Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.9% → 99.3%

Time: 35.5s

Alternatives: 27

Speedup: 7.3×

• 54.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* 3 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (/ (- (+ t_0 (* 2 x2)) x1) t_1)))
  (+
   x1
   (+
    (+
     (+
      (+
       (*
        (+
         (* (* (* 2 x1) t_2) (- t_2 3))
         (* (* x1 x1) (- (* 4 t_2) 6)))
        t_1)
       (* t_0 t_2))
      (* (* x1 x1) x1))
     x1)
    (* 3 (/ (- (- t_0 (* 2 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 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4 * t$95$2), $MachinePrecision] - 6), $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 * N[(N[(N[(t$95$0 - N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Initial Program: 70.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* 3 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (/ (- (+ t_0 (* 2 x2)) x1) t_1)))
  (+
   x1
   (+
    (+
     (+
      (+
       (*
        (+
         (* (* (* 2 x1) t_2) (- t_2 3))
         (* (* x1 x1) (- (* 4 t_2) 6)))
        t_1)
       (* t_0 t_2))
      (* (* x1 x1) x1))
     x1)
    (* 3 (/ (- (- t_0 (* 2 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 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4 * t$95$2), $MachinePrecision] - 6), $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 * N[(N[(N[(t$95$0 - N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Alternative 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot x1 - -1\\ t_3 := \left(3 \cdot x1\right) \cdot x1\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_1}\\ t_5 := t\_3 \cdot t\_4\\ t_6 := 3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_1}\\ t_7 := \frac{\left(\left(x2 + x2\right) - x1\right) + t\_3}{t\_2}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_4 - 6\right)\right) \cdot t\_1 + t\_5\right) + t\_0\right) + x1\right) + t\_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(t\_2, \left(\left(4 \cdot t\_7 - 6\right) \cdot x1\right), x1, \left(3 + \left(\left(x1 - t\_3\right) - \left(x2 + x2\right)\right) \cdot \frac{1}{t\_2}\right), \left(t\_7 \cdot \left(x1 + x1\right)\right)\right) + t\_5\right) + t\_0\right) + x1\right) + t\_6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* x1 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (- (* x1 x1) -1))
       (t_3 (* (* 3 x1) x1))
       (t_4 (/ (- (+ t_3 (* 2 x2)) x1) t_1))
       (t_5 (* t_3 t_4))
       (t_6 (* 3 (/ (- (- t_3 (* 2 x2)) x1) t_1)))
       (t_7 (/ (+ (- (+ x2 x2) x1) t_3) t_2)))
  (if (<=
       (+
        x1
        (+
         (+
          (+
           (+
            (*
             (+
              (* (* (* 2 x1) t_4) (- t_4 3))
              (* (* x1 x1) (- (* 4 t_4) 6)))
             t_1)
            t_5)
           t_0)
          x1)
         t_6))
       INFINITY)
    (+
     x1
     (+
      (+
       (+
        (+
         (134-z0z1z2z3z4
          t_2
          (* (- (* 4 t_7) 6) x1)
          x1
          (+ 3 (* (- (- x1 t_3) (+ x2 x2)) (/ 1 t_2)))
          (* t_7 (+ x1 x1)))
         t_5)
        t_0)
       x1)
      t_6))
    (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9)))))

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 70.9%

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

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

      3. lift-+.f64 N/A

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

   3. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right)} + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \color{blue}{\left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right)}, \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \color{blue}{\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. mult-flip N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \color{blue}{\left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{1}{x1 \cdot x1 - -1}}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. metadata-eval N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. lift--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{neg}\left(-1\right)}{\color{blue}{x1 \cdot x1 - -1}}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      6. sub-negate-rev N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{neg}\left(-1\right)}{\color{blue}{\mathsf{neg}\left(\left(-1 - x1 \cdot x1\right)\right)}}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      7. lift--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(\color{blue}{\left(-1 - x1 \cdot x1\right)}\right)}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      8. frac-2neg N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\frac{-1}{-1 - x1 \cdot x1}}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      9. lift-/.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\frac{-1}{-1 - x1 \cdot x1}}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

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

          \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \color{blue}{\left(3 + \left(\mathsf{neg}\left(\left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right)\right)\right) \cdot \frac{-1}{-1 - x1 \cdot x1}\right)}, \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      11. lower-+.f64 N/A

          \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \color{blue}{\left(3 + \left(\mathsf{neg}\left(\left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right)\right)\right) \cdot \frac{-1}{-1 - x1 \cdot x1}\right)}, \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 + \color{blue}{\left(\mathsf{neg}\left(\left(\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1\right)\right)\right) \cdot \frac{-1}{-1 - x1 \cdot x1}}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \color{blue}{\left(3 + \left(\left(x1 - \left(3 \cdot x1\right) \cdot x1\right) - \left(x2 + x2\right)\right) \cdot \frac{1}{x1 \cdot x1 - -1}\right)}, \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   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 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot x1 - -1\\ t_3 := \left(3 \cdot x1\right) \cdot x1\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_1}\\ t_5 := t\_3 \cdot t\_4\\ t_6 := 3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_1}\\ t_7 := \frac{\left(\left(x2 + x2\right) - x1\right) + t\_3}{t\_2}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_4 - 6\right)\right) \cdot t\_1 + t\_5\right) + t\_0\right) + x1\right) + t\_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(t\_2, \left(\left(4 \cdot t\_7 - 6\right) \cdot x1\right), x1, \left(3 - t\_7\right), \left(t\_7 \cdot \left(x1 + x1\right)\right)\right) + t\_5\right) + t\_0\right) + x1\right) + t\_6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* x1 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (- (* x1 x1) -1))
       (t_3 (* (* 3 x1) x1))
       (t_4 (/ (- (+ t_3 (* 2 x2)) x1) t_1))
       (t_5 (* t_3 t_4))
       (t_6 (* 3 (/ (- (- t_3 (* 2 x2)) x1) t_1)))
       (t_7 (/ (+ (- (+ x2 x2) x1) t_3) t_2)))
  (if (<=
       (+
        x1
        (+
         (+
          (+
           (+
            (*
             (+
              (* (* (* 2 x1) t_4) (- t_4 3))
              (* (* x1 x1) (- (* 4 t_4) 6)))
             t_1)
            t_5)
           t_0)
          x1)
         t_6))
       INFINITY)
    (+
     x1
     (+
      (+
       (+
        (+
         (134-z0z1z2z3z4
          t_2
          (* (- (* 4 t_7) 6) x1)
          x1
          (- 3 t_7)
          (* t_7 (+ x1 x1)))
         t_5)
        t_0)
       x1)
      t_6))
    (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9)))))

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 70.9%

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

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

      3. lift-+.f64 N/A

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

   3. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right)} + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   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 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* x1 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (* (* 3 x1) x1))
       (t_3 (/ (- (+ t_2 (* 2 x2)) x1) t_1))
       (t_4 (- (* x1 x1) -1))
       (t_5 (/ (+ (- (+ x2 x2) x1) t_2) t_4)))
  (if (<=
       (+
        x1
        (+
         (+
          (+
           (+
            (*
             (+
              (* (* (* 2 x1) t_3) (- t_3 3))
              (* (* x1 x1) (- (* 4 t_3) 6)))
             t_1)
            (* t_2 t_3))
           t_0)
          x1)
         (* 3 (/ (- (- t_2 (* 2 x2)) x1) t_1))))
       INFINITY)
    (+
     (-
      (*
       (-
        (* (- (* 4 t_5) 6) (* x1 x1))
        (* (- 3 t_5) (* t_5 (+ x1 x1))))
       t_4)
      (- (* (* -3 (* x1 x1)) t_5) t_0))
     (+ (- x1 (* -3 (/ (- t_2 (+ (+ x2 x2) x1)) t_4))) x1))
    (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9)))))

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

Java

public static 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 = (x1 * x1) - -1.0;
	double t_5 = (((x2 + x2) - x1) + t_2) / t_4;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_1) + (t_2 * t_3)) + t_0) + x1) + (3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)))) <= Double.POSITIVE_INFINITY) {
		tmp = ((((((4.0 * t_5) - 6.0) * (x1 * x1)) - ((3.0 - t_5) * (t_5 * (x1 + x1)))) * t_4) - (((-3.0 * (x1 * x1)) * t_5) - t_0)) + ((x1 - (-3.0 * ((t_2 - ((x2 + x2) + x1)) / t_4))) + x1);
	} else {
		tmp = x1 + (((Math.pow(x1, 4.0) * 6.0) + x1) + 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	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 = (x1 * x1) - -1.0
	t_5 = (((x2 + x2) - x1) + t_2) / t_4
	tmp = 0
	if (x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_1) + (t_2 * t_3)) + t_0) + x1) + (3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)))) <= math.inf:
		tmp = ((((((4.0 * t_5) - 6.0) * (x1 * x1)) - ((3.0 - t_5) * (t_5 * (x1 + x1)))) * t_4) - (((-3.0 * (x1 * x1)) * t_5) - t_0)) + ((x1 - (-3.0 * ((t_2 - ((x2 + x2) + x1)) / t_4))) + x1)
	else:
		tmp = x1 + (((math.pow(x1, 4.0) * 6.0) + x1) + 9.0)
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x1, x2)
	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 = (x1 * x1) - -1.0;
	t_5 = (((x2 + x2) - x1) + t_2) / t_4;
	tmp = 0.0;
	if ((x1 + (((((((((2.0 * x1) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0))) * t_1) + (t_2 * t_3)) + t_0) + x1) + (3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)))) <= Inf)
		tmp = ((((((4.0 * t_5) - 6.0) * (x1 * x1)) - ((3.0 - t_5) * (t_5 * (x1 + x1)))) * t_4) - (((-3.0 * (x1 * x1)) * t_5) - t_0)) + ((x1 - (-3.0 * ((t_2 - ((x2 + x2) + x1)) / t_4))) + x1);
	else
		tmp = x1 + ((((x1 ^ 4.0) * 6.0) + x1) + 9.0);
	end
	tmp_2 = 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), $MachinePrecision]}, Block[{t$95$2 = N[(N[(3 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(x2 + x2), $MachinePrecision] - x1), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$4), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2 * x1), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4 * t$95$3), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] + x1), $MachinePrecision] + N[(3 * N[(N[(N[(t$95$2 - N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(N[(N[(4 * t$95$5), $MachinePrecision] - 6), $MachinePrecision] * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(3 - t$95$5), $MachinePrecision] * N[(t$95$5 * N[(x1 + x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision] - N[(N[(N[(-3 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 - N[(-3 * N[(N[(t$95$2 - N[(N[(x2 + x2), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(N[Power[x1, 4], $MachinePrecision] * 6), $MachinePrecision] + x1), $MachinePrecision] + 9), $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 70.9%

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

   3. Applied rewrites 70.9%

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

   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 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := t\_0 \cdot t\_2\\ t_4 := x1 \cdot x1 - -1\\ t_5 := \left(x1 \cdot x1\right) \cdot x1\\ t_6 := \frac{\left(\left(x2 + x2\right) - x1\right) + t\_0}{t\_4}\\ t_7 := x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_3\right) + t\_5\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right)\\ t_8 := \left(x2 + x2\right) - \left(x1 - t\_0\right)\\ \mathbf{if}\;t\_7 \leq 1000000000000000046753818885456127989189605431330410286841364872744016439394555894610368258180303336939076888134044950289326168184662430331474313277416979816387389279864637935586997520238352311022660078293728671385192933261062303434752638026781377548741967884639283445760:\\ \;\;\;\;\left(\left(\left(\left(x1 \cdot x1\right) \cdot \left(\frac{-4}{-1 - x1 \cdot x1} \cdot t\_8 - 6\right) + \left(\frac{t\_8}{t\_4} - 3\right) \cdot \frac{\left(x1 + x1\right) \cdot t\_8}{t\_4}\right) \cdot t\_4 + \left(\frac{t\_0 \cdot t\_8}{t\_4} + t\_5\right)\right) + \left(x1 + \frac{3 \cdot \left(\left(\left(t\_0 - x2\right) - x2\right) - x1\right)}{t\_4}\right)\right) + x1\\ \mathbf{elif}\;t\_7 \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(t\_4, \left(6 \cdot x1\right), x1, \left(3 - t\_6\right), \left(t\_6 \cdot \left(x1 + x1\right)\right)\right) + t\_3\right) + t\_5\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + -1 \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* 3 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (/ (- (+ t_0 (* 2 x2)) x1) t_1))
       (t_3 (* t_0 t_2))
       (t_4 (- (* x1 x1) -1))
       (t_5 (* (* x1 x1) x1))
       (t_6 (/ (+ (- (+ x2 x2) x1) t_0) t_4))
       (t_7
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2 x1) t_2) (- t_2 3))
               (* (* x1 x1) (- (* 4 t_2) 6)))
              t_1)
             t_3)
            t_5)
           x1)
          (* 3 (/ (- (- t_0 (* 2 x2)) x1) t_1)))))
       (t_8 (- (+ x2 x2) (- x1 t_0))))
  (if (<=
       t_7
       1000000000000000046753818885456127989189605431330410286841364872744016439394555894610368258180303336939076888134044950289326168184662430331474313277416979816387389279864637935586997520238352311022660078293728671385192933261062303434752638026781377548741967884639283445760)
    (+
     (+
      (+
       (*
        (+
         (* (* x1 x1) (- (* (/ -4 (- -1 (* x1 x1))) t_8) 6))
         (* (- (/ t_8 t_4) 3) (/ (* (+ x1 x1) t_8) t_4)))
        t_4)
       (+ (/ (* t_0 t_8) t_4) t_5))
      (+ x1 (/ (* 3 (- (- (- t_0 x2) x2) x1)) t_4)))
     x1)
    (if (<= t_7 INFINITY)
      (+
       x1
       (+
        (+
         (+
          (+
           (134-z0z1z2z3z4
            t_4
            (* 6 x1)
            x1
            (- 3 t_6)
            (* t_6 (+ x1 x1)))
           t_3)
          t_5)
         x1)
        (* 3 (+ (* -2 x2) (* -1 x1)))))
      (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9))))))

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)))))) < 1e270

   1. Initial program 70.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-sub N/A

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

      5. mult-flip N/A

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

      6. mult-flip N/A

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

      7. lower-134-z0z1z2z3z4 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(3, \left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right), \left(\frac{1}{x1 \cdot x1 + 1}\right), x1, \left(\frac{1}{x1 \cdot x1 + 1}\right)\right)}\right) \]

   3. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(3, \left(\left(\left(3 \cdot x1\right) \cdot x1 - x2\right) - x2\right), \left(\frac{-1}{-1 - x1 \cdot x1}\right), x1, \left(\frac{-1}{-1 - x1 \cdot x1}\right)\right)}\right) \]

   5. Applied rewrites 66.5%

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

   if 1e270 < (+.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 70.9%

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

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

      3. lift-+.f64 N/A

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

   3. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right)} + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 68.7%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Taylor expanded in x1 around 0

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{-1 \cdot x1}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{-1} \cdot x1\right)\right) \]

      3. lower-*.f64 68.7%

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + -1 \cdot \color{blue}{x1}\right)\right) \]

   9. Applied rewrites 68.7%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]

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

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := \left(3 \cdot x1\right) \cdot x1\\ t_2 := x1 \cdot x1 - -1\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t\_1 + 2 \cdot x2\right) - x1}{t\_3}\\ t_5 := t\_1 \cdot t\_4\\ t_6 := x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_4 - 6\right)\right) \cdot t\_3 + t\_5\right) + t\_0\right) + x1\right) + 3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_3}\right)\\ t_7 := \left(\left(x2 + x2\right) - x1\right) + t\_1\\ t_8 := \frac{t\_7}{t\_2}\\ t_9 := 3 - t\_8\\ t_10 := t\_8 \cdot \left(x1 + x1\right)\\ \mathbf{if}\;t\_6 \leq 49999999999999999737683287595902466157897305225341087810970847365954154269153922568421376:\\ \;\;\;\;\left(\frac{\left(t\_1 - \left(\left(x2 + x2\right) + x1\right)\right) \cdot 3 + \left(\left(\left(\left(4 \cdot t\_8 - 6\right) \cdot \left(x1 \cdot x1\right) - t\_9 \cdot t\_10\right) \cdot t\_2\right) \cdot t\_2 + t\_7 \cdot t\_1\right)}{t\_2} + t\_2 \cdot x1\right) + x1\\ \mathbf{elif}\;t\_6 \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(t\_2, \left(6 \cdot x1\right), x1, t\_9, t\_10\right) + t\_5\right) + t\_0\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + -1 \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* x1 x1) x1))
       (t_1 (* (* 3 x1) x1))
       (t_2 (- (* x1 x1) -1))
       (t_3 (+ (* x1 x1) 1))
       (t_4 (/ (- (+ t_1 (* 2 x2)) x1) t_3))
       (t_5 (* t_1 t_4))
       (t_6
        (+
         x1
         (+
          (+
           (+
            (+
             (*
              (+
               (* (* (* 2 x1) t_4) (- t_4 3))
               (* (* x1 x1) (- (* 4 t_4) 6)))
              t_3)
             t_5)
            t_0)
           x1)
          (* 3 (/ (- (- t_1 (* 2 x2)) x1) t_3)))))
       (t_7 (+ (- (+ x2 x2) x1) t_1))
       (t_8 (/ t_7 t_2))
       (t_9 (- 3 t_8))
       (t_10 (* t_8 (+ x1 x1))))
  (if (<=
       t_6
       49999999999999999737683287595902466157897305225341087810970847365954154269153922568421376)
    (+
     (+
      (/
       (+
        (* (- t_1 (+ (+ x2 x2) x1)) 3)
        (+
         (*
          (* (- (* (- (* 4 t_8) 6) (* x1 x1)) (* t_9 t_10)) t_2)
          t_2)
         (* t_7 t_1)))
       t_2)
      (* t_2 x1))
     x1)
    (if (<= t_6 INFINITY)
      (+
       x1
       (+
        (+
         (+ (+ (134-z0z1z2z3z4 t_2 (* 6 x1) x1 t_9 t_10) t_5) t_0)
         x1)
        (* 3 (+ (* -2 x2) (* -1 x1)))))
      (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9))))))

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)))))) < 5e88

   1. Initial program 70.9%

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

   3. Applied rewrites 66.4%

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

   if 5e88 < (+.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 70.9%

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

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

      3. lift-+.f64 N/A

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

   3. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right)} + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 68.7%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Taylor expanded in x1 around 0

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{-1 \cdot x1}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{-1} \cdot x1\right)\right) \]

      3. lower-*.f64 68.7%

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + -1 \cdot \color{blue}{x1}\right)\right) \]

   9. Applied rewrites 68.7%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]

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

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ t_3 := t\_0 \cdot t\_2\\ t_4 := x1 \cdot x1 - -1\\ t_5 := \left(x1 \cdot x1\right) \cdot x1\\ t_6 := \frac{\left(\left(x2 + x2\right) - x1\right) + t\_0}{t\_4}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_3\right) + t\_5\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(t\_4, \left(6 \cdot x1\right), x1, \left(3 - t\_6\right), \left(t\_6 \cdot \left(x1 + x1\right)\right)\right) + t\_3\right) + t\_5\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + -1 \cdot x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* 3 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (/ (- (+ t_0 (* 2 x2)) x1) t_1))
       (t_3 (* t_0 t_2))
       (t_4 (- (* x1 x1) -1))
       (t_5 (* (* x1 x1) x1))
       (t_6 (/ (+ (- (+ x2 x2) x1) t_0) t_4)))
  (if (<=
       (+
        x1
        (+
         (+
          (+
           (+
            (*
             (+
              (* (* (* 2 x1) t_2) (- t_2 3))
              (* (* x1 x1) (- (* 4 t_2) 6)))
             t_1)
            t_3)
           t_5)
          x1)
         (* 3 (/ (- (- t_0 (* 2 x2)) x1) t_1))))
       INFINITY)
    (+
     x1
     (+
      (+
       (+
        (+
         (134-z0z1z2z3z4 t_4 (* 6 x1) x1 (- 3 t_6) (* t_6 (+ x1 x1)))
         t_3)
        t_5)
       x1)
      (* 3 (+ (* -2 x2) (* -1 x1)))))
    (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9)))))

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 70.9%

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

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

      3. lift-+.f64 N/A

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

   3. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right)} + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 68.7%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Taylor expanded in x1 around 0

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{-1 \cdot x1}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{-1} \cdot x1\right)\right) \]

      3. lower-*.f64 68.7%

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + -1 \cdot \color{blue}{x1}\right)\right) \]

   9. Applied rewrites 68.7%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]

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

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 95.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 + \left({x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{2 + -2 \cdot \left(1 + 3 \cdot t\_0\right)}{x1} + 4 \cdot t\_0\right)}{x1}}{x1}\right) + 9\right)\\ \mathbf{if}\;x1 \leq -1350:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq \frac{7148113328562451}{4611686018427387904}:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (- (* 2 x2) 3))
       (t_1
        (+
         x1
         (+
          (*
           (pow x1 4)
           (+
            6
            (*
             -1
             (/
              (+
               3
               (*
                -1
                (/
                 (+
                  9
                  (+
                   (* -1 (/ (+ 2 (* -2 (+ 1 (* 3 t_0)))) x1))
                   (* 4 t_0)))
                 x1)))
              x1))))
          9))))
  (if (<= x1 -1350)
    t_1
    (if (<= x1 7148113328562451/4611686018427387904)
      (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
      t_1))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 + ((pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((2.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + (4.0 * t_0))) / x1))) / x1)))) + 9.0);
	double tmp;
	if (x1 <= -1350.0) {
		tmp = t_1;
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 + (((x1 ** 4.0d0) * (6.0d0 + ((-1.0d0) * ((3.0d0 + ((-1.0d0) * ((9.0d0 + (((-1.0d0) * ((2.0d0 + ((-2.0d0) * (1.0d0 + (3.0d0 * t_0)))) / x1)) + (4.0d0 * t_0))) / x1))) / x1)))) + 9.0d0)
    if (x1 <= (-1350.0d0)) then
        tmp = t_1
    else if (x1 <= 0.00155d0) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 + ((Math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((2.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + (4.0 * t_0))) / x1))) / x1)))) + 9.0);
	double tmp;
	if (x1 <= -1350.0) {
		tmp = t_1;
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 + ((math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((2.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + (4.0 * t_0))) / x1))) / x1)))) + 9.0)
	tmp = 0
	if x1 <= -1350.0:
		tmp = t_1
	elif x1 <= 0.00155:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 + Float64(Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-1.0 * Float64(Float64(3.0 + Float64(-1.0 * Float64(Float64(9.0 + Float64(Float64(-1.0 * Float64(Float64(2.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_0)))) / x1)) + Float64(4.0 * t_0))) / x1))) / x1)))) + 9.0))
	tmp = 0.0
	if (x1 <= -1350.0)
		tmp = t_1;
	elseif (x1 <= 0.00155)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 + (((x1 ^ 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((2.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + (4.0 * t_0))) / x1))) / x1)))) + 9.0);
	tmp = 0.0;
	if (x1 <= -1350.0)
		tmp = t_1;
	elseif (x1 <= 0.00155)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2 * x2), $MachinePrecision] - 3), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(N[Power[x1, 4], $MachinePrecision] * N[(6 + N[(-1 * N[(N[(3 + N[(-1 * N[(N[(9 + N[(N[(-1 * N[(N[(2 + N[(-2 * N[(1 + N[(3 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] + N[(4 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 9), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1350], t$95$1, If[LessEqual[x1, 7148113328562451/4611686018427387904], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1350 or 0.0015499999999999999 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around -inf

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

   10. Applied rewrites 47.6%

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

   if -1350 < x1 < 0.0015499999999999999

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

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

Alternative 8: 95.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := 4 \cdot t\_0\\ \mathbf{if}\;x1 \leq -1350:\\ \;\;\;\;{x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + \left(-1 \cdot \frac{1 + -2 \cdot \left(1 + 3 \cdot t\_0\right)}{x1} + t\_1\right)}{x1}}{x1}\right)\\ \mathbf{elif}\;x1 \leq \frac{7148113328562451}{4611686018427387904}:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + t\_1}{x1}}{x1}\right) + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (- (* 2 x2) 3)) (t_1 (* 4 t_0)))
  (if (<= x1 -1350)
    (*
     (pow x1 4)
     (+
      6
      (*
       -1
       (/
        (+
         3
         (*
          -1
          (/
           (+ 9 (+ (* -1 (/ (+ 1 (* -2 (+ 1 (* 3 t_0)))) x1)) t_1))
           x1)))
        x1))))
    (if (<= x1 7148113328562451/4611686018427387904)
      (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
      (+
       x1
       (+
        (+
         (*
          (pow x1 4)
          (+ 6 (* -1 (/ (+ 3 (* -1 (/ (+ 9 t_1) x1))) x1))))
         x1)
        9))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * t_0;
	double tmp;
	if (x1 <= -1350.0) {
		tmp = pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((1.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + t_1)) / x1))) / x1)));
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (((pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + t_1) / x1))) / x1)))) + x1) + 9.0);
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = 4.0d0 * t_0
    if (x1 <= (-1350.0d0)) then
        tmp = (x1 ** 4.0d0) * (6.0d0 + ((-1.0d0) * ((3.0d0 + ((-1.0d0) * ((9.0d0 + (((-1.0d0) * ((1.0d0 + ((-2.0d0) * (1.0d0 + (3.0d0 * t_0)))) / x1)) + t_1)) / x1))) / x1)))
    else if (x1 <= 0.00155d0) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = x1 + ((((x1 ** 4.0d0) * (6.0d0 + ((-1.0d0) * ((3.0d0 + ((-1.0d0) * ((9.0d0 + t_1) / x1))) / x1)))) + x1) + 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = 4.0 * t_0;
	double tmp;
	if (x1 <= -1350.0) {
		tmp = Math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((1.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + t_1)) / x1))) / x1)));
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (((Math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + t_1) / x1))) / x1)))) + x1) + 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = 4.0 * t_0
	tmp = 0
	if x1 <= -1350.0:
		tmp = math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((1.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + t_1)) / x1))) / x1)))
	elif x1 <= 0.00155:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = x1 + (((math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + t_1) / x1))) / x1)))) + x1) + 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(4.0 * t_0)
	tmp = 0.0
	if (x1 <= -1350.0)
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-1.0 * Float64(Float64(3.0 + Float64(-1.0 * Float64(Float64(9.0 + Float64(Float64(-1.0 * Float64(Float64(1.0 + Float64(-2.0 * Float64(1.0 + Float64(3.0 * t_0)))) / x1)) + t_1)) / x1))) / x1))));
	elseif (x1 <= 0.00155)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-1.0 * Float64(Float64(3.0 + Float64(-1.0 * Float64(Float64(9.0 + t_1) / x1))) / x1)))) + x1) + 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = 4.0 * t_0;
	tmp = 0.0;
	if (x1 <= -1350.0)
		tmp = (x1 ^ 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + ((-1.0 * ((1.0 + (-2.0 * (1.0 + (3.0 * t_0)))) / x1)) + t_1)) / x1))) / x1)));
	elseif (x1 <= 0.00155)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = x1 + ((((x1 ^ 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + t_1) / x1))) / x1)))) + x1) + 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2 * x2), $MachinePrecision] - 3), $MachinePrecision]}, Block[{t$95$1 = N[(4 * t$95$0), $MachinePrecision]}, If[LessEqual[x1, -1350], N[(N[Power[x1, 4], $MachinePrecision] * N[(6 + N[(-1 * N[(N[(3 + N[(-1 * N[(N[(9 + N[(N[(-1 * N[(N[(1 + N[(-2 * N[(1 + N[(3 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7148113328562451/4611686018427387904], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(N[Power[x1, 4], $MachinePrecision] * N[(6 + N[(-1 * N[(N[(3 + N[(-1 * N[(N[(9 + t$95$1), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + 9), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1350

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 81.0%

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

   7. Applied rewrites 81.0%

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

   8. Taylor expanded in x1 around -inf

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

   10. Applied rewrites 48.1%

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

   if -1350 < x1 < 0.0015499999999999999

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

       \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

   if 0.0015499999999999999 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

   10. Applied rewrites 47.9%

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

Alternative 9: 95.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_0 := {x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1}}{x1}\right) + x1\\ \mathbf{if}\;x1 \leq -1350:\\ \;\;\;\;x1 + \left(t\_0 + \left(-6 \cdot x2 + -3 \cdot x1\right)\right)\\ \mathbf{elif}\;x1 \leq \frac{7148113328562451}{4611686018427387904}:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t\_0 + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0
        (+
         (*
          (pow x1 4)
          (+
           6
           (*
            -1
            (/ (+ 3 (* -1 (/ (+ 9 (* 4 (- (* 2 x2) 3))) x1))) x1))))
         x1)))
  (if (<= x1 -1350)
    (+ x1 (+ t_0 (+ (* -6 x2) (* -3 x1))))
    (if (<= x1 7148113328562451/4611686018427387904)
      (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
      (+ x1 (+ t_0 9))))))

C

double code(double x1, double x2) {
	double t_0 = (pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1;
	double tmp;
	if (x1 <= -1350.0) {
		tmp = x1 + (t_0 + ((-6.0 * x2) + (-3.0 * x1)));
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (t_0 + 9.0);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = ((x1 ** 4.0d0) * (6.0d0 + ((-1.0d0) * ((3.0d0 + ((-1.0d0) * ((9.0d0 + (4.0d0 * ((2.0d0 * x2) - 3.0d0))) / x1))) / x1)))) + x1
    if (x1 <= (-1350.0d0)) then
        tmp = x1 + (t_0 + (((-6.0d0) * x2) + ((-3.0d0) * x1)))
    else if (x1 <= 0.00155d0) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = x1 + (t_0 + 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (Math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1;
	double tmp;
	if (x1 <= -1350.0) {
		tmp = x1 + (t_0 + ((-6.0 * x2) + (-3.0 * x1)));
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (t_0 + 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1
	tmp = 0
	if x1 <= -1350.0:
		tmp = x1 + (t_0 + ((-6.0 * x2) + (-3.0 * x1)))
	elif x1 <= 0.00155:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = x1 + (t_0 + 9.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-1.0 * Float64(Float64(3.0 + Float64(-1.0 * Float64(Float64(9.0 + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0))) / x1))) / x1)))) + x1)
	tmp = 0.0
	if (x1 <= -1350.0)
		tmp = Float64(x1 + Float64(t_0 + Float64(Float64(-6.0 * x2) + Float64(-3.0 * x1))));
	elseif (x1 <= 0.00155)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = Float64(x1 + Float64(t_0 + 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = ((x1 ^ 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1;
	tmp = 0.0;
	if (x1 <= -1350.0)
		tmp = x1 + (t_0 + ((-6.0 * x2) + (-3.0 * x1)));
	elseif (x1 <= 0.00155)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = x1 + (t_0 + 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[Power[x1, 4], $MachinePrecision] * N[(6 + N[(-1 * N[(N[(3 + N[(-1 * N[(N[(9 + N[(4 * N[(N[(2 * x2), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]}, If[LessEqual[x1, -1350], N[(x1 + N[(t$95$0 + N[(N[(-6 * x2), $MachinePrecision] + N[(-3 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7148113328562451/4611686018427387904], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + 9), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1350

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 81.0%

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

   7. Applied rewrites 81.0%

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

   8. Taylor expanded in x1 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

   10. Applied rewrites 61.2%

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

   if -1350 < x1 < 0.0015499999999999999

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

       \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

   if 0.0015499999999999999 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

   10. Applied rewrites 47.9%

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

Alternative 10: 95.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_0 := x1 + \left(\left({x1}^{4} \cdot \left(6 + -1 \cdot \frac{3 + -1 \cdot \frac{9 + 4 \cdot \left(2 \cdot x2 - 3\right)}{x1}}{x1}\right) + x1\right) + 9\right)\\ \mathbf{if}\;x1 \leq -1350:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq \frac{7148113328562451}{4611686018427387904}:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0
        (+
         x1
         (+
          (+
           (*
            (pow x1 4)
            (+
             6
             (*
              -1
              (/ (+ 3 (* -1 (/ (+ 9 (* 4 (- (* 2 x2) 3))) x1))) x1))))
           x1)
          9))))
  (if (<= x1 -1350)
    t_0
    (if (<= x1 7148113328562451/4611686018427387904)
      (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
      t_0))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (((pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1) + 9.0);
	double tmp;
	if (x1 <= -1350.0) {
		tmp = t_0;
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((((x1 ** 4.0d0) * (6.0d0 + ((-1.0d0) * ((3.0d0 + ((-1.0d0) * ((9.0d0 + (4.0d0 * ((2.0d0 * x2) - 3.0d0))) / x1))) / x1)))) + x1) + 9.0d0)
    if (x1 <= (-1350.0d0)) then
        tmp = t_0
    else if (x1 <= 0.00155d0) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (((Math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1) + 9.0);
	double tmp;
	if (x1 <= -1350.0) {
		tmp = t_0;
	} else if (x1 <= 0.00155) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (((math.pow(x1, 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1) + 9.0)
	tmp = 0
	if x1 <= -1350.0:
		tmp = t_0
	elif x1 <= 0.00155:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(Float64((x1 ^ 4.0) * Float64(6.0 + Float64(-1.0 * Float64(Float64(3.0 + Float64(-1.0 * Float64(Float64(9.0 + Float64(4.0 * Float64(Float64(2.0 * x2) - 3.0))) / x1))) / x1)))) + x1) + 9.0))
	tmp = 0.0
	if (x1 <= -1350.0)
		tmp = t_0;
	elseif (x1 <= 0.00155)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((((x1 ^ 4.0) * (6.0 + (-1.0 * ((3.0 + (-1.0 * ((9.0 + (4.0 * ((2.0 * x2) - 3.0))) / x1))) / x1)))) + x1) + 9.0);
	tmp = 0.0;
	if (x1 <= -1350.0)
		tmp = t_0;
	elseif (x1 <= 0.00155)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(N[(N[Power[x1, 4], $MachinePrecision] * N[(6 + N[(-1 * N[(N[(3 + N[(-1 * N[(N[(9 + N[(4 * N[(N[(2 * x2), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + 9), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1350], t$95$0, If[LessEqual[x1, 7148113328562451/4611686018427387904], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1350 or 0.0015499999999999999 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

   10. Applied rewrites 47.9%

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

   if -1350 < x1 < 0.0015499999999999999

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

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

Alternative 11: 94.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \left(x1 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot x1 - -1\\ t_3 := \left(3 \cdot x1\right) \cdot x1\\ t_4 := \frac{\left(t\_3 + 2 \cdot x2\right) - x1}{t\_1}\\ t_5 := t\_3 \cdot t\_4\\ t_6 := 3 \cdot \frac{\left(t\_3 - 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_4\right) \cdot \left(t\_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_4 - 6\right)\right) \cdot t\_1 + t\_5\right) + t\_0\right) + x1\right) + t\_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(t\_2, \left(6 \cdot x1\right), x1, \left(3 - 2 \cdot x2\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + t\_3}{t\_2} \cdot \left(x1 + x1\right)\right)\right) + t\_5\right) + t\_0\right) + x1\right) + t\_6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* x1 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (- (* x1 x1) -1))
       (t_3 (* (* 3 x1) x1))
       (t_4 (/ (- (+ t_3 (* 2 x2)) x1) t_1))
       (t_5 (* t_3 t_4))
       (t_6 (* 3 (/ (- (- t_3 (* 2 x2)) x1) t_1))))
  (if (<=
       (+
        x1
        (+
         (+
          (+
           (+
            (*
             (+
              (* (* (* 2 x1) t_4) (- t_4 3))
              (* (* x1 x1) (- (* 4 t_4) 6)))
             t_1)
            t_5)
           t_0)
          x1)
         t_6))
       INFINITY)
    (+
     x1
     (+
      (+
       (+
        (+
         (134-z0z1z2z3z4
          t_2
          (* 6 x1)
          x1
          (- 3 (* 2 x2))
          (* (/ (+ (- (+ x2 x2) x1) t_3) t_2) (+ x1 x1)))
         t_5)
        t_0)
       x1)
      t_6))
    (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9)))))

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 70.9%

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

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

      3. lift-+.f64 N/A

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

   3. Applied rewrites 70.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\left(4 \cdot \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} - 6\right) \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right)} + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 68.7%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(\color{blue}{6} \cdot x1\right), x1, \left(3 - \frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   7. Taylor expanded in x1 around 0

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \color{blue}{\left(3 - 2 \cdot x2\right)}, \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - \color{blue}{2 \cdot x2}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. lower-*.f64 65.8%

         \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \left(3 - 2 \cdot \color{blue}{x2}\right), \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   9. Applied rewrites 65.8%

      \[\leadsto x1 + \left(\left(\left(\left(\mathsf{134\_z0z1z2z3z4}\left(\left(x1 \cdot x1 - -1\right), \left(6 \cdot x1\right), x1, \color{blue}{\left(3 - 2 \cdot x2\right)}, \left(\frac{\left(\left(x2 + x2\right) - x1\right) + \left(3 \cdot x1\right) \cdot x1}{x1 \cdot x1 - -1} \cdot \left(x1 + x1\right)\right)\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   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 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 93.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x1 \leq -31:\\ \;\;\;\;x1 + \left(\left({x1}^{4} \cdot \left(6 - 3 \cdot \frac{1}{x1}\right) + x1\right) + -6 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 300000000000000000:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (if (<= x1 -31)
  (+ x1 (+ (+ (* (pow x1 4) (- 6 (* 3 (/ 1 x1)))) x1) (* -6 x2)))
  (if (<= x1 300000000000000000)
    (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
    (+
     x1
     (+
      (+ (* (pow x1 3) (- (* 6 x1) 3)) x1)
      (+ (* -6 x2) (* -3 x1)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -31.0) {
		tmp = x1 + (((pow(x1, 4.0) * (6.0 - (3.0 * (1.0 / x1)))) + x1) + (-6.0 * x2));
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (((pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * 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 (x1 <= (-31.0d0)) then
        tmp = x1 + ((((x1 ** 4.0d0) * (6.0d0 - (3.0d0 * (1.0d0 / x1)))) + x1) + ((-6.0d0) * x2))
    else if (x1 <= 3d+17) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = x1 + ((((x1 ** 3.0d0) * ((6.0d0 * x1) - 3.0d0)) + x1) + (((-6.0d0) * x2) + ((-3.0d0) * x1)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -31.0) {
		tmp = x1 + (((Math.pow(x1, 4.0) * (6.0 - (3.0 * (1.0 / x1)))) + x1) + (-6.0 * x2));
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (((Math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -31.0:
		tmp = x1 + (((math.pow(x1, 4.0) * (6.0 - (3.0 * (1.0 / x1)))) + x1) + (-6.0 * x2))
	elif x1 <= 3e+17:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = x1 + (((math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * x1)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -31.0)
		tmp = Float64(x1 + Float64(Float64(Float64((x1 ^ 4.0) * Float64(6.0 - Float64(3.0 * Float64(1.0 / x1)))) + x1) + Float64(-6.0 * x2)));
	elseif (x1 <= 3e+17)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(Float64((x1 ^ 3.0) * Float64(Float64(6.0 * x1) - 3.0)) + x1) + Float64(Float64(-6.0 * x2) + Float64(-3.0 * x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -31.0)
		tmp = x1 + ((((x1 ^ 4.0) * (6.0 - (3.0 * (1.0 / x1)))) + x1) + (-6.0 * x2));
	elseif (x1 <= 3e+17)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = x1 + ((((x1 ^ 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -31], N[(x1 + N[(N[(N[(N[Power[x1, 4], $MachinePrecision] * N[(6 - N[(3 * N[(1 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(-6 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 300000000000000000], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(N[Power[x1, 3], $MachinePrecision] * N[(N[(6 * x1), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(N[(-6 * x2), $MachinePrecision] + N[(-3 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -31

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around 0

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

      1. lower-*.f64 69.2%

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

   7. Applied rewrites 69.2%

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

   if -31 < x1 < 3e17

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

       \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

   if 3e17 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 81.0%

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

   7. Applied rewrites 81.0%

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

   8. Taylor expanded in x1 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right) \]

      4. lower-*.f64 81.0%

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right) \]

   10. Applied rewrites 81.0%

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

Alternative 13: 93.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_0 := x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right)\\ \mathbf{if}\;x1 \leq -31:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 300000000000000000:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0
        (+
         x1
         (+
          (+ (* (pow x1 3) (- (* 6 x1) 3)) x1)
          (+ (* -6 x2) (* -3 x1))))))
  (if (<= x1 -31)
    t_0
    (if (<= x1 300000000000000000)
      (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
      t_0))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (((pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * x1)));
	double tmp;
	if (x1 <= -31.0) {
		tmp = t_0;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((((x1 ** 3.0d0) * ((6.0d0 * x1) - 3.0d0)) + x1) + (((-6.0d0) * x2) + ((-3.0d0) * x1)))
    if (x1 <= (-31.0d0)) then
        tmp = t_0
    else if (x1 <= 3d+17) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (((Math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * x1)));
	double tmp;
	if (x1 <= -31.0) {
		tmp = t_0;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (((math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * x1)))
	tmp = 0
	if x1 <= -31.0:
		tmp = t_0
	elif x1 <= 3e+17:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(Float64((x1 ^ 3.0) * Float64(Float64(6.0 * x1) - 3.0)) + x1) + Float64(Float64(-6.0 * x2) + Float64(-3.0 * x1))))
	tmp = 0.0
	if (x1 <= -31.0)
		tmp = t_0;
	elseif (x1 <= 3e+17)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((((x1 ^ 3.0) * ((6.0 * x1) - 3.0)) + x1) + ((-6.0 * x2) + (-3.0 * x1)));
	tmp = 0.0;
	if (x1 <= -31.0)
		tmp = t_0;
	elseif (x1 <= 3e+17)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(N[(N[Power[x1, 3], $MachinePrecision] * N[(N[(6 * x1), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(N[(-6 * x2), $MachinePrecision] + N[(-3 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -31], t$95$0, If[LessEqual[x1, 300000000000000000], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -31 or 3e17 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 81.0%

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

   7. Applied rewrites 81.0%

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

   8. Taylor expanded in x1 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right) \]

      4. lower-*.f64 81.0%

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + \left(-6 \cdot x2 + -3 \cdot x1\right)\right) \]

   10. Applied rewrites 81.0%

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

   if -31 < x1 < 3e17

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

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

Alternative 14: 93.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x1 \leq -850:\\ \;\;\;\;\left(9 + \left(\left(6 - \frac{3}{x1}\right) \cdot {x1}^{4} + x1\right)\right) + x1\\ \mathbf{elif}\;x1 \leq 300000000000000000:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (if (<= x1 -850)
  (+ (+ 9 (+ (* (- 6 (/ 3 x1)) (pow x1 4)) x1)) x1)
  (if (<= x1 300000000000000000)
    (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
    (+ x1 (+ (+ (* (pow x1 3) (- (* 6 x1) 3)) x1) 9)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -850.0) {
		tmp = (9.0 + (((6.0 - (3.0 / x1)) * pow(x1, 4.0)) + x1)) + x1;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (((pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0);
	}
	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 <= (-850.0d0)) then
        tmp = (9.0d0 + (((6.0d0 - (3.0d0 / x1)) * (x1 ** 4.0d0)) + x1)) + x1
    else if (x1 <= 3d+17) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = x1 + ((((x1 ** 3.0d0) * ((6.0d0 * x1) - 3.0d0)) + x1) + 9.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -850.0) {
		tmp = (9.0 + (((6.0 - (3.0 / x1)) * Math.pow(x1, 4.0)) + x1)) + x1;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = x1 + (((Math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -850.0:
		tmp = (9.0 + (((6.0 - (3.0 / x1)) * math.pow(x1, 4.0)) + x1)) + x1
	elif x1 <= 3e+17:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = x1 + (((math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -850.0)
		tmp = Float64(Float64(9.0 + Float64(Float64(Float64(6.0 - Float64(3.0 / x1)) * (x1 ^ 4.0)) + x1)) + x1);
	elseif (x1 <= 3e+17)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(Float64((x1 ^ 3.0) * Float64(Float64(6.0 * x1) - 3.0)) + x1) + 9.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -850.0)
		tmp = (9.0 + (((6.0 - (3.0 / x1)) * (x1 ^ 4.0)) + x1)) + x1;
	elseif (x1 <= 3e+17)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = x1 + ((((x1 ^ 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -850], N[(N[(9 + N[(N[(N[(6 - N[(3 / x1), $MachinePrecision]), $MachinePrecision] * N[Power[x1, 4], $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision], If[LessEqual[x1, 300000000000000000], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(N[Power[x1, 3], $MachinePrecision] * N[(N[(6 * x1), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + 9), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -850

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

      1. lift-+.f64 N/A

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

   9. Applied rewrites 46.0%

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

   if -850 < x1 < 3e17

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

       \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

   if 3e17 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right) \]

      3. lower--.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right) \]

      4. lower-*.f64 46.0%

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right) \]

   10. Applied rewrites 46.0%

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

Alternative 15: 93.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_0 := x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right)\\ \mathbf{if}\;x1 \leq -850:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 300000000000000000:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (+ x1 (+ (+ (* (pow x1 3) (- (* 6 x1) 3)) x1) 9))))
  (if (<= x1 -850)
    t_0
    (if (<= x1 300000000000000000)
      (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
      t_0))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (((pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0);
	double tmp;
	if (x1 <= -850.0) {
		tmp = t_0;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((((x1 ** 3.0d0) * ((6.0d0 * x1) - 3.0d0)) + x1) + 9.0d0)
    if (x1 <= (-850.0d0)) then
        tmp = t_0
    else if (x1 <= 3d+17) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (((Math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0);
	double tmp;
	if (x1 <= -850.0) {
		tmp = t_0;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (((math.pow(x1, 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0)
	tmp = 0
	if x1 <= -850.0:
		tmp = t_0
	elif x1 <= 3e+17:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(Float64((x1 ^ 3.0) * Float64(Float64(6.0 * x1) - 3.0)) + x1) + 9.0))
	tmp = 0.0
	if (x1 <= -850.0)
		tmp = t_0;
	elseif (x1 <= 3e+17)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((((x1 ^ 3.0) * ((6.0 * x1) - 3.0)) + x1) + 9.0);
	tmp = 0.0;
	if (x1 <= -850.0)
		tmp = t_0;
	elseif (x1 <= 3e+17)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(N[(N[Power[x1, 3], $MachinePrecision] * N[(N[(6 * x1), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + 9), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -850], t$95$0, If[LessEqual[x1, 300000000000000000], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -850 or 3e17 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right) \]

      3. lower--.f64 N/A

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right) \]

      4. lower-*.f64 46.0%

         \[\leadsto x1 + \left(\left({x1}^{3} \cdot \left(6 \cdot x1 - 3\right) + x1\right) + 9\right) \]

   10. Applied rewrites 46.0%

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

   if -850 < x1 < 3e17

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

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

Alternative 16: 93.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_0 := x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right)\\ \mathbf{if}\;x1 \leq -850:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 300000000000000000:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (+ x1 (+ (+ (* (pow x1 4) 6) x1) 9))))
  (if (<= x1 -850)
    t_0
    (if (<= x1 300000000000000000)
      (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))
      t_0))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (((pow(x1, 4.0) * 6.0) + x1) + 9.0);
	double tmp;
	if (x1 <= -850.0) {
		tmp = t_0;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((((x1 ** 4.0d0) * 6.0d0) + x1) + 9.0d0)
    if (x1 <= (-850.0d0)) then
        tmp = t_0
    else if (x1 <= 3d+17) then
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (((Math.pow(x1, 4.0) * 6.0) + x1) + 9.0);
	double tmp;
	if (x1 <= -850.0) {
		tmp = t_0;
	} else if (x1 <= 3e+17) {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (((math.pow(x1, 4.0) * 6.0) + x1) + 9.0)
	tmp = 0
	if x1 <= -850.0:
		tmp = t_0
	elif x1 <= 3e+17:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(Float64((x1 ^ 4.0) * 6.0) + x1) + 9.0))
	tmp = 0.0
	if (x1 <= -850.0)
		tmp = t_0;
	elseif (x1 <= 3e+17)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((((x1 ^ 4.0) * 6.0) + x1) + 9.0);
	tmp = 0.0;
	if (x1 <= -850.0)
		tmp = t_0;
	elseif (x1 <= 3e+17)
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(N[(N[Power[x1, 4], $MachinePrecision] * 6), $MachinePrecision] + x1), $MachinePrecision] + 9), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -850], t$95$0, If[LessEqual[x1, 300000000000000000], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -850 or 3e17 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 56.4%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in x1 around inf

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x1 around inf

      \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.7%

       \[\leadsto x1 + \left(\left({x1}^{4} \cdot 6 + x1\right) + 9\right) \]

   if -850 < x1 < 3e17

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

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

Alternative 17: 76.5% accurate, 7.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x1 \leq -10500000000000000498709617261614356196923244486430150744980861873802189582763267457024:\\ \;\;\;\;-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (if (<=
     x1
     -10500000000000000498709617261614356196923244486430150744980861873802189582763267457024)
  (+ (* -6 x2) (* x1 (- (* x1 (+ 9 (* -19 x1))) 1)))
  (+ (* -1 x1) (* x2 (- (+ (* -12 x1) (* 8 (* x1 x2))) 6)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+85) {
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	} else {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	}
	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 <= (-1.05d+85)) then
        tmp = ((-6.0d0) * x2) + (x1 * ((x1 * (9.0d0 + ((-19.0d0) * x1))) - 1.0d0))
    else
        tmp = ((-1.0d0) * x1) + (x2 * ((((-12.0d0) * x1) + (8.0d0 * (x1 * x2))) - 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+85) {
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	} else {
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.05e+85:
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0))
	else:
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.05e+85)
		tmp = Float64(Float64(-6.0 * x2) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0)));
	else
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(Float64(-12.0 * x1) + Float64(8.0 * Float64(x1 * x2))) - 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.05e+85)
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	else
		tmp = (-1.0 * x1) + (x2 * (((-12.0 * x1) + (8.0 * (x1 * x2))) - 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -10500000000000000498709617261614356196923244486430150744980861873802189582763267457024], N[(N[(-6 * x2), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9 + N[(-19 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(N[(-12 * x1), $MachinePrecision] + N[(8 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.05e85

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in x2 around 0

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

      1. lower--.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-+.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-*.f64 54.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   7. Applied rewrites 54.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

   if -1.05e85 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

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

       1. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)} - 6\right) \]

       3. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - \color{blue}{6}\right) \]

       4. lower--.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       5. lower-+.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       6. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       7. lower-*.f64 N/A

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

       8. lower-*.f64 60.7%

          \[\leadsto -1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) \]

   13. Applied rewrites 60.7%

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

Alternative 18: 70.8% accurate, 8.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x1 \leq -10500000000000000498709617261614356196923244486430150744980861873802189582763267457024:\\ \;\;\;\;-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (if (<=
     x1
     -10500000000000000498709617261614356196923244486430150744980861873802189582763267457024)
  (+ (* -6 x2) (* x1 (- (* x1 (+ 9 (* -19 x1))) 1)))
  (+ (* -6 x2) (* x1 (- (* x2 (- (* 8 x2) 12)) 1)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+85) {
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	} else {
		tmp = (-6.0 * x2) + (x1 * ((x2 * ((8.0 * x2) - 12.0)) - 1.0));
	}
	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 <= (-1.05d+85)) then
        tmp = ((-6.0d0) * x2) + (x1 * ((x1 * (9.0d0 + ((-19.0d0) * x1))) - 1.0d0))
    else
        tmp = ((-6.0d0) * x2) + (x1 * ((x2 * ((8.0d0 * x2) - 12.0d0)) - 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.05e+85) {
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	} else {
		tmp = (-6.0 * x2) + (x1 * ((x2 * ((8.0 * x2) - 12.0)) - 1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.05e+85:
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0))
	else:
		tmp = (-6.0 * x2) + (x1 * ((x2 * ((8.0 * x2) - 12.0)) - 1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.05e+85)
		tmp = Float64(Float64(-6.0 * x2) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0)));
	else
		tmp = Float64(Float64(-6.0 * x2) + Float64(x1 * Float64(Float64(x2 * Float64(Float64(8.0 * x2) - 12.0)) - 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.05e+85)
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	else
		tmp = (-6.0 * x2) + (x1 * ((x2 * ((8.0 * x2) - 12.0)) - 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -10500000000000000498709617261614356196923244486430150744980861873802189582763267457024], N[(N[(-6 * x2), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9 + N[(-19 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-6 * x2), $MachinePrecision] + N[(x1 * N[(N[(x2 * N[(N[(8 * x2), $MachinePrecision] - 12), $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.05e85

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in x2 around 0

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

      1. lower--.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-+.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-*.f64 54.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   7. Applied rewrites 54.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

   if -1.05e85 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right) \]

      3. lower-*.f64 55.0%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right) \]

   7. Applied rewrites 55.0%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 64.5% accurate, 8.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x1 \leq \frac{3389627864620585}{65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032}:\\ \;\;\;\;-6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (if (<=
     x1
     3389627864620585/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032)
  (+ (* -6 x2) (* x1 (- (* x1 (+ 9 (* -19 x1))) 1)))
  (* x1 (- (* 4 (* x2 (- (* 2 x2) 3))) 1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 5.2e-77) {
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	} else {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	}
	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 <= 5.2d-77) then
        tmp = ((-6.0d0) * x2) + (x1 * ((x1 * (9.0d0 + ((-19.0d0) * x1))) - 1.0d0))
    else
        tmp = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 5.2e-77) {
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	} else {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 5.2e-77:
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0))
	else:
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 5.2e-77)
		tmp = Float64(Float64(-6.0 * x2) + Float64(x1 * Float64(Float64(x1 * Float64(9.0 + Float64(-19.0 * x1))) - 1.0)));
	else
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 5.2e-77)
		tmp = (-6.0 * x2) + (x1 * ((x1 * (9.0 + (-19.0 * x1))) - 1.0));
	else
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 3389627864620585/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032], N[(N[(-6 * x2), $MachinePrecision] + N[(x1 * N[(N[(x1 * N[(9 + N[(-19 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(4 * N[(x2 * N[(N[(2 * x2), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 5.2000000000000002e-77

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in x2 around 0

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

      1. lower--.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      3. lower-+.f64 N/A

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

      4. lower-*.f64 54.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - 1\right) \]

   7. Applied rewrites 54.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + -19 \cdot x1\right) - \color{blue}{1}\right) \]

   if 5.2000000000000002e-77 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 33.0%

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

   10. Applied rewrites 33.0%

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

Alternative 20: 56.6% accurate, 7.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x1 \leq -25999999999999997256817825017964609482768800836853525517434880:\\ \;\;\;\;x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1}{x2}\right)\\ \mathbf{elif}\;x1 \leq \frac{3389627864620585}{65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032}:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (if (<=
     x1
     -25999999999999997256817825017964609482768800836853525517434880)
  (* x2 (+ (* -12 x1) (* -1 (/ x1 x2))))
  (if (<=
       x1
       3389627864620585/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032)
    (+ (* -1 x1) (* x2 -6))
    (* x1 (- (* 4 (* x2 (- (* 2 x2) 3))) 1)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.6e+61) {
		tmp = x2 * ((-12.0 * x1) + (-1.0 * (x1 / x2)));
	} else if (x1 <= 5.2e-77) {
		tmp = (-1.0 * x1) + (x2 * -6.0);
	} else {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	}
	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 <= (-2.6d+61)) then
        tmp = x2 * (((-12.0d0) * x1) + ((-1.0d0) * (x1 / x2)))
    else if (x1 <= 5.2d-77) then
        tmp = ((-1.0d0) * x1) + (x2 * (-6.0d0))
    else
        tmp = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -2.6e+61) {
		tmp = x2 * ((-12.0 * x1) + (-1.0 * (x1 / x2)));
	} else if (x1 <= 5.2e-77) {
		tmp = (-1.0 * x1) + (x2 * -6.0);
	} else {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -2.6e+61:
		tmp = x2 * ((-12.0 * x1) + (-1.0 * (x1 / x2)))
	elif x1 <= 5.2e-77:
		tmp = (-1.0 * x1) + (x2 * -6.0)
	else:
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -2.6e+61)
		tmp = Float64(x2 * Float64(Float64(-12.0 * x1) + Float64(-1.0 * Float64(x1 / x2))));
	elseif (x1 <= 5.2e-77)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * -6.0));
	else
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -2.6e+61)
		tmp = x2 * ((-12.0 * x1) + (-1.0 * (x1 / x2)));
	elseif (x1 <= 5.2e-77)
		tmp = (-1.0 * x1) + (x2 * -6.0);
	else
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -25999999999999997256817825017964609482768800836853525517434880], N[(x2 * N[(N[(-12 * x1), $MachinePrecision] + N[(-1 * N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3389627864620585/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * -6), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(4 * N[(x2 * N[(N[(2 * x2), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.5999999999999997e61

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around inf

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

       1. lower-*.f64 N/A

          \[\leadsto x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1}{\color{blue}{x2}}\right) \]

       2. lower-+.f64 N/A

          \[\leadsto x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1}{x2}\right) \]

       3. lower-*.f64 N/A

          \[\leadsto x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1}{x2}\right) \]

       4. lower-*.f64 N/A

          \[\leadsto x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1}{x2}\right) \]

       5. lower-/.f64 25.5%

          \[\leadsto x2 \cdot \left(-12 \cdot x1 + -1 \cdot \frac{x1}{x2}\right) \]

   13. Applied rewrites 25.5%

       \[\leadsto x2 \cdot \left(-12 \cdot x1 + -1 \cdot \color{blue}{\frac{x1}{x2}}\right) \]

   if -2.5999999999999997e61 < x1 < 5.2000000000000002e-77

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto -1 \cdot x1 + x2 \cdot -6 \]
   9. Step-by-step derivation

   10. Applied rewrites 38.8%

       \[\leadsto -1 \cdot x1 + x2 \cdot -6 \]

   if 5.2000000000000002e-77 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 33.0%

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

   10. Applied rewrites 33.0%

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

Alternative 21: 51.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x1 \leq \frac{3389627864620585}{65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032}:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 1\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (if (<=
     x1
     3389627864620585/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032)
  (+ (* -1 x1) (* x2 (- (* -12 x1) 6)))
  (* x1 (- (* 4 (* x2 (- (* 2 x2) 3))) 1))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 5.2e-77) {
		tmp = (-1.0 * x1) + (x2 * ((-12.0 * x1) - 6.0));
	} else {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	}
	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 <= 5.2d-77) then
        tmp = ((-1.0d0) * x1) + (x2 * (((-12.0d0) * x1) - 6.0d0))
    else
        tmp = x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 5.2e-77) {
		tmp = (-1.0 * x1) + (x2 * ((-12.0 * x1) - 6.0));
	} else {
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 5.2e-77:
		tmp = (-1.0 * x1) + (x2 * ((-12.0 * x1) - 6.0))
	else:
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 5.2e-77)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(-12.0 * x1) - 6.0)));
	else
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 5.2e-77)
		tmp = (-1.0 * x1) + (x2 * ((-12.0 * x1) - 6.0));
	else
		tmp = x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 3389627864620585/65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(-12 * x1), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(4 * N[(x2 * N[(N[(2 * x2), $MachinePrecision] - 3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < 5.2000000000000002e-77

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   if 5.2000000000000002e-77 < x1

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 33.0%

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

   10. Applied rewrites 33.0%

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

Alternative 22: 44.7% accurate, 13.5× speedup

Math

\[-1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (+ (* -1 x1) (* x2 (- (* -12 x1) 6))))

C

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

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 = ((-1.0d0) * x1) + (x2 * (((-12.0d0) * x1) - 6.0d0))
end function

Java

public static double code(double x1, double x2) {
	return (-1.0 * x1) + (x2 * ((-12.0 * x1) - 6.0));
}

Python

def code(x1, x2):
	return (-1.0 * x1) + (x2 * ((-12.0 * x1) - 6.0))

Julia

function code(x1, x2)
	return Float64(Float64(-1.0 * x1) + Float64(x2 * Float64(Float64(-12.0 * x1) - 6.0)))
end

MATLAB

function tmp = code(x1, x2)
	tmp = (-1.0 * x1) + (x2 * ((-12.0 * x1) - 6.0));
end

Wolfram

code[x1_, x2_] := N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * N[(N[(-12 * x1), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

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

2. Taylor expanded in x1 around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower--.f64 N/A

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

4. Applied rewrites 55.0%

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

5. Taylor expanded in x2 around 0

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

   1. lower-+.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

   3. lower-*.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

   4. lower--.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   5. lower-*.f64 44.7%

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

7. Applied rewrites 44.7%

   \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]
8. Add Preprocessing

Alternative 23: 44.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \leq 1000000000000000000161765076786456438212668646231659438295495017101117499225738747865260243034213915253779773568180337416027445820567779199643391541606026068611150746122284976177256650044200527276807327067690462112661427500197051226489898260678763391449376088547292320814127957486330655468919122263277568:\\ \;\;\;\;-1 \cdot x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-12 \cdot x2 - 1\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* 3 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (/ (- (+ t_0 (* 2 x2)) x1) t_1)))
  (if (<=
       (+
        x1
        (+
         (+
          (+
           (+
            (*
             (+
              (* (* (* 2 x1) t_2) (- t_2 3))
              (* (* x1 x1) (- (* 4 t_2) 6)))
             t_1)
            (* t_0 t_2))
           (* (* x1 x1) x1))
          x1)
         (* 3 (/ (- (- t_0 (* 2 x2)) x1) t_1))))
       1000000000000000000161765076786456438212668646231659438295495017101117499225738747865260243034213915253779773568180337416027445820567779199643391541606026068611150746122284976177256650044200527276807327067690462112661427500197051226489898260678763391449376088547292320814127957486330655468919122263277568)
    (+ (* -1 x1) (* x2 -6))
    (* x1 (- (* -12 x2) 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;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+303) {
		tmp = (-1.0 * x1) + (x2 * -6.0);
	} else {
		tmp = x1 * ((-12.0 * x2) - 1.0);
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((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)))) <= 1d+303) then
        tmp = ((-1.0d0) * x1) + (x2 * (-6.0d0))
    else
        tmp = x1 * (((-12.0d0) * x2) - 1.0d0)
    end if
    code = tmp
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;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+303) {
		tmp = (-1.0 * x1) + (x2 * -6.0);
	} else {
		tmp = x1 * ((-12.0 * x2) - 1.0);
	}
	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
	tmp = 0
	if (x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+303:
		tmp = (-1.0 * x1) + (x2 * -6.0)
	else:
		tmp = x1 * ((-12.0 * x2) - 1.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= 1e+303)
		tmp = Float64(Float64(-1.0 * x1) + Float64(x2 * -6.0));
	else
		tmp = Float64(x1 * Float64(Float64(-12.0 * x2) - 1.0));
	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;
	tmp = 0.0;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+303)
		tmp = (-1.0 * x1) + (x2 * -6.0);
	else
		tmp = x1 * ((-12.0 * x2) - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4 * t$95$2), $MachinePrecision] - 6), $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 * N[(N[(N[(t$95$0 - N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1000000000000000000161765076786456438212668646231659438295495017101117499225738747865260243034213915253779773568180337416027445820567779199643391541606026068611150746122284976177256650044200527276807327067690462112661427500197051226489898260678763391449376088547292320814127957486330655468919122263277568], N[(N[(-1 * x1), $MachinePrecision] + N[(x2 * -6), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(-12 * x2), $MachinePrecision] - 1), $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)))))) < 1e303

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around 0

      \[\leadsto -1 \cdot x1 + x2 \cdot -6 \]
   9. Step-by-step derivation

   10. Applied rewrites 38.8%

       \[\leadsto -1 \cdot x1 + x2 \cdot -6 \]

   if 1e303 < (+.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 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 37.7% accurate, 11.4× speedup

Math

\[\begin{array}{l} t_0 := x2 \cdot \left(-12 \cdot x1 - 6\right)\\ \mathbf{if}\;x2 \leq \frac{-352281387416075}{146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x2 \leq \frac{1780551949697837}{50872912848509630386961759877939283730657641008879914553804457182037637617627197811290223700497087789481581959483591006819830334885554237978846405428549423569451580654251209705071092879576217840034217957579701248029256805705844583825408}:\\ \;\;\;\;x1 \cdot -1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* x2 (- (* -12 x1) 6))))
  (if (<=
       x2
       -352281387416075/146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936)
    t_0
    (if (<=
         x2
         1780551949697837/50872912848509630386961759877939283730657641008879914553804457182037637617627197811290223700497087789481581959483591006819830334885554237978846405428549423569451580654251209705071092879576217840034217957579701248029256805705844583825408)
      (* x1 -1)
      t_0))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((-12.0 * x1) - 6.0);
	double tmp;
	if (x2 <= -2.4e-93) {
		tmp = t_0;
	} else if (x2 <= 3.5e-221) {
		tmp = x1 * -1.0;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x2 * (((-12.0d0) * x1) - 6.0d0)
    if (x2 <= (-2.4d-93)) then
        tmp = t_0
    else if (x2 <= 3.5d-221) then
        tmp = x1 * (-1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * ((-12.0 * x1) - 6.0);
	double tmp;
	if (x2 <= -2.4e-93) {
		tmp = t_0;
	} else if (x2 <= 3.5e-221) {
		tmp = x1 * -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * ((-12.0 * x1) - 6.0)
	tmp = 0
	if x2 <= -2.4e-93:
		tmp = t_0
	elif x2 <= 3.5e-221:
		tmp = x1 * -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(-12.0 * x1) - 6.0))
	tmp = 0.0
	if (x2 <= -2.4e-93)
		tmp = t_0;
	elseif (x2 <= 3.5e-221)
		tmp = Float64(x1 * -1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * ((-12.0 * x1) - 6.0);
	tmp = 0.0;
	if (x2 <= -2.4e-93)
		tmp = t_0;
	elseif (x2 <= 3.5e-221)
		tmp = x1 * -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(-12 * x1), $MachinePrecision] - 6), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -352281387416075/146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936], t$95$0, If[LessEqual[x2, 1780551949697837/50872912848509630386961759877939283730657641008879914553804457182037637617627197811290223700497087789481581959483591006819830334885554237978846405428549423569451580654251209705071092879576217840034217957579701248029256805705844583825408], N[(x1 * -1), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.4000000000000001e-93 or 3.4999999999999999e-221 < x2

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around inf

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

       1. lower-*.f64 N/A

          \[\leadsto x2 \cdot \left(-12 \cdot x1 - 6\right) \]

       2. lower--.f64 N/A

          \[\leadsto x2 \cdot \left(-12 \cdot x1 - 6\right) \]

       3. lower-*.f64 32.8%

          \[\leadsto x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   13. Applied rewrites 32.8%

       \[\leadsto x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

   if -2.4000000000000001e-93 < x2 < 3.4999999999999999e-221

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

       \[\leadsto x1 \cdot -1 \]
   12. Step-by-step derivation

   13. Applied rewrites 13.9%

       \[\leadsto x1 \cdot -1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 20.3% accurate, 21.3× speedup

Math

\[x1 \cdot \left(-12 \cdot x2 - 1\right) \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (* x1 (- (* -12 x2) 1)))

C

double code(double x1, double x2) {
	return x1 * ((-12.0 * x2) - 1.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 * (((-12.0d0) * x2) - 1.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x1 * ((-12.0 * x2) - 1.0);
}

Python

def code(x1, x2):
	return x1 * ((-12.0 * x2) - 1.0)

Julia

function code(x1, x2)
	return Float64(x1 * Float64(Float64(-12.0 * x2) - 1.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 * ((-12.0 * x2) - 1.0);
end

Wolfram

code[x1_, x2_] := N[(x1 * N[(N[(-12 * x2), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.9%

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

2. Taylor expanded in x1 around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower--.f64 N/A

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

4. Applied rewrites 55.0%

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

5. Taylor expanded in x2 around 0

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

   1. lower-+.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

   3. lower-*.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

   4. lower--.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   5. lower-*.f64 44.7%

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

7. Applied rewrites 44.7%

   \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

8. Taylor expanded in x1 around inf

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

   1. lower-*.f64 N/A

      \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   2. lower--.f64 N/A

      \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   3. lower-*.f64 20.3%

      \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

10. Applied rewrites 20.3%

    \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]
11. Add Preprocessing

Alternative 26: 19.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \leq 10000000000000000065284077450682265568456642148886267118448844545520511777838181142510337509988867035816342470187175785193750117648543530356184548650438281396224:\\ \;\;\;\;x1 \cdot -1\\ \mathbf{else}:\\ \;\;\;\;-12 \cdot \left(x1 \cdot x2\right)\\ \end{array} \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (let* ((t_0 (* (* 3 x1) x1))
       (t_1 (+ (* x1 x1) 1))
       (t_2 (/ (- (+ t_0 (* 2 x2)) x1) t_1)))
  (if (<=
       (+
        x1
        (+
         (+
          (+
           (+
            (*
             (+
              (* (* (* 2 x1) t_2) (- t_2 3))
              (* (* x1 x1) (- (* 4 t_2) 6)))
             t_1)
            (* t_0 t_2))
           (* (* x1 x1) x1))
          x1)
         (* 3 (/ (- (- t_0 (* 2 x2)) x1) t_1))))
       10000000000000000065284077450682265568456642148886267118448844545520511777838181142510337509988867035816342470187175785193750117648543530356184548650438281396224)
    (* x1 -1)
    (* -12 (* x1 x2)))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+160) {
		tmp = x1 * -1.0;
	} else {
		tmp = -12.0 * (x1 * 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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((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)))) <= 1d+160) then
        tmp = x1 * (-1.0d0)
    else
        tmp = (-12.0d0) * (x1 * x2)
    end if
    code = tmp
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;
	double tmp;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+160) {
		tmp = x1 * -1.0;
	} else {
		tmp = -12.0 * (x1 * x2);
	}
	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
	tmp = 0
	if (x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+160:
		tmp = x1 * -1.0
	else:
		tmp = -12.0 * (x1 * x2)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)))) <= 1e+160)
		tmp = Float64(x1 * -1.0);
	else
		tmp = Float64(-12.0 * Float64(x1 * x2));
	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;
	tmp = 0.0;
	if ((x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))) <= 1e+160)
		tmp = x1 * -1.0;
	else
		tmp = -12.0 * (x1 * x2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4 * t$95$2), $MachinePrecision] - 6), $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 * N[(N[(N[(t$95$0 - N[(2 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 10000000000000000065284077450682265568456642148886267118448844545520511777838181142510337509988867035816342470187175785193750117648543530356184548650438281396224], N[(x1 * -1), $MachinePrecision], N[(-12 * N[(x1 * x2), $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)))))) < 1e160

   1. Initial program 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around 0

       \[\leadsto x1 \cdot -1 \]
   12. Step-by-step derivation

   13. Applied rewrites 13.9%

       \[\leadsto x1 \cdot -1 \]

   if 1e160 < (+.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 70.9%

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

   2. Taylor expanded in x1 around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in x2 around 0

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

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

      4. lower--.f64 N/A

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

      5. lower-*.f64 44.7%

         \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

   8. Taylor expanded in x1 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      2. lower--.f64 N/A

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

      3. lower-*.f64 20.3%

         \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   10. Applied rewrites 20.3%

       \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

   11. Taylor expanded in x2 around inf

       \[\leadsto -12 \cdot \left(x1 \cdot x2\right) \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -12 \cdot \left(x1 \cdot x2\right) \]

       2. lower-*.f64 9.1%

          \[\leadsto -12 \cdot \left(x1 \cdot x2\right) \]

   13. Applied rewrites 9.1%

       \[\leadsto -12 \cdot \left(x1 \cdot x2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 13.9% accurate, 49.7× speedup

Math

\[x1 \cdot -1 \]

FPCore

(FPCore (x1 x2)
  :precision binary64
  (* x1 -1))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x1, x2)
use fmin_fmax_functions
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 * (-1.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x1 * -1.0;
}

Python

def code(x1, x2):
	return x1 * -1.0

Julia

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

MATLAB

function tmp = code(x1, x2)
	tmp = x1 * -1.0;
end

Wolfram

code[x1_, x2_] := N[(x1 * -1), $MachinePrecision]

Derivation

1. Initial program 70.9%

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

2. Taylor expanded in x1 around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower--.f64 N/A

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

4. Applied rewrites 55.0%

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

5. Taylor expanded in x2 around 0

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

   1. lower-+.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \color{blue}{\left(-12 \cdot x1 - 6\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(\color{blue}{-12 \cdot x1} - 6\right) \]

   3. lower-*.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - \color{blue}{6}\right) \]

   4. lower--.f64 N/A

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

   5. lower-*.f64 44.7%

      \[\leadsto -1 \cdot x1 + x2 \cdot \left(-12 \cdot x1 - 6\right) \]

7. Applied rewrites 44.7%

   \[\leadsto -1 \cdot x1 + \color{blue}{x2 \cdot \left(-12 \cdot x1 - 6\right)} \]

8. Taylor expanded in x1 around inf

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

   1. lower-*.f64 N/A

      \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   2. lower--.f64 N/A

      \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

   3. lower-*.f64 20.3%

      \[\leadsto x1 \cdot \left(-12 \cdot x2 - 1\right) \]

10. Applied rewrites 20.3%

    \[\leadsto x1 \cdot \left(-12 \cdot x2 - \color{blue}{1}\right) \]

11. Taylor expanded in x2 around 0

    \[\leadsto x1 \cdot -1 \]
12. Step-by-step derivation

13. Applied rewrites 13.9%

    \[\leadsto x1 \cdot -1 \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))))))