 3.0) * t_2), Float64(2.0 * x1), Float64(Float64(Float64(Float64(4.0 * t_1) / fma(x1, x1, 1.0)) - 6.0) * Float64(x1 * x1))), fma(x1, x1, 1.0), Float64(t_2 * t_0)) + x1)))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = Float64(Float64(Float64(9.0 * x1) - 1.0) * x1);
	elseif (x1 <= -0.012)
		tmp = t_3;
	elseif (x1 <= 0.0095)
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	elseif (x1 <= 5e+74)
		tmp = t_3;
	else
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(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[(x2 * 2.0 + t$95$0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(N[(N[(N[(N[(t$95$2 - 3.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(2.0 * x1), $MachinePrecision] + N[(N[(N[(N[(4.0 * t$95$1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$2 * t$95$0), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1), $MachinePrecision], If[LessEqual[x1, -0.012], t$95$3, If[LessEqual[x1, 0.0095], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+74], t$95$3, N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.00000000000000004e154

   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

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

   5. Applied rewrites 83.3%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.3%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 76.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 100.0%

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

   if -1.00000000000000004e154 < x1 < -0.012 or 0.00949999999999999976 < x1 < 4.99999999999999963e74

   1. Initial program 67.7%

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 96.2%

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

   if -0.012 < x1 < 0.00949999999999999976

   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

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

   5. Applied rewrites 88.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 88.5%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 99.7%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]

   if 4.99999999999999963e74 < x1

   1. Initial program 44.6%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 10.7%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 100.0%

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

Alternative 9: 95.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 3, 1\right), -2, 1\right)}{-x1}\right) - -9}{x1}, -1, 3\right)}{x1}, -1, 6\right) \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}, -1, 3\right)}{x1}, -1, 6\right) \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5)
   (*
    (fma
     (/
      (fma
       (/
        (-
         (fma
          (fma 2.0 x2 -3.0)
          4.0
          (/ (fma (fma (fma 2.0 x2 -3.0) 3.0 1.0) -2.0 1.0) (- x1)))
         -9.0)
        x1)
       -1.0
       3.0)
      x1)
     -1.0
     6.0)
    (pow x1 4.0))
   (if (<= x1 9.2e+22)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
        x2
        (* (fma 9.0 x1 -2.0) x1))))
     (*
      (fma
       (/ (fma (/ (fma (fma 2.0 x2 -3.0) 4.0 9.0) x1) -1.0 3.0) x1)
       -1.0
       6.0)
      (pow x1 4.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5) {
		tmp = fma((fma(((fma(fma(2.0, x2, -3.0), 4.0, (fma(fma(fma(2.0, x2, -3.0), 3.0, 1.0), -2.0, 1.0) / -x1)) - -9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * pow(x1, 4.0);
	} else if (x1 <= 9.2e+22) {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	} else {
		tmp = fma((fma((fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * pow(x1, 4.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5)
		tmp = Float64(fma(Float64(fma(Float64(Float64(fma(fma(2.0, x2, -3.0), 4.0, Float64(fma(fma(fma(2.0, x2, -3.0), 3.0, 1.0), -2.0, 1.0) / Float64(-x1))) - -9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * (x1 ^ 4.0));
	elseif (x1 <= 9.2e+22)
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	else
		tmp = Float64(fma(Float64(fma(Float64(fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * (x1 ^ 4.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5], N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 3.0 + 1.0), $MachinePrecision] * -2.0 + 1.0), $MachinePrecision] / (-x1)), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 3.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 6.0), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.2e+22], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 3.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 6.0), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5

   1. Initial program 26.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 90.6%

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

   if -5.5 < x1 < 9.2000000000000008e22

   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

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

   5. Applied rewrites 87.5%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.6%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.3%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]

   if 9.2000000000000008e22 < x1

   1. Initial program 55.7%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 93.5%

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

Alternative 10: 95.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}, -1, 3\right)}{x1}, -1, 6\right) \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5)
   (* (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0) (* x1 x1))
   (if (<= x1 9.2e+22)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
        x2
        (* (fma 9.0 x1 -2.0) x1))))
     (*
      (fma
       (/ (fma (/ (fma (fma 2.0 x2 -3.0) 4.0 9.0) x1) -1.0 3.0) x1)
       -1.0
       6.0)
      (pow x1 4.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5) {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	} else if (x1 <= 9.2e+22) {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	} else {
		tmp = fma((fma((fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * pow(x1, 4.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5)
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(x1 * x1));
	elseif (x1 <= 9.2e+22)
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	else
		tmp = Float64(fma(Float64(fma(Float64(fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * (x1 ^ 4.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5], N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.2e+22], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 3.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 6.0), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5

   1. Initial program 26.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 90.4%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 68.7%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 90.4%

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

   if -5.5 < x1 < 9.2000000000000008e22

   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

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

   5. Applied rewrites 87.5%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.6%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.3%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]

   if 9.2000000000000008e22 < x1

   1. Initial program 55.7%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 93.5%

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

Alternative 11: 95.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-8 \cdot \frac{x2}{x1 \cdot x1}, -1, 6\right) \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5)
   (* (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0) (* x1 x1))
   (if (<= x1 9.2e+22)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
        x2
        (* (fma 9.0 x1 -2.0) x1))))
     (* (fma (* -8.0 (/ x2 (* x1 x1))) -1.0 6.0) (pow x1 4.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5) {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	} else if (x1 <= 9.2e+22) {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	} else {
		tmp = fma((-8.0 * (x2 / (x1 * x1))), -1.0, 6.0) * pow(x1, 4.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5)
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(x1 * x1));
	elseif (x1 <= 9.2e+22)
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	else
		tmp = Float64(fma(Float64(-8.0 * Float64(x2 / Float64(x1 * x1))), -1.0, 6.0) * (x1 ^ 4.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5], N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.2e+22], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-8.0 * N[(x2 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -1.0 + 6.0), $MachinePrecision] * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5

   1. Initial program 26.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 90.4%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 68.7%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 90.4%

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

   if -5.5 < x1 < 9.2000000000000008e22

   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

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

   5. Applied rewrites 87.5%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.6%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.3%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]

   if 9.2000000000000008e22 < x1

   1. Initial program 55.7%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 93.5%

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

   6. Taylor expanded in x2 around inf

      \[\leadsto \mathsf{fma}\left(-8 \cdot \frac{x2}{{x1}^{2}}, -1, 6\right) \cdot {x1}^{4} \]
   7. Step-by-step derivation

   8. Applied rewrites 93.5%

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

Alternative 12: 95.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5:\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq 9.2 \cdot 10^{+22}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right), 4, 9\right)}{x1}, -1, 3\right)}{x1}, -1, 6\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.5)
   (* (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0) (* x1 x1))
   (if (<= x1 9.2e+22)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
        x2
        (* (fma 9.0 x1 -2.0) x1))))
     (*
      (fma
       (/ (fma (/ (fma (fma 2.0 x2 -3.0) 4.0 9.0) x1) -1.0 3.0) x1)
       -1.0
       6.0)
      (* (* x1 x1) (* x1 x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.5) {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	} else if (x1 <= 9.2e+22) {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	} else {
		tmp = fma((fma((fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * ((x1 * x1) * (x1 * x1));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.5)
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(x1 * x1));
	elseif (x1 <= 9.2e+22)
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	else
		tmp = Float64(fma(Float64(fma(Float64(fma(fma(2.0, x2, -3.0), 4.0, 9.0) / x1), -1.0, 3.0) / x1), -1.0, 6.0) * Float64(Float64(x1 * x1) * Float64(x1 * x1)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.5], N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 9.2e+22], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * 4.0 + 9.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 3.0), $MachinePrecision] / x1), $MachinePrecision] * -1.0 + 6.0), $MachinePrecision] * N[(N[(x1 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.5

   1. Initial program 26.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 90.4%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 68.7%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 90.4%

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

   if -5.5 < x1 < 9.2000000000000008e22

   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

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

   5. Applied rewrites 87.5%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.6%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.3%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]

   if 9.2000000000000008e22 < x1

   1. Initial program 55.7%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 93.5%

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

   7. Applied rewrites 93.5%

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

Alternative 13: 95.6% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \lor \neg \left(x1 \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -5.5) (not (<= x1 9.2e+22)))
   (* (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0) (* x1 x1))
   (+
    x1
    (fma
     x2
     -6.0
     (fma
      (fma (fma 12.0 x1 -12.0) x1 (* (* x2 x1) 8.0))
      x2
      (* (fma 9.0 x1 -2.0) x1))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.5) || !(x1 <= 9.2e+22)) {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	} else {
		tmp = x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, ((x2 * x1) * 8.0)), x2, (fma(9.0, x1, -2.0) * x1)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -5.5) || !(x1 <= 9.2e+22))
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(x1 * x1));
	else
		tmp = Float64(x1 + fma(x2, -6.0, fma(fma(fma(12.0, x1, -12.0), x1, Float64(Float64(x2 * x1) * 8.0)), x2, Float64(fma(9.0, x1, -2.0) * x1))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -5.5], N[Not[LessEqual[x1, 9.2e+22]], $MachinePrecision]], N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + N[(N[(x2 * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] * x2 + N[(N[(9.0 * x1 + -2.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.5 or 9.2000000000000008e22 < x1

   1. Initial program 40.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 41.3%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 91.9%

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

   if -5.5 < x1 < 9.2000000000000008e22

   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

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

   5. Applied rewrites 87.5%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.6%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around 0

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right) + x1 \cdot \left(12 \cdot x1 - 12\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.3%

       \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \lor \neg \left(x1 \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, \left(x2 \cdot x1\right) \cdot 8\right), x2, \mathsf{fma}\left(9, x1, -2\right) \cdot x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 95.5% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \lor \neg \left(x1 \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9 \cdot x1 - 1, x1, \mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right) \cdot x2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -5.5) (not (<= x1 9.2e+22)))
   (* (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0) (* x1 x1))
   (fma
    (- (* 9.0 x1) 1.0)
    x1
    (* (fma (* x2 x1) 8.0 (fma (fma 12.0 x1 -12.0) x1 -6.0)) x2))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.5) || !(x1 <= 9.2e+22)) {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	} else {
		tmp = fma(((9.0 * x1) - 1.0), x1, (fma((x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)) * x2));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -5.5) || !(x1 <= 9.2e+22))
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(x1 * x1));
	else
		tmp = fma(Float64(Float64(9.0 * x1) - 1.0), x1, Float64(fma(Float64(x2 * x1), 8.0, fma(fma(12.0, x1, -12.0), x1, -6.0)) * x2));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -5.5], N[Not[LessEqual[x1, 9.2e+22]], $MachinePrecision]], N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1 + N[(N[(N[(x2 * x1), $MachinePrecision] * 8.0 + N[(N[(12.0 * x1 + -12.0), $MachinePrecision] * x1 + -6.0), $MachinePrecision]), $MachinePrecision] * x2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.5 or 9.2000000000000008e22 < x1

   1. Initial program 40.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 41.3%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 91.9%

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

   if -5.5 < x1 < 9.2000000000000008e22

   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

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

   5. Applied rewrites 87.5%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 87.4%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 87.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 98.2%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \lor \neg \left(x1 \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9 \cdot x1 - 1, x1, \mathsf{fma}\left(x2 \cdot x1, 8, \mathsf{fma}\left(\mathsf{fma}\left(12, x1, -12\right), x1, -6\right)\right) \cdot x2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 89.8% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \lor \neg \left(x1 \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2\right) \cdot 4 - 1, x1, -6 \cdot x2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -5.5) (not (<= x1 9.2e+22)))
   (* (- (fma (fma 6.0 x1 -3.0) x1 (* (fma x2 2.0 -3.0) 4.0)) -9.0) (* x1 x1))
   (fma (- (* (* (fma 2.0 x2 -3.0) x2) 4.0) 1.0) x1 (* -6.0 x2))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -5.5) || !(x1 <= 9.2e+22)) {
		tmp = (fma(fma(6.0, x1, -3.0), x1, (fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * (x1 * x1);
	} else {
		tmp = fma((((fma(2.0, x2, -3.0) * x2) * 4.0) - 1.0), x1, (-6.0 * x2));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -5.5) || !(x1 <= 9.2e+22))
		tmp = Float64(Float64(fma(fma(6.0, x1, -3.0), x1, Float64(fma(x2, 2.0, -3.0) * 4.0)) - -9.0) * Float64(x1 * x1));
	else
		tmp = fma(Float64(Float64(Float64(fma(2.0, x2, -3.0) * x2) * 4.0) - 1.0), x1, Float64(-6.0 * x2));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -5.5], N[Not[LessEqual[x1, 9.2e+22]], $MachinePrecision]], N[(N[(N[(N[(6.0 * x1 + -3.0), $MachinePrecision] * x1 + N[(N[(x2 * 2.0 + -3.0), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - -9.0), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * x2), $MachinePrecision] * 4.0), $MachinePrecision] - 1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.5 or 9.2000000000000008e22 < x1

   1. Initial program 40.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 41.3%

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

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 91.9%

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

   if -5.5 < x1 < 9.2000000000000008e22

   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

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

   5. Applied rewrites 86.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \lor \neg \left(x1 \leq 9.2 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\mathsf{fma}\left(6, x1, -3\right), x1, \mathsf{fma}\left(x2, 2, -3\right) \cdot 4\right) - -9\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2\right) \cdot 4 - 1, x1, -6 \cdot x2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.4% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+78}:\\ \;\;\;\;\left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(9 \cdot x1 - 1, x1, -6 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \left(\left(x2 \cdot x2\right) \cdot 8\right) \cdot x1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1 \cdot x1, x1, -6 \cdot x2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.6e+78)
   (* (* -3.0 x1) (* x1 x1))
   (if (<= x1 3.5e-9)
     (fma (- (* 9.0 x1) 1.0) x1 (* -6.0 x2))
     (if (<= x1 3.6e+76)
       (+ x1 (fma x2 -6.0 (* (* (* x2 x2) 8.0) x1)))
       (+ x1 (fma (* x1 x1) x1 (* -6.0 x2)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.6e+78) {
		tmp = (-3.0 * x1) * (x1 * x1);
	} else if (x1 <= 3.5e-9) {
		tmp = fma(((9.0 * x1) - 1.0), x1, (-6.0 * x2));
	} else if (x1 <= 3.6e+76) {
		tmp = x1 + fma(x2, -6.0, (((x2 * x2) * 8.0) * x1));
	} else {
		tmp = x1 + fma((x1 * x1), x1, (-6.0 * x2));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.6e+78)
		tmp = Float64(Float64(-3.0 * x1) * Float64(x1 * x1));
	elseif (x1 <= 3.5e-9)
		tmp = fma(Float64(Float64(9.0 * x1) - 1.0), x1, Float64(-6.0 * x2));
	elseif (x1 <= 3.6e+76)
		tmp = Float64(x1 + fma(x2, -6.0, Float64(Float64(Float64(x2 * x2) * 8.0) * x1)));
	else
		tmp = Float64(x1 + fma(Float64(x1 * x1), x1, Float64(-6.0 * x2)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.6e+78], N[(N[(-3.0 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.5e-9], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.6e+76], N[(x1 + N[(x2 * -6.0 + N[(N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.6000000000000002e78

   1. Initial program 11.8%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 81.5%

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

   9. Taylor expanded in x1 around inf

      \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 89.3%

       \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]

   if -5.6000000000000002e78 < x1 < 3.4999999999999999e-9

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 81.2%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 81.1%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 82.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 67.9%

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

   if 3.4999999999999999e-9 < x1 < 3.6000000000000003e76

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 45.1%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 45.1%

      \[\leadsto x1 + \mathsf{fma}\left(x2, \color{blue}{-6}, \mathsf{fma}\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2, 4, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, 14 \cdot x2\right) - 6\right), x1, -2\right)\right) \cdot x1\right) \]

   8. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(x2, -6, 8 \cdot \left(x1 \cdot {x2}^{2}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.8%

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

   if 3.6000000000000003e76 < x1

   1. Initial program 44.6%

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

   4. Applied rewrites 48.9%

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

   5. Taylor expanded in x1 around 0

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

   7. Applied rewrites 78.1%

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

Alternative 17: 80.3% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.6 \cdot 10^{+80}:\\ \;\;\;\;\left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(\left(\mathsf{fma}\left(2, x2, -3\right) \cdot x2\right) \cdot 4 - 1, x1, -6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1 \cdot x1, x1, -6 \cdot x2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.6e+80)
   (* (* -3.0 x1) (* x1 x1))
   (if (<= x1 3.6e+76)
     (fma (- (* (* (fma 2.0 x2 -3.0) x2) 4.0) 1.0) x1 (* -6.0 x2))
     (+ x1 (fma (* x1 x1) x1 (* -6.0 x2))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.6e+80) {
		tmp = (-3.0 * x1) * (x1 * x1);
	} else if (x1 <= 3.6e+76) {
		tmp = fma((((fma(2.0, x2, -3.0) * x2) * 4.0) - 1.0), x1, (-6.0 * x2));
	} else {
		tmp = x1 + fma((x1 * x1), x1, (-6.0 * x2));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.6e+80)
		tmp = Float64(Float64(-3.0 * x1) * Float64(x1 * x1));
	elseif (x1 <= 3.6e+76)
		tmp = fma(Float64(Float64(Float64(fma(2.0, x2, -3.0) * x2) * 4.0) - 1.0), x1, Float64(-6.0 * x2));
	else
		tmp = Float64(x1 + fma(Float64(x1 * x1), x1, Float64(-6.0 * x2)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.6e+80], N[(N[(-3.0 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.6e+76], N[(N[(N[(N[(N[(2.0 * x2 + -3.0), $MachinePrecision] * x2), $MachinePrecision] * 4.0), $MachinePrecision] - 1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.59999999999999995e80

   1. Initial program 11.8%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 81.5%

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

   9. Taylor expanded in x1 around inf

      \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 89.3%

       \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]

   if -3.59999999999999995e80 < x1 < 3.6000000000000003e76

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 78.3%

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

   if 3.6000000000000003e76 < x1

   1. Initial program 44.6%

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

   4. Applied rewrites 48.9%

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

   5. Taylor expanded in x1 around 0

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

   7. Applied rewrites 78.1%

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

Alternative 18: 73.4% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+78}:\\ \;\;\;\;\left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(9 \cdot x1 - 1, x1, -6 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;x1 + \left(\left(x2 \cdot x2\right) \cdot x1\right) \cdot 8\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x1 \cdot x1, x1, -6 \cdot x2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -5.6e+78)
   (* (* -3.0 x1) (* x1 x1))
   (if (<= x1 3.5e-9)
     (fma (- (* 9.0 x1) 1.0) x1 (* -6.0 x2))
     (if (<= x1 3.6e+76)
       (+ x1 (* (* (* x2 x2) x1) 8.0))
       (+ x1 (fma (* x1 x1) x1 (* -6.0 x2)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -5.6e+78) {
		tmp = (-3.0 * x1) * (x1 * x1);
	} else if (x1 <= 3.5e-9) {
		tmp = fma(((9.0 * x1) - 1.0), x1, (-6.0 * x2));
	} else if (x1 <= 3.6e+76) {
		tmp = x1 + (((x2 * x2) * x1) * 8.0);
	} else {
		tmp = x1 + fma((x1 * x1), x1, (-6.0 * x2));
	}
	return tmp;
}

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -5.6e+78)
		tmp = Float64(Float64(-3.0 * x1) * Float64(x1 * x1));
	elseif (x1 <= 3.5e-9)
		tmp = fma(Float64(Float64(9.0 * x1) - 1.0), x1, Float64(-6.0 * x2));
	elseif (x1 <= 3.6e+76)
		tmp = Float64(x1 + Float64(Float64(Float64(x2 * x2) * x1) * 8.0));
	else
		tmp = Float64(x1 + fma(Float64(x1 * x1), x1, Float64(-6.0 * x2)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -5.6e+78], N[(N[(-3.0 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.5e-9], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.6e+76], N[(x1 + N[(N[(N[(x2 * x2), $MachinePrecision] * x1), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 * x1), $MachinePrecision] * x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.6000000000000002e78

   1. Initial program 11.8%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 81.5%

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

   9. Taylor expanded in x1 around inf

      \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 89.3%

       \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]

   if -5.6000000000000002e78 < x1 < 3.4999999999999999e-9

   1. Initial program 98.7%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 81.2%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 81.1%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 82.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 67.9%

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

   if 3.4999999999999999e-9 < x1 < 3.6000000000000003e76

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 45.1%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

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

   8. Applied rewrites 45.8%

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

   if 3.6000000000000003e76 < x1

   1. Initial program 44.6%

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

   4. Applied rewrites 48.9%

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

   5. Taylor expanded in x1 around 0

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

   7. Applied rewrites 78.1%

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

Alternative 19: 60.1% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.1:\\ \;\;\;\;\left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq -2.35 \cdot 10^{-150} \lor \neg \left(x1 \leq 9.2 \cdot 10^{-72}\right):\\ \;\;\;\;\left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.1)
   (* (* -3.0 x1) (* x1 x1))
   (if (or (<= x1 -2.35e-150) (not (<= x1 9.2e-72)))
     (* (- (* 9.0 x1) 1.0) x1)
     (* -6.0 x2))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.1) {
		tmp = (-3.0 * x1) * (x1 * x1);
	} else if ((x1 <= -2.35e-150) || !(x1 <= 9.2e-72)) {
		tmp = ((9.0 * x1) - 1.0) * x1;
	} else {
		tmp = -6.0 * x2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.1d0)) then
        tmp = ((-3.0d0) * x1) * (x1 * x1)
    else if ((x1 <= (-2.35d-150)) .or. (.not. (x1 <= 9.2d-72))) then
        tmp = ((9.0d0 * x1) - 1.0d0) * x1
    else
        tmp = (-6.0d0) * x2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.1) {
		tmp = (-3.0 * x1) * (x1 * x1);
	} else if ((x1 <= -2.35e-150) || !(x1 <= 9.2e-72)) {
		tmp = ((9.0 * x1) - 1.0) * x1;
	} else {
		tmp = -6.0 * x2;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.1:
		tmp = (-3.0 * x1) * (x1 * x1)
	elif (x1 <= -2.35e-150) or not (x1 <= 9.2e-72):
		tmp = ((9.0 * x1) - 1.0) * x1
	else:
		tmp = -6.0 * x2
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.1)
		tmp = Float64(Float64(-3.0 * x1) * Float64(x1 * x1));
	elseif ((x1 <= -2.35e-150) || !(x1 <= 9.2e-72))
		tmp = Float64(Float64(Float64(9.0 * x1) - 1.0) * x1);
	else
		tmp = Float64(-6.0 * x2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.1)
		tmp = (-3.0 * x1) * (x1 * x1);
	elseif ((x1 <= -2.35e-150) || ~((x1 <= 9.2e-72)))
		tmp = ((9.0 * x1) - 1.0) * x1;
	else
		tmp = -6.0 * x2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.1], N[(N[(-3.0 * x1), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -2.35e-150], N[Not[LessEqual[x1, 9.2e-72]], $MachinePrecision]], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1), $MachinePrecision], N[(-6.0 * x2), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.10000000000000009

   1. Initial program 26.9%

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

   3. Taylor expanded in x1 around -inf

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

   5. Applied rewrites 90.4%

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

   6. Taylor expanded in x1 around 0

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

   8. Applied rewrites 68.7%

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

   9. Taylor expanded in x1 around inf

      \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 73.3%

       \[\leadsto \left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right) \]

   if -3.10000000000000009 < x1 < -2.3499999999999999e-150 or 9.19999999999999978e-72 < x1

   1. Initial program 76.5%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 65.3%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 70.0%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 68.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 43.2%

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

   if -2.3499999999999999e-150 < x1 < 9.19999999999999978e-72

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 64.3%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1:\\ \;\;\;\;\left(-3 \cdot x1\right) \cdot \left(x1 \cdot x1\right)\\ \mathbf{elif}\;x1 \leq -2.35 \cdot 10^{-150} \lor \neg \left(x1 \leq 9.2 \cdot 10^{-72}\right):\\ \;\;\;\;\left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 56.3% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.35 \cdot 10^{-150} \lor \neg \left(x1 \leq 9.2 \cdot 10^{-72}\right):\\ \;\;\;\;\left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.35e-150) (not (<= x1 9.2e-72)))
   (* (- (* 9.0 x1) 1.0) x1)
   (* -6.0 x2)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.35e-150) || !(x1 <= 9.2e-72)) {
		tmp = ((9.0 * x1) - 1.0) * x1;
	} else {
		tmp = -6.0 * x2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.35d-150)) .or. (.not. (x1 <= 9.2d-72))) then
        tmp = ((9.0d0 * x1) - 1.0d0) * x1
    else
        tmp = (-6.0d0) * x2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.35e-150) || !(x1 <= 9.2e-72)) {
		tmp = ((9.0 * x1) - 1.0) * x1;
	} else {
		tmp = -6.0 * x2;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.35e-150) or not (x1 <= 9.2e-72):
		tmp = ((9.0 * x1) - 1.0) * x1
	else:
		tmp = -6.0 * x2
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.35e-150) || !(x1 <= 9.2e-72))
		tmp = Float64(Float64(Float64(9.0 * x1) - 1.0) * x1);
	else
		tmp = Float64(-6.0 * x2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.35e-150) || ~((x1 <= 9.2e-72)))
		tmp = ((9.0 * x1) - 1.0) * x1;
	else
		tmp = -6.0 * x2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.35e-150], N[Not[LessEqual[x1, 9.2e-72]], $MachinePrecision]], N[(N[(N[(9.0 * x1), $MachinePrecision] - 1.0), $MachinePrecision] * x1), $MachinePrecision], N[(-6.0 * x2), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.3499999999999999e-150 or 9.19999999999999978e-72 < x1

   1. Initial program 58.7%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 59.3%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 66.1%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x1 around 0

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

   11. Applied rewrites 60.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, \mathsf{fma}\left(-2, x2, 3\right)\right), 2, \mathsf{fma}\left(\mathsf{fma}\left(x2, 2, 3\right), 3, \mathsf{fma}\left(14, x2, -6\right)\right)\right), x1, \left(\mathsf{fma}\left(x2, 2, -3\right) \cdot x2\right) \cdot 4\right) - 1, x1, -6 \cdot x2\right)} \]

   12. Taylor expanded in x2 around 0

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

   14. Applied rewrites 46.0%

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

   if -2.3499999999999999e-150 < x1 < 9.19999999999999978e-72

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 64.3%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.35 \cdot 10^{-150} \lor \neg \left(x1 \leq 9.2 \cdot 10^{-72}\right):\\ \;\;\;\;\left(9 \cdot x1 - 1\right) \cdot x1\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.1% accurate, 14.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.1 \cdot 10^{-87} \lor \neg \left(x2 \leq 2.5 \cdot 10^{-150}\right):\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;x1 + -2 \cdot x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.1e-87) (not (<= x2 2.5e-150)))
   (* -6.0 x2)
   (+ x1 (* -2.0 x1))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.1e-87) || !(x2 <= 2.5e-150)) {
		tmp = -6.0 * x2;
	} else {
		tmp = x1 + (-2.0 * x1);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-2.1d-87)) .or. (.not. (x2 <= 2.5d-150))) then
        tmp = (-6.0d0) * x2
    else
        tmp = x1 + ((-2.0d0) * x1)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.1e-87) || !(x2 <= 2.5e-150)) {
		tmp = -6.0 * x2;
	} else {
		tmp = x1 + (-2.0 * x1);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.1e-87) or not (x2 <= 2.5e-150):
		tmp = -6.0 * x2
	else:
		tmp = x1 + (-2.0 * x1)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.1e-87) || !(x2 <= 2.5e-150))
		tmp = Float64(-6.0 * x2);
	else
		tmp = Float64(x1 + Float64(-2.0 * x1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2.1e-87) || ~((x2 <= 2.5e-150)))
		tmp = -6.0 * x2;
	else
		tmp = x1 + (-2.0 * x1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.1e-87], N[Not[LessEqual[x2, 2.5e-150]], $MachinePrecision]], N[(-6.0 * x2), $MachinePrecision], N[(x1 + N[(-2.0 * x1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.10000000000000007e-87 or 2.49999999999999995e-150 < x2

   1. Initial program 70.7%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 29.5%

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

   if -2.10000000000000007e-87 < x2 < 2.49999999999999995e-150

   1. Initial program 73.1%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 72.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.8%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(9 \cdot x1 - 2\right)} \]

   11. Applied rewrites 60.5%

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

   12. Taylor expanded in x1 around 0

       \[\leadsto x1 + -2 \cdot x1 \]
   13. Step-by-step derivation

   14. Applied rewrites 35.9%

       \[\leadsto x1 + -2 \cdot x1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.1 \cdot 10^{-87} \lor \neg \left(x2 \leq 2.5 \cdot 10^{-150}\right):\\ \;\;\;\;-6 \cdot x2\\ \mathbf{else}:\\ \;\;\;\;x1 + -2 \cdot x1\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.4% accurate, 14.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.1 \cdot 10^{-87}:\\ \;\;\;\;-6 \cdot x2\\ \mathbf{elif}\;x2 \leq 9 \cdot 10^{-151}:\\ \;\;\;\;x1 + -2 \cdot x1\\ \mathbf{else}:\\ \;\;\;\;x1 + -6 \cdot x2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.1e-87)
   (* -6.0 x2)
   (if (<= x2 9e-151) (+ x1 (* -2.0 x1)) (+ x1 (* -6.0 x2)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.1e-87) {
		tmp = -6.0 * x2;
	} else if (x2 <= 9e-151) {
		tmp = x1 + (-2.0 * x1);
	} else {
		tmp = x1 + (-6.0 * x2);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-2.1d-87)) then
        tmp = (-6.0d0) * x2
    else if (x2 <= 9d-151) then
        tmp = x1 + ((-2.0d0) * x1)
    else
        tmp = x1 + ((-6.0d0) * x2)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.1e-87) {
		tmp = -6.0 * x2;
	} else if (x2 <= 9e-151) {
		tmp = x1 + (-2.0 * x1);
	} else {
		tmp = x1 + (-6.0 * x2);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.1e-87:
		tmp = -6.0 * x2
	elif x2 <= 9e-151:
		tmp = x1 + (-2.0 * x1)
	else:
		tmp = x1 + (-6.0 * x2)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.1e-87)
		tmp = Float64(-6.0 * x2);
	elseif (x2 <= 9e-151)
		tmp = Float64(x1 + Float64(-2.0 * x1));
	else
		tmp = Float64(x1 + Float64(-6.0 * x2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.1e-87)
		tmp = -6.0 * x2;
	elseif (x2 <= 9e-151)
		tmp = x1 + (-2.0 * x1);
	else
		tmp = x1 + (-6.0 * x2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.1e-87], N[(-6.0 * x2), $MachinePrecision], If[LessEqual[x2, 9e-151], N[(x1 + N[(-2.0 * x1), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(-6.0 * x2), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2.10000000000000007e-87

   1. Initial program 71.1%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 31.1%

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

   if -2.10000000000000007e-87 < x2 < 9.0000000000000005e-151

   1. Initial program 73.1%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 72.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, x2, -\mathsf{fma}\left(2, x2, -3\right)\right), 2, \mathsf{fma}\left(3 - -2 \cdot x2, 3, x2 \cdot 14\right) - 6\right), x1, -2\right)\right), x1, -6 \cdot x2\right)} \]

   6. Taylor expanded in x2 around inf

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), x2 \cdot \left(\left(9 \cdot \frac{x1}{x2} + 12 \cdot x1\right) - 2 \cdot \frac{1}{x2}\right)\right), x1, -6 \cdot x2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.8%

      \[\leadsto x1 + \mathsf{fma}\left(\mathsf{fma}\left(4 \cdot x2, \mathsf{fma}\left(2, x2, -3\right), \left(\mathsf{fma}\left(\frac{x1}{x2}, 9, 12 \cdot x1\right) - \frac{2}{x2}\right) \cdot x2\right), x1, -6 \cdot x2\right) \]

   9. Taylor expanded in x2 around 0

      \[\leadsto x1 + x1 \cdot \color{blue}{\left(9 \cdot x1 - 2\right)} \]

   11. Applied rewrites 60.5%

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

   12. Taylor expanded in x1 around 0

       \[\leadsto x1 + -2 \cdot x1 \]
   13. Step-by-step derivation

   14. Applied rewrites 35.9%

       \[\leadsto x1 + -2 \cdot x1 \]

   if 9.0000000000000005e-151 < x2

   1. Initial program 70.2%

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

   3. Taylor expanded in x1 around 0

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

   5. Applied rewrites 28.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 26.3% accurate, 49.7× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.5%

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

3. Taylor expanded in x1 around 0

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

5. Applied rewrites 23.6%

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

Reproduce

herbie shell --seed 2025018 
(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))))))