(* (+ (* (+ z2 (+ z1 z0)) z2) (* z1 z0)) (/ (* (+ z2 (+ z1 z0)) z2) (* (- (* (+ (+ z2 (+ z1 z0)) z2) (+ (+ z2 (+ z1 z0)) z2)) 1) (* (+ (+ z2 (+ z1 z0)) z2) (+ (+ z2 (+ z1 z0)) z2)))))

Percentage Accurate: 47.4% → 88.2%

Time: 5.8s

Alternatives: 19

Speedup: 2.1×

Specification

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_0 \cdot z2\\ t_3 := t\_1 \cdot t\_1\\ \left(t\_2 + z1 \cdot z0\right) \cdot \frac{t\_2}{\left(t\_3 - 1\right) \cdot t\_3} \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_0 z2))
       (t_3 (* t_1 t_1)))
  (* (+ t_2 (* z1 z0)) (/ t_2 (* (- t_3 1.0) t_3)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_0 * z2;
	double t_3 = t_1 * t_1;
	return (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3));
}

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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_0 * z2
    t_3 = t_1 * t_1
    code = (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0d0) * t_3))
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_0 * z2;
	double t_3 = t_1 * t_1;
	return (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3));
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_0 * z2
	t_3 = t_1 * t_1
	return (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3))

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_0 * z2)
	t_3 = Float64(t_1 * t_1)
	return Float64(Float64(t_2 + Float64(z1 * z0)) * Float64(t_2 / Float64(Float64(t_3 - 1.0) * t_3)))
end

MATLAB

function tmp = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_0 * z2;
	t_3 = t_1 * t_1;
	tmp = (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3));
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * t$95$1), $MachinePrecision]}, N[(N[(t$95$2 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 / N[(N[(t$95$3 - 1.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Initial Program: 47.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_0 \cdot z2\\ t_3 := t\_1 \cdot t\_1\\ \left(t\_2 + z1 \cdot z0\right) \cdot \frac{t\_2}{\left(t\_3 - 1\right) \cdot t\_3} \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_0 z2))
       (t_3 (* t_1 t_1)))
  (* (+ t_2 (* z1 z0)) (/ t_2 (* (- t_3 1.0) t_3)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_0 * z2;
	double t_3 = t_1 * t_1;
	return (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3));
}

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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_0 * z2
    t_3 = t_1 * t_1
    code = (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0d0) * t_3))
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_0 * z2;
	double t_3 = t_1 * t_1;
	return (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3));
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_0 * z2
	t_3 = t_1 * t_1
	return (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3))

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_0 * z2)
	t_3 = Float64(t_1 * t_1)
	return Float64(Float64(t_2 + Float64(z1 * z0)) * Float64(t_2 / Float64(Float64(t_3 - 1.0) * t_3)))
end

MATLAB

function tmp = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_0 * z2;
	t_3 = t_1 * t_1;
	tmp = (t_2 + (z1 * z0)) * (t_2 / ((t_3 - 1.0) * t_3));
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * t$95$1), $MachinePrecision]}, N[(N[(t$95$2 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 / N[(N[(t$95$3 - 1.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Alternative 1: 88.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ \mathbf{if}\;\left(t\_3 + z1 \cdot z0\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2} \leq 0.1:\\ \;\;\;\;\frac{\frac{t\_0}{t\_1 - -1}}{t\_1 - 1} \cdot \left(\frac{\frac{z2}{t\_1}}{t\_1} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2)))
  (if (<= (* (+ t_3 (* z1 z0)) (/ t_3 (* (- t_2 1.0) t_2))) 0.1)
    (*
     (/ (/ t_0 (- t_1 -1.0)) (- t_1 1.0))
     (* (/ (/ z2 t_1) t_1) (+ (* z0 z1) (* (+ (+ z0 z1) z2) z2))))
    (/
     (-
      (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
      (* 0.125 (+ z0 z1)))
     z2))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1) {
		tmp = ((t_0 / (t_1 - -1.0)) / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0d0) * t_2))) <= 0.1d0) then
        tmp = ((t_0 / (t_1 - (-1.0d0))) / (t_1 - 1.0d0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)))
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1) {
		tmp = ((t_0 / (t_1 - -1.0)) / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	tmp = 0
	if ((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1:
		tmp = ((t_0 / (t_1 - -1.0)) / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)))
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	tmp = 0.0
	if (Float64(Float64(t_3 + Float64(z1 * z0)) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2))) <= 0.1)
		tmp = Float64(Float64(Float64(t_0 / Float64(t_1 - -1.0)) / Float64(t_1 - 1.0)) * Float64(Float64(Float64(z2 / t_1) / t_1) * Float64(Float64(z0 * z1) + Float64(Float64(Float64(z0 + z1) + z2) * z2))));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	tmp = 0.0;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1)
		tmp = ((t_0 / (t_1 - -1.0)) / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)));
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.1], N[(N[(N[(t$95$0 / N[(t$95$1 - -1.0), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(z2 / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(N[(z0 * z1), $MachinePrecision] + N[(N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 0.10000000000000001

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. difference-of-sqr-1 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(z2 + \left(\left(z0 + z1\right) + z2\right)\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \color{blue}{\left(\left(z0 + z1\right) + z2\right)}\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z0 + z1\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. associate-+l+ N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\color{blue}{\left(z2 + \left(z1 + z0\right)\right)} + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   7. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - -1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   if 0.10000000000000001 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ t_4 := \left(z0 + z1\right) + z2\\ t_5 := t\_4 \cdot z2\\ t_6 := t\_4 + z2\\ t_7 := t\_6 \cdot t\_6\\ \mathbf{if}\;\left(t\_3 + z1 \cdot z0\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2} \leq 0.1:\\ \;\;\;\;\frac{z0 \cdot z1 + t\_5}{t\_7 - 1} \cdot \frac{t\_5}{t\_7}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2))
       (t_4 (+ (+ z0 z1) z2))
       (t_5 (* t_4 z2))
       (t_6 (+ t_4 z2))
       (t_7 (* t_6 t_6)))
  (if (<= (* (+ t_3 (* z1 z0)) (/ t_3 (* (- t_2 1.0) t_2))) 0.1)
    (* (/ (+ (* z0 z1) t_5) (- t_7 1.0)) (/ t_5 t_7))
    (/
     (-
      (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
      (* 0.125 (+ z0 z1)))
     z2))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (z0 + z1) + z2;
	double t_5 = t_4 * z2;
	double t_6 = t_4 + z2;
	double t_7 = t_6 * t_6;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1) {
		tmp = (((z0 * z1) + t_5) / (t_7 - 1.0)) * (t_5 / t_7);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    t_4 = (z0 + z1) + z2
    t_5 = t_4 * z2
    t_6 = t_4 + z2
    t_7 = t_6 * t_6
    if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0d0) * t_2))) <= 0.1d0) then
        tmp = (((z0 * z1) + t_5) / (t_7 - 1.0d0)) * (t_5 / t_7)
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (z0 + z1) + z2;
	double t_5 = t_4 * z2;
	double t_6 = t_4 + z2;
	double t_7 = t_6 * t_6;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1) {
		tmp = (((z0 * z1) + t_5) / (t_7 - 1.0)) * (t_5 / t_7);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	t_4 = (z0 + z1) + z2
	t_5 = t_4 * z2
	t_6 = t_4 + z2
	t_7 = t_6 * t_6
	tmp = 0
	if ((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1:
		tmp = (((z0 * z1) + t_5) / (t_7 - 1.0)) * (t_5 / t_7)
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	t_4 = Float64(Float64(z0 + z1) + z2)
	t_5 = Float64(t_4 * z2)
	t_6 = Float64(t_4 + z2)
	t_7 = Float64(t_6 * t_6)
	tmp = 0.0
	if (Float64(Float64(t_3 + Float64(z1 * z0)) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2))) <= 0.1)
		tmp = Float64(Float64(Float64(Float64(z0 * z1) + t_5) / Float64(t_7 - 1.0)) * Float64(t_5 / t_7));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	t_4 = (z0 + z1) + z2;
	t_5 = t_4 * z2;
	t_6 = t_4 + z2;
	t_7 = t_6 * t_6;
	tmp = 0.0;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1)
		tmp = (((z0 * z1) + t_5) / (t_7 - 1.0)) * (t_5 / t_7);
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * z2), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 + z2), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 * t$95$6), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.1], N[(N[(N[(N[(z0 * z1), $MachinePrecision] + t$95$5), $MachinePrecision] / N[(t$95$7 - 1.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 / t$95$7), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 0.10000000000000001

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      5. times-frac N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}} \]

   3. Applied rewrites 57.8%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{\left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \]

   if 0.10000000000000001 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ t_4 := \left(z0 + z1\right) + z2\\ t_5 := t\_4 + z2\\ t_6 := t\_5 \cdot t\_5\\ \mathbf{if}\;\left(t\_3 + z1 \cdot z0\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2} \leq 0.1:\\ \;\;\;\;\left(\left(z0 \cdot z1 + t\_4 \cdot z2\right) \cdot \frac{t\_4}{t\_6 - 1}\right) \cdot \frac{z2}{t\_6}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2))
       (t_4 (+ (+ z0 z1) z2))
       (t_5 (+ t_4 z2))
       (t_6 (* t_5 t_5)))
  (if (<= (* (+ t_3 (* z1 z0)) (/ t_3 (* (- t_2 1.0) t_2))) 0.1)
    (* (* (+ (* z0 z1) (* t_4 z2)) (/ t_4 (- t_6 1.0))) (/ z2 t_6))
    (/
     (-
      (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
      (* 0.125 (+ z0 z1)))
     z2))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (z0 + z1) + z2;
	double t_5 = t_4 + z2;
	double t_6 = t_5 * t_5;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1) {
		tmp = (((z0 * z1) + (t_4 * z2)) * (t_4 / (t_6 - 1.0))) * (z2 / t_6);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    t_4 = (z0 + z1) + z2
    t_5 = t_4 + z2
    t_6 = t_5 * t_5
    if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0d0) * t_2))) <= 0.1d0) then
        tmp = (((z0 * z1) + (t_4 * z2)) * (t_4 / (t_6 - 1.0d0))) * (z2 / t_6)
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (z0 + z1) + z2;
	double t_5 = t_4 + z2;
	double t_6 = t_5 * t_5;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1) {
		tmp = (((z0 * z1) + (t_4 * z2)) * (t_4 / (t_6 - 1.0))) * (z2 / t_6);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	t_4 = (z0 + z1) + z2
	t_5 = t_4 + z2
	t_6 = t_5 * t_5
	tmp = 0
	if ((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1:
		tmp = (((z0 * z1) + (t_4 * z2)) * (t_4 / (t_6 - 1.0))) * (z2 / t_6)
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	t_4 = Float64(Float64(z0 + z1) + z2)
	t_5 = Float64(t_4 + z2)
	t_6 = Float64(t_5 * t_5)
	tmp = 0.0
	if (Float64(Float64(t_3 + Float64(z1 * z0)) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2))) <= 0.1)
		tmp = Float64(Float64(Float64(Float64(z0 * z1) + Float64(t_4 * z2)) * Float64(t_4 / Float64(t_6 - 1.0))) * Float64(z2 / t_6));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	t_4 = (z0 + z1) + z2;
	t_5 = t_4 + z2;
	t_6 = t_5 * t_5;
	tmp = 0.0;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= 0.1)
		tmp = (((z0 * z1) + (t_4 * z2)) * (t_4 / (t_6 - 1.0))) * (z2 / t_6);
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + z2), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 * t$95$5), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.1], N[(N[(N[(N[(z0 * z1), $MachinePrecision] + N[(t$95$4 * z2), $MachinePrecision]), $MachinePrecision] * N[(t$95$4 / N[(t$95$6 - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z2 / t$95$6), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 0.10000000000000001

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      5. times-frac N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1}\right) \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}} \]

   3. Applied rewrites 56.1%

      \[\leadsto \color{blue}{\left(\left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right) \cdot \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}\right) \cdot \frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \]

   if 0.10000000000000001 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 83.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(\mathsf{min}\left(z1, z0\right) + \mathsf{max}\left(z1, z0\right)\right)\\ t_1 := t\_0 \cdot z2\\ t_2 := \mathsf{max}\left(z1, z0\right) + z2\\ t_3 := \mathsf{max}\left(z1, z0\right) + \mathsf{min}\left(z1, z0\right)\\ t_4 := t\_3 + z2\\ t_5 := t\_2 + z2\\ t_6 := t\_4 + z2\\ t_7 := t\_6 \cdot t\_6\\ t_8 := t\_0 + z2\\ t_9 := t\_8 \cdot t\_8\\ t_10 := \left(t\_1 + \mathsf{min}\left(z1, z0\right) \cdot \mathsf{max}\left(z1, z0\right)\right) \cdot \frac{t\_1}{\left(t\_9 - 1\right) \cdot t\_9}\\ t_11 := \mathsf{max}\left(z1, z0\right) \cdot \mathsf{min}\left(z1, z0\right)\\ \mathbf{if}\;t\_10 \leq -5 \cdot 10^{-286}:\\ \;\;\;\;t\_10\\ \mathbf{elif}\;t\_10 \leq 0:\\ \;\;\;\;\frac{t\_2}{t\_5 \cdot t\_5 - 1} \cdot \left(\frac{\frac{z2}{t\_8}}{t\_8} \cdot \left(t\_11 + t\_2 \cdot z2\right)\right)\\ \mathbf{elif}\;t\_10 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\left(\left(t\_11 + t\_4 \cdot z2\right) \cdot t\_4\right) \cdot \frac{z2}{\left(t\_7 - 1\right) \cdot t\_7}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot \mathsf{max}\left(z1, z0\right) + 2 \cdot \mathsf{min}\left(z1, z0\right)\right)\right) - 0.125 \cdot t\_3}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ (fmin z1 z0) (fmax z1 z0))))
       (t_1 (* t_0 z2))
       (t_2 (+ (fmax z1 z0) z2))
       (t_3 (+ (fmax z1 z0) (fmin z1 z0)))
       (t_4 (+ t_3 z2))
       (t_5 (+ t_2 z2))
       (t_6 (+ t_4 z2))
       (t_7 (* t_6 t_6))
       (t_8 (+ t_0 z2))
       (t_9 (* t_8 t_8))
       (t_10
        (*
         (+ t_1 (* (fmin z1 z0) (fmax z1 z0)))
         (/ t_1 (* (- t_9 1.0) t_9))))
       (t_11 (* (fmax z1 z0) (fmin z1 z0))))
  (if (<= t_10 -5e-286)
    t_10
    (if (<= t_10 0.0)
      (*
       (/ t_2 (- (* t_5 t_5) 1.0))
       (* (/ (/ z2 t_8) t_8) (+ t_11 (* t_2 z2))))
      (if (<= t_10 4e-11)
        (* (* (+ t_11 (* t_4 z2)) t_4) (/ z2 (* (- t_7 1.0) t_7)))
        (/
         (-
          (+
           (* 0.0625 z2)
           (* 0.0625 (+ (* 2.0 (fmax z1 z0)) (* 2.0 (fmin z1 z0)))))
          (* 0.125 t_3))
         z2))))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0));
	double t_1 = t_0 * z2;
	double t_2 = fmax(z1, z0) + z2;
	double t_3 = fmax(z1, z0) + fmin(z1, z0);
	double t_4 = t_3 + z2;
	double t_5 = t_2 + z2;
	double t_6 = t_4 + z2;
	double t_7 = t_6 * t_6;
	double t_8 = t_0 + z2;
	double t_9 = t_8 * t_8;
	double t_10 = (t_1 + (fmin(z1, z0) * fmax(z1, z0))) * (t_1 / ((t_9 - 1.0) * t_9));
	double t_11 = fmax(z1, z0) * fmin(z1, z0);
	double tmp;
	if (t_10 <= -5e-286) {
		tmp = t_10;
	} else if (t_10 <= 0.0) {
		tmp = (t_2 / ((t_5 * t_5) - 1.0)) * (((z2 / t_8) / t_8) * (t_11 + (t_2 * z2)));
	} else if (t_10 <= 4e-11) {
		tmp = ((t_11 + (t_4 * z2)) * t_4) * (z2 / ((t_7 - 1.0) * t_7));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_3)) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0))
    t_1 = t_0 * z2
    t_2 = fmax(z1, z0) + z2
    t_3 = fmax(z1, z0) + fmin(z1, z0)
    t_4 = t_3 + z2
    t_5 = t_2 + z2
    t_6 = t_4 + z2
    t_7 = t_6 * t_6
    t_8 = t_0 + z2
    t_9 = t_8 * t_8
    t_10 = (t_1 + (fmin(z1, z0) * fmax(z1, z0))) * (t_1 / ((t_9 - 1.0d0) * t_9))
    t_11 = fmax(z1, z0) * fmin(z1, z0)
    if (t_10 <= (-5d-286)) then
        tmp = t_10
    else if (t_10 <= 0.0d0) then
        tmp = (t_2 / ((t_5 * t_5) - 1.0d0)) * (((z2 / t_8) / t_8) * (t_11 + (t_2 * z2)))
    else if (t_10 <= 4d-11) then
        tmp = ((t_11 + (t_4 * z2)) * t_4) * (z2 / ((t_7 - 1.0d0) * t_7))
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * fmax(z1, z0)) + (2.0d0 * fmin(z1, z0))))) - (0.125d0 * t_3)) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0));
	double t_1 = t_0 * z2;
	double t_2 = fmax(z1, z0) + z2;
	double t_3 = fmax(z1, z0) + fmin(z1, z0);
	double t_4 = t_3 + z2;
	double t_5 = t_2 + z2;
	double t_6 = t_4 + z2;
	double t_7 = t_6 * t_6;
	double t_8 = t_0 + z2;
	double t_9 = t_8 * t_8;
	double t_10 = (t_1 + (fmin(z1, z0) * fmax(z1, z0))) * (t_1 / ((t_9 - 1.0) * t_9));
	double t_11 = fmax(z1, z0) * fmin(z1, z0);
	double tmp;
	if (t_10 <= -5e-286) {
		tmp = t_10;
	} else if (t_10 <= 0.0) {
		tmp = (t_2 / ((t_5 * t_5) - 1.0)) * (((z2 / t_8) / t_8) * (t_11 + (t_2 * z2)));
	} else if (t_10 <= 4e-11) {
		tmp = ((t_11 + (t_4 * z2)) * t_4) * (z2 / ((t_7 - 1.0) * t_7));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_3)) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0))
	t_1 = t_0 * z2
	t_2 = fmax(z1, z0) + z2
	t_3 = fmax(z1, z0) + fmin(z1, z0)
	t_4 = t_3 + z2
	t_5 = t_2 + z2
	t_6 = t_4 + z2
	t_7 = t_6 * t_6
	t_8 = t_0 + z2
	t_9 = t_8 * t_8
	t_10 = (t_1 + (fmin(z1, z0) * fmax(z1, z0))) * (t_1 / ((t_9 - 1.0) * t_9))
	t_11 = fmax(z1, z0) * fmin(z1, z0)
	tmp = 0
	if t_10 <= -5e-286:
		tmp = t_10
	elif t_10 <= 0.0:
		tmp = (t_2 / ((t_5 * t_5) - 1.0)) * (((z2 / t_8) / t_8) * (t_11 + (t_2 * z2)))
	elif t_10 <= 4e-11:
		tmp = ((t_11 + (t_4 * z2)) * t_4) * (z2 / ((t_7 - 1.0) * t_7))
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_3)) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(fmin(z1, z0) + fmax(z1, z0)))
	t_1 = Float64(t_0 * z2)
	t_2 = Float64(fmax(z1, z0) + z2)
	t_3 = Float64(fmax(z1, z0) + fmin(z1, z0))
	t_4 = Float64(t_3 + z2)
	t_5 = Float64(t_2 + z2)
	t_6 = Float64(t_4 + z2)
	t_7 = Float64(t_6 * t_6)
	t_8 = Float64(t_0 + z2)
	t_9 = Float64(t_8 * t_8)
	t_10 = Float64(Float64(t_1 + Float64(fmin(z1, z0) * fmax(z1, z0))) * Float64(t_1 / Float64(Float64(t_9 - 1.0) * t_9)))
	t_11 = Float64(fmax(z1, z0) * fmin(z1, z0))
	tmp = 0.0
	if (t_10 <= -5e-286)
		tmp = t_10;
	elseif (t_10 <= 0.0)
		tmp = Float64(Float64(t_2 / Float64(Float64(t_5 * t_5) - 1.0)) * Float64(Float64(Float64(z2 / t_8) / t_8) * Float64(t_11 + Float64(t_2 * z2))));
	elseif (t_10 <= 4e-11)
		tmp = Float64(Float64(Float64(t_11 + Float64(t_4 * z2)) * t_4) * Float64(z2 / Float64(Float64(t_7 - 1.0) * t_7)));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * fmax(z1, z0)) + Float64(2.0 * fmin(z1, z0))))) - Float64(0.125 * t_3)) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (min(z1, z0) + max(z1, z0));
	t_1 = t_0 * z2;
	t_2 = max(z1, z0) + z2;
	t_3 = max(z1, z0) + min(z1, z0);
	t_4 = t_3 + z2;
	t_5 = t_2 + z2;
	t_6 = t_4 + z2;
	t_7 = t_6 * t_6;
	t_8 = t_0 + z2;
	t_9 = t_8 * t_8;
	t_10 = (t_1 + (min(z1, z0) * max(z1, z0))) * (t_1 / ((t_9 - 1.0) * t_9));
	t_11 = max(z1, z0) * min(z1, z0);
	tmp = 0.0;
	if (t_10 <= -5e-286)
		tmp = t_10;
	elseif (t_10 <= 0.0)
		tmp = (t_2 / ((t_5 * t_5) - 1.0)) * (((z2 / t_8) / t_8) * (t_11 + (t_2 * z2)));
	elseif (t_10 <= 4e-11)
		tmp = ((t_11 + (t_4 * z2)) * t_4) * (z2 / ((t_7 - 1.0) * t_7));
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * max(z1, z0)) + (2.0 * min(z1, z0))))) - (0.125 * t_3)) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(N[Min[z1, z0], $MachinePrecision] + N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$2 = N[(N[Max[z1, z0], $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$3 = N[(N[Max[z1, z0], $MachinePrecision] + N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + z2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 + z2), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 + z2), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$8 * t$95$8), $MachinePrecision]}, Block[{t$95$10 = N[(N[(t$95$1 + N[(N[Min[z1, z0], $MachinePrecision] * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 / N[(N[(t$95$9 - 1.0), $MachinePrecision] * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(N[Max[z1, z0], $MachinePrecision] * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$10, -5e-286], t$95$10, If[LessEqual[t$95$10, 0.0], N[(N[(t$95$2 / N[(N[(t$95$5 * t$95$5), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(z2 / t$95$8), $MachinePrecision] / t$95$8), $MachinePrecision] * N[(t$95$11 + N[(t$95$2 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$10, 4e-11], N[(N[(N[(t$95$11 + N[(t$95$4 * z2), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(z2 / N[(N[(t$95$7 - 1.0), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * t$95$3), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -5.0000000000000004e-286

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   if -5.0000000000000004e-286 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 0.0

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z1 around 0

      \[\leadsto \frac{\color{blue}{z0} + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 52.5%

      \[\leadsto \frac{\color{blue}{z0} + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   9. Taylor expanded in z1 around 0

      \[\leadsto \frac{z0 + z2}{\left(\left(\color{blue}{z0} + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 54.3%

       \[\leadsto \frac{z0 + z2}{\left(\left(\color{blue}{z0} + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   12. Taylor expanded in z1 around 0

       \[\leadsto \frac{z0 + z2}{\left(\left(z0 + z2\right) + z2\right) \cdot \left(\left(\color{blue}{z0} + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 52.3%

       \[\leadsto \frac{z0 + z2}{\left(\left(z0 + z2\right) + z2\right) \cdot \left(\left(\color{blue}{z0} + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   15. Taylor expanded in z1 around 0

       \[\leadsto \frac{z0 + z2}{\left(\left(z0 + z2\right) + z2\right) \cdot \left(\left(z0 + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\color{blue}{z0} + z2\right) \cdot z2\right)\right) \]
   16. Step-by-step derivation

   17. Applied rewrites 53.4%

       \[\leadsto \frac{z0 + z2}{\left(\left(z0 + z2\right) + z2\right) \cdot \left(\left(z0 + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\color{blue}{z0} + z2\right) \cdot z2\right)\right) \]

   if 0.0 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      4. associate-/l* N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot \frac{z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}\right)} \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(z2 + \left(z1 + z0\right)\right)\right) \cdot \frac{z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

   3. Applied rewrites 31.0%

      \[\leadsto \color{blue}{\left(\left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right) \cdot \left(\left(z0 + z1\right) + z2\right)\right) \cdot \frac{z2}{\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)\right)}} \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 81.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ t_4 := \left(t\_3 + z1 \cdot z0\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2}\\ \mathbf{if}\;t\_4 \leq -4 \cdot 10^{-304}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{1}{t\_1 - 1} \cdot \left(\frac{\frac{z2}{t\_1}}{t\_1} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2))
       (t_4 (* (+ t_3 (* z1 z0)) (/ t_3 (* (- t_2 1.0) t_2)))))
  (if (<= t_4 -4e-304)
    t_4
    (if (<= t_4 4e-11)
      (*
       (/ 1.0 (- t_1 1.0))
       (* (/ (/ z2 t_1) t_1) (+ (* z0 z1) (* (+ (+ z0 z1) z2) z2))))
      (/
       (-
        (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
        (* 0.125 (+ z0 z1)))
       z2)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2));
	double tmp;
	if (t_4 <= -4e-304) {
		tmp = t_4;
	} else if (t_4 <= 4e-11) {
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0d0) * t_2))
    if (t_4 <= (-4d-304)) then
        tmp = t_4
    else if (t_4 <= 4d-11) then
        tmp = (1.0d0 / (t_1 - 1.0d0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)))
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2));
	double tmp;
	if (t_4 <= -4e-304) {
		tmp = t_4;
	} else if (t_4 <= 4e-11) {
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))
	tmp = 0
	if t_4 <= -4e-304:
		tmp = t_4
	elif t_4 <= 4e-11:
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)))
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	t_4 = Float64(Float64(t_3 + Float64(z1 * z0)) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2)))
	tmp = 0.0
	if (t_4 <= -4e-304)
		tmp = t_4;
	elseif (t_4 <= 4e-11)
		tmp = Float64(Float64(1.0 / Float64(t_1 - 1.0)) * Float64(Float64(Float64(z2 / t_1) / t_1) * Float64(Float64(z0 * z1) + Float64(Float64(Float64(z0 + z1) + z2) * z2))));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2));
	tmp = 0.0;
	if (t_4 <= -4e-304)
		tmp = t_4;
	elseif (t_4 <= 4e-11)
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((z0 * z1) + (((z0 + z1) + z2) * z2)));
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -4e-304], t$95$4, If[LessEqual[t$95$4, 4e-11], N[(N[(1.0 / N[(t$95$1 - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(z2 / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(N[(z0 * z1), $MachinePrecision] + N[(N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -3.9999999999999999e-304

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   if -3.9999999999999999e-304 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. difference-of-sqr-1 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(z2 + \left(\left(z0 + z1\right) + z2\right)\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \color{blue}{\left(\left(z0 + z1\right) + z2\right)}\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z0 + z1\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. associate-+l+ N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\color{blue}{\left(z2 + \left(z1 + z0\right)\right)} + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   7. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - -1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 81.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \left(z0 + z1\right) + z2\\ t_1 := z2 + \left(z1 + z0\right)\\ t_2 := t\_1 + z2\\ t_3 := t\_2 \cdot t\_2\\ t_4 := t\_1 \cdot z2\\ t_5 := t\_4 + z1 \cdot z0\\ t_6 := t\_5 \cdot \frac{t\_4}{\left(t\_3 - 1\right) \cdot t\_3}\\ t_7 := t\_0 + z2\\ \mathbf{if}\;t\_6 \leq -4 \cdot 10^{-304}:\\ \;\;\;\;t\_5 \cdot \frac{t\_4}{t\_7 \cdot \left(\left(t\_7 \cdot t\_7 - 1\right) \cdot t\_7\right)}\\ \mathbf{elif}\;t\_6 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{1}{t\_2 - 1} \cdot \left(\frac{\frac{z2}{t\_2}}{t\_2} \cdot \left(z0 \cdot z1 + t\_0 \cdot z2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ (+ z0 z1) z2))
       (t_1 (+ z2 (+ z1 z0)))
       (t_2 (+ t_1 z2))
       (t_3 (* t_2 t_2))
       (t_4 (* t_1 z2))
       (t_5 (+ t_4 (* z1 z0)))
       (t_6 (* t_5 (/ t_4 (* (- t_3 1.0) t_3))))
       (t_7 (+ t_0 z2)))
  (if (<= t_6 -4e-304)
    (* t_5 (/ t_4 (* t_7 (* (- (* t_7 t_7) 1.0) t_7))))
    (if (<= t_6 4e-11)
      (*
       (/ 1.0 (- t_2 1.0))
       (* (/ (/ z2 t_2) t_2) (+ (* z0 z1) (* t_0 z2))))
      (/
       (-
        (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
        (* 0.125 (+ z0 z1)))
       z2)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = (z0 + z1) + z2;
	double t_1 = z2 + (z1 + z0);
	double t_2 = t_1 + z2;
	double t_3 = t_2 * t_2;
	double t_4 = t_1 * z2;
	double t_5 = t_4 + (z1 * z0);
	double t_6 = t_5 * (t_4 / ((t_3 - 1.0) * t_3));
	double t_7 = t_0 + z2;
	double tmp;
	if (t_6 <= -4e-304) {
		tmp = t_5 * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)));
	} else if (t_6 <= 4e-11) {
		tmp = (1.0 / (t_2 - 1.0)) * (((z2 / t_2) / t_2) * ((z0 * z1) + (t_0 * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = (z0 + z1) + z2
    t_1 = z2 + (z1 + z0)
    t_2 = t_1 + z2
    t_3 = t_2 * t_2
    t_4 = t_1 * z2
    t_5 = t_4 + (z1 * z0)
    t_6 = t_5 * (t_4 / ((t_3 - 1.0d0) * t_3))
    t_7 = t_0 + z2
    if (t_6 <= (-4d-304)) then
        tmp = t_5 * (t_4 / (t_7 * (((t_7 * t_7) - 1.0d0) * t_7)))
    else if (t_6 <= 4d-11) then
        tmp = (1.0d0 / (t_2 - 1.0d0)) * (((z2 / t_2) / t_2) * ((z0 * z1) + (t_0 * z2)))
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = (z0 + z1) + z2;
	double t_1 = z2 + (z1 + z0);
	double t_2 = t_1 + z2;
	double t_3 = t_2 * t_2;
	double t_4 = t_1 * z2;
	double t_5 = t_4 + (z1 * z0);
	double t_6 = t_5 * (t_4 / ((t_3 - 1.0) * t_3));
	double t_7 = t_0 + z2;
	double tmp;
	if (t_6 <= -4e-304) {
		tmp = t_5 * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)));
	} else if (t_6 <= 4e-11) {
		tmp = (1.0 / (t_2 - 1.0)) * (((z2 / t_2) / t_2) * ((z0 * z1) + (t_0 * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = (z0 + z1) + z2
	t_1 = z2 + (z1 + z0)
	t_2 = t_1 + z2
	t_3 = t_2 * t_2
	t_4 = t_1 * z2
	t_5 = t_4 + (z1 * z0)
	t_6 = t_5 * (t_4 / ((t_3 - 1.0) * t_3))
	t_7 = t_0 + z2
	tmp = 0
	if t_6 <= -4e-304:
		tmp = t_5 * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)))
	elif t_6 <= 4e-11:
		tmp = (1.0 / (t_2 - 1.0)) * (((z2 / t_2) / t_2) * ((z0 * z1) + (t_0 * z2)))
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(Float64(z0 + z1) + z2)
	t_1 = Float64(z2 + Float64(z1 + z0))
	t_2 = Float64(t_1 + z2)
	t_3 = Float64(t_2 * t_2)
	t_4 = Float64(t_1 * z2)
	t_5 = Float64(t_4 + Float64(z1 * z0))
	t_6 = Float64(t_5 * Float64(t_4 / Float64(Float64(t_3 - 1.0) * t_3)))
	t_7 = Float64(t_0 + z2)
	tmp = 0.0
	if (t_6 <= -4e-304)
		tmp = Float64(t_5 * Float64(t_4 / Float64(t_7 * Float64(Float64(Float64(t_7 * t_7) - 1.0) * t_7))));
	elseif (t_6 <= 4e-11)
		tmp = Float64(Float64(1.0 / Float64(t_2 - 1.0)) * Float64(Float64(Float64(z2 / t_2) / t_2) * Float64(Float64(z0 * z1) + Float64(t_0 * z2))));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = (z0 + z1) + z2;
	t_1 = z2 + (z1 + z0);
	t_2 = t_1 + z2;
	t_3 = t_2 * t_2;
	t_4 = t_1 * z2;
	t_5 = t_4 + (z1 * z0);
	t_6 = t_5 * (t_4 / ((t_3 - 1.0) * t_3));
	t_7 = t_0 + z2;
	tmp = 0.0;
	if (t_6 <= -4e-304)
		tmp = t_5 * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)));
	elseif (t_6 <= 4e-11)
		tmp = (1.0 / (t_2 - 1.0)) * (((z2 / t_2) / t_2) * ((z0 * z1) + (t_0 * z2)));
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$1 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + z2), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * z2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 * N[(t$95$4 / N[(N[(t$95$3 - 1.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$0 + z2), $MachinePrecision]}, If[LessEqual[t$95$6, -4e-304], N[(t$95$5 * N[(t$95$4 / N[(t$95$7 * N[(N[(N[(t$95$7 * t$95$7), $MachinePrecision] - 1.0), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$6, 4e-11], N[(N[(1.0 / N[(t$95$2 - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(z2 / t$95$2), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(N[(z0 * z1), $MachinePrecision] + N[(t$95$0 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -3.9999999999999999e-304

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}} \]

      4. *-commutative N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      6. lift-+.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\color{blue}{\left(z2 + \left(z1 + z0\right)\right)} + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\color{blue}{\left(\left(z1 + z0\right) + z2\right)} + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\color{blue}{\left(\left(z1 + z0\right) + z2\right)} + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\color{blue}{\left(z1 + z0\right)} + z2\right) + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      10. +-commutative N/A

          \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\color{blue}{\left(z0 + z1\right)} + z2\right) + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      11. lower-+.f64 N/A

          \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\color{blue}{\left(z0 + z1\right)} + z2\right) + z2\right) \cdot \left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      12. lower-*.f64 47.4%

          \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \color{blue}{\left(\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

   3. Applied rewrites 47.4%

      \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)\right)}} \]

   if -3.9999999999999999e-304 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. difference-of-sqr-1 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(z2 + \left(\left(z0 + z1\right) + z2\right)\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \color{blue}{\left(\left(z0 + z1\right) + z2\right)}\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z0 + z1\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. associate-+l+ N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\color{blue}{\left(z2 + \left(z1 + z0\right)\right)} + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   7. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - -1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 79.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := \left(z0 + z1\right) + z2\\ t_4 := t\_3 + z2\\ t_5 := t\_4 \cdot t\_4\\ t_6 := t\_0 \cdot z2\\ t_7 := \left(t\_6 + z1 \cdot z0\right) \cdot \frac{t\_6}{\left(t\_2 - 1\right) \cdot t\_2}\\ t_8 := z0 \cdot z1 + t\_3 \cdot z2\\ \mathbf{if}\;t\_7 \leq -4 \cdot 10^{-304}:\\ \;\;\;\;\left(t\_8 \cdot t\_3\right) \cdot \frac{z2}{\left(t\_5 - 1\right) \cdot t\_5}\\ \mathbf{elif}\;t\_7 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{1}{t\_1 - 1} \cdot \left(\frac{\frac{z2}{t\_1}}{t\_1} \cdot t\_8\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (+ (+ z0 z1) z2))
       (t_4 (+ t_3 z2))
       (t_5 (* t_4 t_4))
       (t_6 (* t_0 z2))
       (t_7 (* (+ t_6 (* z1 z0)) (/ t_6 (* (- t_2 1.0) t_2))))
       (t_8 (+ (* z0 z1) (* t_3 z2))))
  (if (<= t_7 -4e-304)
    (* (* t_8 t_3) (/ z2 (* (- t_5 1.0) t_5)))
    (if (<= t_7 4e-11)
      (* (/ 1.0 (- t_1 1.0)) (* (/ (/ z2 t_1) t_1) t_8))
      (/
       (-
        (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
        (* 0.125 (+ z0 z1)))
       z2)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = (z0 + z1) + z2;
	double t_4 = t_3 + z2;
	double t_5 = t_4 * t_4;
	double t_6 = t_0 * z2;
	double t_7 = (t_6 + (z1 * z0)) * (t_6 / ((t_2 - 1.0) * t_2));
	double t_8 = (z0 * z1) + (t_3 * z2);
	double tmp;
	if (t_7 <= -4e-304) {
		tmp = (t_8 * t_3) * (z2 / ((t_5 - 1.0) * t_5));
	} else if (t_7 <= 4e-11) {
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * t_8);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = (z0 + z1) + z2
    t_4 = t_3 + z2
    t_5 = t_4 * t_4
    t_6 = t_0 * z2
    t_7 = (t_6 + (z1 * z0)) * (t_6 / ((t_2 - 1.0d0) * t_2))
    t_8 = (z0 * z1) + (t_3 * z2)
    if (t_7 <= (-4d-304)) then
        tmp = (t_8 * t_3) * (z2 / ((t_5 - 1.0d0) * t_5))
    else if (t_7 <= 4d-11) then
        tmp = (1.0d0 / (t_1 - 1.0d0)) * (((z2 / t_1) / t_1) * t_8)
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = (z0 + z1) + z2;
	double t_4 = t_3 + z2;
	double t_5 = t_4 * t_4;
	double t_6 = t_0 * z2;
	double t_7 = (t_6 + (z1 * z0)) * (t_6 / ((t_2 - 1.0) * t_2));
	double t_8 = (z0 * z1) + (t_3 * z2);
	double tmp;
	if (t_7 <= -4e-304) {
		tmp = (t_8 * t_3) * (z2 / ((t_5 - 1.0) * t_5));
	} else if (t_7 <= 4e-11) {
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * t_8);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = (z0 + z1) + z2
	t_4 = t_3 + z2
	t_5 = t_4 * t_4
	t_6 = t_0 * z2
	t_7 = (t_6 + (z1 * z0)) * (t_6 / ((t_2 - 1.0) * t_2))
	t_8 = (z0 * z1) + (t_3 * z2)
	tmp = 0
	if t_7 <= -4e-304:
		tmp = (t_8 * t_3) * (z2 / ((t_5 - 1.0) * t_5))
	elif t_7 <= 4e-11:
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * t_8)
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(Float64(z0 + z1) + z2)
	t_4 = Float64(t_3 + z2)
	t_5 = Float64(t_4 * t_4)
	t_6 = Float64(t_0 * z2)
	t_7 = Float64(Float64(t_6 + Float64(z1 * z0)) * Float64(t_6 / Float64(Float64(t_2 - 1.0) * t_2)))
	t_8 = Float64(Float64(z0 * z1) + Float64(t_3 * z2))
	tmp = 0.0
	if (t_7 <= -4e-304)
		tmp = Float64(Float64(t_8 * t_3) * Float64(z2 / Float64(Float64(t_5 - 1.0) * t_5)));
	elseif (t_7 <= 4e-11)
		tmp = Float64(Float64(1.0 / Float64(t_1 - 1.0)) * Float64(Float64(Float64(z2 / t_1) / t_1) * t_8));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = (z0 + z1) + z2;
	t_4 = t_3 + z2;
	t_5 = t_4 * t_4;
	t_6 = t_0 * z2;
	t_7 = (t_6 + (z1 * z0)) * (t_6 / ((t_2 - 1.0) * t_2));
	t_8 = (z0 * z1) + (t_3 * z2);
	tmp = 0.0;
	if (t_7 <= -4e-304)
		tmp = (t_8 * t_3) * (z2 / ((t_5 - 1.0) * t_5));
	elseif (t_7 <= 4e-11)
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * t_8);
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + z2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$7 = N[(N[(t$95$6 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$6 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(z0 * z1), $MachinePrecision] + N[(t$95$3 * z2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$7, -4e-304], N[(N[(t$95$8 * t$95$3), $MachinePrecision] * N[(z2 / N[(N[(t$95$5 - 1.0), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$7, 4e-11], N[(N[(1.0 / N[(t$95$1 - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(z2 / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision] * t$95$8), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -3.9999999999999999e-304

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

      4. associate-/l* N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot \frac{z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}\right)} \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(z2 + \left(z1 + z0\right)\right)\right) \cdot \frac{z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

   3. Applied rewrites 31.0%

      \[\leadsto \color{blue}{\left(\left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right) \cdot \left(\left(z0 + z1\right) + z2\right)\right) \cdot \frac{z2}{\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)\right)}} \]

   if -3.9999999999999999e-304 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. difference-of-sqr-1 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(z2 + \left(\left(z0 + z1\right) + z2\right)\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \color{blue}{\left(\left(z0 + z1\right) + z2\right)}\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z0 + z1\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. associate-+l+ N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\color{blue}{\left(z2 + \left(z1 + z0\right)\right)} + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   7. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - -1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 79.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(\mathsf{min}\left(z1, z0\right) + \mathsf{max}\left(z1, z0\right)\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ t_4 := \mathsf{min}\left(z1, z0\right) + z2\\ t_5 := t\_4 \cdot z2\\ t_6 := \mathsf{max}\left(z1, z0\right) + \mathsf{min}\left(z1, z0\right)\\ t_7 := \mathsf{min}\left(z1, z0\right) \cdot \mathsf{max}\left(z1, z0\right)\\ t_8 := \left(t\_3 + t\_7\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2}\\ t_9 := t\_4 + z2\\ t_10 := t\_9 \cdot t\_9\\ \mathbf{if}\;t\_8 \leq -5 \cdot 10^{-286}:\\ \;\;\;\;\left(t\_5 + t\_7\right) \cdot \frac{t\_5}{\left(t\_10 - 1\right) \cdot t\_10}\\ \mathbf{elif}\;t\_8 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{1}{t\_1 - 1} \cdot \left(\frac{\frac{z2}{t\_1}}{t\_1} \cdot \left(\mathsf{max}\left(z1, z0\right) \cdot \mathsf{min}\left(z1, z0\right) + \left(t\_6 + z2\right) \cdot z2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot \mathsf{max}\left(z1, z0\right) + 2 \cdot \mathsf{min}\left(z1, z0\right)\right)\right) - 0.125 \cdot t\_6}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ (fmin z1 z0) (fmax z1 z0))))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2))
       (t_4 (+ (fmin z1 z0) z2))
       (t_5 (* t_4 z2))
       (t_6 (+ (fmax z1 z0) (fmin z1 z0)))
       (t_7 (* (fmin z1 z0) (fmax z1 z0)))
       (t_8 (* (+ t_3 t_7) (/ t_3 (* (- t_2 1.0) t_2))))
       (t_9 (+ t_4 z2))
       (t_10 (* t_9 t_9)))
  (if (<= t_8 -5e-286)
    (* (+ t_5 t_7) (/ t_5 (* (- t_10 1.0) t_10)))
    (if (<= t_8 4e-11)
      (*
       (/ 1.0 (- t_1 1.0))
       (*
        (/ (/ z2 t_1) t_1)
        (+ (* (fmax z1 z0) (fmin z1 z0)) (* (+ t_6 z2) z2))))
      (/
       (-
        (+
         (* 0.0625 z2)
         (* 0.0625 (+ (* 2.0 (fmax z1 z0)) (* 2.0 (fmin z1 z0)))))
        (* 0.125 t_6))
       z2)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0));
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = fmin(z1, z0) + z2;
	double t_5 = t_4 * z2;
	double t_6 = fmax(z1, z0) + fmin(z1, z0);
	double t_7 = fmin(z1, z0) * fmax(z1, z0);
	double t_8 = (t_3 + t_7) * (t_3 / ((t_2 - 1.0) * t_2));
	double t_9 = t_4 + z2;
	double t_10 = t_9 * t_9;
	double tmp;
	if (t_8 <= -5e-286) {
		tmp = (t_5 + t_7) * (t_5 / ((t_10 - 1.0) * t_10));
	} else if (t_8 <= 4e-11) {
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((fmax(z1, z0) * fmin(z1, z0)) + ((t_6 + z2) * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_6)) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0))
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    t_4 = fmin(z1, z0) + z2
    t_5 = t_4 * z2
    t_6 = fmax(z1, z0) + fmin(z1, z0)
    t_7 = fmin(z1, z0) * fmax(z1, z0)
    t_8 = (t_3 + t_7) * (t_3 / ((t_2 - 1.0d0) * t_2))
    t_9 = t_4 + z2
    t_10 = t_9 * t_9
    if (t_8 <= (-5d-286)) then
        tmp = (t_5 + t_7) * (t_5 / ((t_10 - 1.0d0) * t_10))
    else if (t_8 <= 4d-11) then
        tmp = (1.0d0 / (t_1 - 1.0d0)) * (((z2 / t_1) / t_1) * ((fmax(z1, z0) * fmin(z1, z0)) + ((t_6 + z2) * z2)))
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * fmax(z1, z0)) + (2.0d0 * fmin(z1, z0))))) - (0.125d0 * t_6)) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0));
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = fmin(z1, z0) + z2;
	double t_5 = t_4 * z2;
	double t_6 = fmax(z1, z0) + fmin(z1, z0);
	double t_7 = fmin(z1, z0) * fmax(z1, z0);
	double t_8 = (t_3 + t_7) * (t_3 / ((t_2 - 1.0) * t_2));
	double t_9 = t_4 + z2;
	double t_10 = t_9 * t_9;
	double tmp;
	if (t_8 <= -5e-286) {
		tmp = (t_5 + t_7) * (t_5 / ((t_10 - 1.0) * t_10));
	} else if (t_8 <= 4e-11) {
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((fmax(z1, z0) * fmin(z1, z0)) + ((t_6 + z2) * z2)));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_6)) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0))
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	t_4 = fmin(z1, z0) + z2
	t_5 = t_4 * z2
	t_6 = fmax(z1, z0) + fmin(z1, z0)
	t_7 = fmin(z1, z0) * fmax(z1, z0)
	t_8 = (t_3 + t_7) * (t_3 / ((t_2 - 1.0) * t_2))
	t_9 = t_4 + z2
	t_10 = t_9 * t_9
	tmp = 0
	if t_8 <= -5e-286:
		tmp = (t_5 + t_7) * (t_5 / ((t_10 - 1.0) * t_10))
	elif t_8 <= 4e-11:
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((fmax(z1, z0) * fmin(z1, z0)) + ((t_6 + z2) * z2)))
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_6)) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(fmin(z1, z0) + fmax(z1, z0)))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	t_4 = Float64(fmin(z1, z0) + z2)
	t_5 = Float64(t_4 * z2)
	t_6 = Float64(fmax(z1, z0) + fmin(z1, z0))
	t_7 = Float64(fmin(z1, z0) * fmax(z1, z0))
	t_8 = Float64(Float64(t_3 + t_7) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2)))
	t_9 = Float64(t_4 + z2)
	t_10 = Float64(t_9 * t_9)
	tmp = 0.0
	if (t_8 <= -5e-286)
		tmp = Float64(Float64(t_5 + t_7) * Float64(t_5 / Float64(Float64(t_10 - 1.0) * t_10)));
	elseif (t_8 <= 4e-11)
		tmp = Float64(Float64(1.0 / Float64(t_1 - 1.0)) * Float64(Float64(Float64(z2 / t_1) / t_1) * Float64(Float64(fmax(z1, z0) * fmin(z1, z0)) + Float64(Float64(t_6 + z2) * z2))));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * fmax(z1, z0)) + Float64(2.0 * fmin(z1, z0))))) - Float64(0.125 * t_6)) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (min(z1, z0) + max(z1, z0));
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	t_4 = min(z1, z0) + z2;
	t_5 = t_4 * z2;
	t_6 = max(z1, z0) + min(z1, z0);
	t_7 = min(z1, z0) * max(z1, z0);
	t_8 = (t_3 + t_7) * (t_3 / ((t_2 - 1.0) * t_2));
	t_9 = t_4 + z2;
	t_10 = t_9 * t_9;
	tmp = 0.0;
	if (t_8 <= -5e-286)
		tmp = (t_5 + t_7) * (t_5 / ((t_10 - 1.0) * t_10));
	elseif (t_8 <= 4e-11)
		tmp = (1.0 / (t_1 - 1.0)) * (((z2 / t_1) / t_1) * ((max(z1, z0) * min(z1, z0)) + ((t_6 + z2) * z2)));
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * max(z1, z0)) + (2.0 * min(z1, z0))))) - (0.125 * t_6)) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(N[Min[z1, z0], $MachinePrecision] + N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$4 = N[(N[Min[z1, z0], $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * z2), $MachinePrecision]}, Block[{t$95$6 = N[(N[Max[z1, z0], $MachinePrecision] + N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[Min[z1, z0], $MachinePrecision] * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(t$95$3 + t$95$7), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t$95$4 + z2), $MachinePrecision]}, Block[{t$95$10 = N[(t$95$9 * t$95$9), $MachinePrecision]}, If[LessEqual[t$95$8, -5e-286], N[(N[(t$95$5 + t$95$7), $MachinePrecision] * N[(t$95$5 / N[(N[(t$95$10 - 1.0), $MachinePrecision] * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$8, 4e-11], N[(N[(1.0 / N[(t$95$1 - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(z2 / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(N[(N[Max[z1, z0], $MachinePrecision] * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$6 + z2), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * t$95$6), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -5.0000000000000004e-286

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \left(\color{blue}{\left(z1 + z2\right)} \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 45.1%

         \[\leadsto \left(\left(z1 + \color{blue}{z2}\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   4. Applied rewrites 45.1%

      \[\leadsto \left(\color{blue}{\left(z1 + z2\right)} \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z1 + z2\right)} \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 44.8%

         \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + \color{blue}{z2}\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   7. Applied rewrites 44.8%

      \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z1 + z2\right)} \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   9. Step-by-step derivation

      1. lower-+.f64 45.3%

         \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + \color{blue}{z2}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   10. Applied rewrites 45.3%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   11. Taylor expanded in z0 around 0

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   12. Step-by-step derivation

       1. lower-+.f64 44.8%

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + \color{blue}{z2}\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   13. Applied rewrites 44.8%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   14. Taylor expanded in z0 around 0

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   15. Step-by-step derivation

       1. lower-+.f64 41.3%

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + \color{blue}{z2}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   16. Applied rewrites 41.3%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   17. Taylor expanded in z0 around 0

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right)\right)} \]
   18. Step-by-step derivation

       1. lower-+.f64 31.9%

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + \color{blue}{z2}\right) + z2\right)\right)} \]

   19. Applied rewrites 31.9%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right)\right)} \]

   if -5.0000000000000004e-286 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. difference-of-sqr-1 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\color{blue}{\left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(z2 + \left(\left(z0 + z1\right) + z2\right)\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \color{blue}{\left(\left(z0 + z1\right) + z2\right)}\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z0 + z1\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(z2 + \left(\color{blue}{\left(z1 + z0\right)} + z2\right)\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. associate-+l+ N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\color{blue}{\left(z2 + \left(z1 + z0\right)\right)} + z2\right) + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)} + 1\right) \cdot \left(\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1\right)} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   7. Applied rewrites 61.1%

      \[\leadsto \color{blue}{\frac{\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - -1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   8. Taylor expanded in z1 around inf

      \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 44.9%

       \[\leadsto \frac{\color{blue}{1}}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 79.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(\mathsf{min}\left(z1, z0\right) + \mathsf{max}\left(z1, z0\right)\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ t_4 := \left(\mathsf{min}\left(z1, z0\right) + z2\right) \cdot z2\\ t_5 := \mathsf{max}\left(z1, z0\right) + \mathsf{min}\left(z1, z0\right)\\ t_6 := t\_5 + z2\\ t_7 := \left(z2 + \mathsf{min}\left(z1, z0\right)\right) + z2\\ t_8 := t\_6 + z2\\ t_9 := \mathsf{min}\left(z1, z0\right) \cdot \mathsf{max}\left(z1, z0\right)\\ t_10 := \left(t\_3 + t\_9\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2}\\ \mathbf{if}\;t\_10 \leq -2 \cdot 10^{-181}:\\ \;\;\;\;\left(t\_4 + t\_9\right) \cdot \frac{t\_4}{t\_7 \cdot \left(\left(t\_7 \cdot t\_7 - 1\right) \cdot t\_7\right)}\\ \mathbf{elif}\;t\_10 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{\mathsf{max}\left(z1, z0\right) \cdot \mathsf{min}\left(z1, z0\right) + t\_6 \cdot z2}{t\_8 \cdot t\_8 - 1} \cdot \frac{z2}{t\_5}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot \mathsf{max}\left(z1, z0\right) + 2 \cdot \mathsf{min}\left(z1, z0\right)\right)\right) - 0.125 \cdot t\_5}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ (fmin z1 z0) (fmax z1 z0))))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2))
       (t_4 (* (+ (fmin z1 z0) z2) z2))
       (t_5 (+ (fmax z1 z0) (fmin z1 z0)))
       (t_6 (+ t_5 z2))
       (t_7 (+ (+ z2 (fmin z1 z0)) z2))
       (t_8 (+ t_6 z2))
       (t_9 (* (fmin z1 z0) (fmax z1 z0)))
       (t_10 (* (+ t_3 t_9) (/ t_3 (* (- t_2 1.0) t_2)))))
  (if (<= t_10 -2e-181)
    (* (+ t_4 t_9) (/ t_4 (* t_7 (* (- (* t_7 t_7) 1.0) t_7))))
    (if (<= t_10 4e-11)
      (*
       (/
        (+ (* (fmax z1 z0) (fmin z1 z0)) (* t_6 z2))
        (- (* t_8 t_8) 1.0))
       (/ z2 t_5))
      (/
       (-
        (+
         (* 0.0625 z2)
         (* 0.0625 (+ (* 2.0 (fmax z1 z0)) (* 2.0 (fmin z1 z0)))))
        (* 0.125 t_5))
       z2)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0));
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (fmin(z1, z0) + z2) * z2;
	double t_5 = fmax(z1, z0) + fmin(z1, z0);
	double t_6 = t_5 + z2;
	double t_7 = (z2 + fmin(z1, z0)) + z2;
	double t_8 = t_6 + z2;
	double t_9 = fmin(z1, z0) * fmax(z1, z0);
	double t_10 = (t_3 + t_9) * (t_3 / ((t_2 - 1.0) * t_2));
	double tmp;
	if (t_10 <= -2e-181) {
		tmp = (t_4 + t_9) * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)));
	} else if (t_10 <= 4e-11) {
		tmp = (((fmax(z1, z0) * fmin(z1, z0)) + (t_6 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / t_5);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_5)) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0))
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    t_4 = (fmin(z1, z0) + z2) * z2
    t_5 = fmax(z1, z0) + fmin(z1, z0)
    t_6 = t_5 + z2
    t_7 = (z2 + fmin(z1, z0)) + z2
    t_8 = t_6 + z2
    t_9 = fmin(z1, z0) * fmax(z1, z0)
    t_10 = (t_3 + t_9) * (t_3 / ((t_2 - 1.0d0) * t_2))
    if (t_10 <= (-2d-181)) then
        tmp = (t_4 + t_9) * (t_4 / (t_7 * (((t_7 * t_7) - 1.0d0) * t_7)))
    else if (t_10 <= 4d-11) then
        tmp = (((fmax(z1, z0) * fmin(z1, z0)) + (t_6 * z2)) / ((t_8 * t_8) - 1.0d0)) * (z2 / t_5)
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * fmax(z1, z0)) + (2.0d0 * fmin(z1, z0))))) - (0.125d0 * t_5)) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0));
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (fmin(z1, z0) + z2) * z2;
	double t_5 = fmax(z1, z0) + fmin(z1, z0);
	double t_6 = t_5 + z2;
	double t_7 = (z2 + fmin(z1, z0)) + z2;
	double t_8 = t_6 + z2;
	double t_9 = fmin(z1, z0) * fmax(z1, z0);
	double t_10 = (t_3 + t_9) * (t_3 / ((t_2 - 1.0) * t_2));
	double tmp;
	if (t_10 <= -2e-181) {
		tmp = (t_4 + t_9) * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)));
	} else if (t_10 <= 4e-11) {
		tmp = (((fmax(z1, z0) * fmin(z1, z0)) + (t_6 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / t_5);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_5)) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (fmin(z1, z0) + fmax(z1, z0))
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	t_4 = (fmin(z1, z0) + z2) * z2
	t_5 = fmax(z1, z0) + fmin(z1, z0)
	t_6 = t_5 + z2
	t_7 = (z2 + fmin(z1, z0)) + z2
	t_8 = t_6 + z2
	t_9 = fmin(z1, z0) * fmax(z1, z0)
	t_10 = (t_3 + t_9) * (t_3 / ((t_2 - 1.0) * t_2))
	tmp = 0
	if t_10 <= -2e-181:
		tmp = (t_4 + t_9) * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)))
	elif t_10 <= 4e-11:
		tmp = (((fmax(z1, z0) * fmin(z1, z0)) + (t_6 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / t_5)
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0))))) - (0.125 * t_5)) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(fmin(z1, z0) + fmax(z1, z0)))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	t_4 = Float64(Float64(fmin(z1, z0) + z2) * z2)
	t_5 = Float64(fmax(z1, z0) + fmin(z1, z0))
	t_6 = Float64(t_5 + z2)
	t_7 = Float64(Float64(z2 + fmin(z1, z0)) + z2)
	t_8 = Float64(t_6 + z2)
	t_9 = Float64(fmin(z1, z0) * fmax(z1, z0))
	t_10 = Float64(Float64(t_3 + t_9) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2)))
	tmp = 0.0
	if (t_10 <= -2e-181)
		tmp = Float64(Float64(t_4 + t_9) * Float64(t_4 / Float64(t_7 * Float64(Float64(Float64(t_7 * t_7) - 1.0) * t_7))));
	elseif (t_10 <= 4e-11)
		tmp = Float64(Float64(Float64(Float64(fmax(z1, z0) * fmin(z1, z0)) + Float64(t_6 * z2)) / Float64(Float64(t_8 * t_8) - 1.0)) * Float64(z2 / t_5));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * fmax(z1, z0)) + Float64(2.0 * fmin(z1, z0))))) - Float64(0.125 * t_5)) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (min(z1, z0) + max(z1, z0));
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	t_4 = (min(z1, z0) + z2) * z2;
	t_5 = max(z1, z0) + min(z1, z0);
	t_6 = t_5 + z2;
	t_7 = (z2 + min(z1, z0)) + z2;
	t_8 = t_6 + z2;
	t_9 = min(z1, z0) * max(z1, z0);
	t_10 = (t_3 + t_9) * (t_3 / ((t_2 - 1.0) * t_2));
	tmp = 0.0;
	if (t_10 <= -2e-181)
		tmp = (t_4 + t_9) * (t_4 / (t_7 * (((t_7 * t_7) - 1.0) * t_7)));
	elseif (t_10 <= 4e-11)
		tmp = (((max(z1, z0) * min(z1, z0)) + (t_6 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / t_5);
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * max(z1, z0)) + (2.0 * min(z1, z0))))) - (0.125 * t_5)) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(N[Min[z1, z0], $MachinePrecision] + N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[Min[z1, z0], $MachinePrecision] + z2), $MachinePrecision] * z2), $MachinePrecision]}, Block[{t$95$5 = N[(N[Max[z1, z0], $MachinePrecision] + N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 + z2), $MachinePrecision]}, Block[{t$95$7 = N[(N[(z2 + N[Min[z1, z0], $MachinePrecision]), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$6 + z2), $MachinePrecision]}, Block[{t$95$9 = N[(N[Min[z1, z0], $MachinePrecision] * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(t$95$3 + t$95$9), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$10, -2e-181], N[(N[(t$95$4 + t$95$9), $MachinePrecision] * N[(t$95$4 / N[(t$95$7 * N[(N[(N[(t$95$7 * t$95$7), $MachinePrecision] - 1.0), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$10, 4e-11], N[(N[(N[(N[(N[Max[z1, z0], $MachinePrecision] * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * z2), $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$8 * t$95$8), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] * N[(z2 / t$95$5), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * t$95$5), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -2.0000000000000001e-181

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \left(\color{blue}{\left(z1 + z2\right)} \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 45.1%

         \[\leadsto \left(\left(z1 + \color{blue}{z2}\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   4. Applied rewrites 45.1%

      \[\leadsto \left(\color{blue}{\left(z1 + z2\right)} \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   5. Taylor expanded in z0 around 0

      \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z1 + z2\right)} \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 44.8%

         \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + \color{blue}{z2}\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   7. Applied rewrites 44.8%

      \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z1 + z2\right)} \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   8. Taylor expanded in z0 around 0

      \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   9. Step-by-step derivation

      1. lower-+.f64 45.3%

         \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + \color{blue}{z2}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   10. Applied rewrites 45.3%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   11. Taylor expanded in z0 around 0

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   12. Step-by-step derivation

       1. lower-+.f64 44.8%

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + \color{blue}{z2}\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   13. Applied rewrites 44.8%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   14. Taylor expanded in z0 around 0

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   15. Step-by-step derivation

       1. lower-+.f64 41.3%

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + \color{blue}{z2}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   16. Applied rewrites 41.3%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\color{blue}{\left(z1 + z2\right)} + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   17. Taylor expanded in z0 around 0

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right)\right)} \]
   18. Step-by-step derivation

       1. lower-+.f64 31.9%

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + \color{blue}{z2}\right) + z2\right)\right)} \]

   19. Applied rewrites 31.9%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\color{blue}{\left(z1 + z2\right)} + z2\right)\right)} \]
   20. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\color{blue}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right)\right)}} \]

       2. lift-*.f64 N/A

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \color{blue}{\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right)\right)}} \]

       3. associate-*r* N/A

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\color{blue}{\left(\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(z1 + z2\right) + z2\right)\right) \cdot \left(\left(z1 + z2\right) + z2\right)}} \]

       4. *-commutative N/A

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\color{blue}{\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(z1 + z2\right) + z2\right)\right)}} \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\color{blue}{\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(\left(\left(z1 + z2\right) + z2\right) \cdot \left(\left(z1 + z2\right) + z2\right) - 1\right) \cdot \left(\left(z1 + z2\right) + z2\right)\right)}} \]

   21. Applied rewrites 31.9%

       \[\leadsto \left(\left(z1 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z1 + z2\right) \cdot z2}{\color{blue}{\left(\left(z2 + z1\right) + z2\right) \cdot \left(\left(\left(\left(z2 + z1\right) + z2\right) \cdot \left(\left(z2 + z1\right) + z2\right) - 1\right) \cdot \left(\left(z2 + z1\right) + z2\right)\right)}} \]

   if -2.0000000000000001e-181 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      5. times-frac N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}} \]

   3. Applied rewrites 57.8%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{\left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2}{z0 + z1}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2}{\color{blue}{z0 + z1}} \]

      2. lower-+.f64 45.8%

         \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2}{z0 + \color{blue}{z1}} \]

   6. Applied rewrites 45.8%

      \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2}{z0 + z1}} \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := \left(z0 + z2\right) + z2\\ t_4 := t\_3 \cdot t\_3\\ t_5 := t\_0 \cdot z2\\ t_6 := \left(t\_5 + z1 \cdot z0\right) \cdot \frac{t\_5}{\left(t\_2 - 1\right) \cdot t\_2}\\ t_7 := \left(z0 + z1\right) + z2\\ t_8 := t\_7 + z2\\ \mathbf{if}\;t\_6 \leq -1 \cdot 10^{-194}:\\ \;\;\;\;\left(\left(\left(z0 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(z0 + z2\right)\right) \cdot \frac{z2}{\left(t\_4 - 1\right) \cdot t\_4}\\ \mathbf{elif}\;t\_6 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{z0 \cdot z1 + t\_7 \cdot z2}{t\_8 \cdot t\_8 - 1} \cdot \frac{z2}{z0 + z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (+ (+ z0 z2) z2))
       (t_4 (* t_3 t_3))
       (t_5 (* t_0 z2))
       (t_6 (* (+ t_5 (* z1 z0)) (/ t_5 (* (- t_2 1.0) t_2))))
       (t_7 (+ (+ z0 z1) z2))
       (t_8 (+ t_7 z2)))
  (if (<= t_6 -1e-194)
    (*
     (* (+ (* (+ z0 z2) z2) (* z1 z0)) (+ z0 z2))
     (/ z2 (* (- t_4 1.0) t_4)))
    (if (<= t_6 4e-11)
      (*
       (/ (+ (* z0 z1) (* t_7 z2)) (- (* t_8 t_8) 1.0))
       (/ z2 (+ z0 z1)))
      (/
       (-
        (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
        (* 0.125 (+ z0 z1)))
       z2)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = (z0 + z2) + z2;
	double t_4 = t_3 * t_3;
	double t_5 = t_0 * z2;
	double t_6 = (t_5 + (z1 * z0)) * (t_5 / ((t_2 - 1.0) * t_2));
	double t_7 = (z0 + z1) + z2;
	double t_8 = t_7 + z2;
	double tmp;
	if (t_6 <= -1e-194) {
		tmp = ((((z0 + z2) * z2) + (z1 * z0)) * (z0 + z2)) * (z2 / ((t_4 - 1.0) * t_4));
	} else if (t_6 <= 4e-11) {
		tmp = (((z0 * z1) + (t_7 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / (z0 + z1));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = (z0 + z2) + z2
    t_4 = t_3 * t_3
    t_5 = t_0 * z2
    t_6 = (t_5 + (z1 * z0)) * (t_5 / ((t_2 - 1.0d0) * t_2))
    t_7 = (z0 + z1) + z2
    t_8 = t_7 + z2
    if (t_6 <= (-1d-194)) then
        tmp = ((((z0 + z2) * z2) + (z1 * z0)) * (z0 + z2)) * (z2 / ((t_4 - 1.0d0) * t_4))
    else if (t_6 <= 4d-11) then
        tmp = (((z0 * z1) + (t_7 * z2)) / ((t_8 * t_8) - 1.0d0)) * (z2 / (z0 + z1))
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = (z0 + z2) + z2;
	double t_4 = t_3 * t_3;
	double t_5 = t_0 * z2;
	double t_6 = (t_5 + (z1 * z0)) * (t_5 / ((t_2 - 1.0) * t_2));
	double t_7 = (z0 + z1) + z2;
	double t_8 = t_7 + z2;
	double tmp;
	if (t_6 <= -1e-194) {
		tmp = ((((z0 + z2) * z2) + (z1 * z0)) * (z0 + z2)) * (z2 / ((t_4 - 1.0) * t_4));
	} else if (t_6 <= 4e-11) {
		tmp = (((z0 * z1) + (t_7 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / (z0 + z1));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = (z0 + z2) + z2
	t_4 = t_3 * t_3
	t_5 = t_0 * z2
	t_6 = (t_5 + (z1 * z0)) * (t_5 / ((t_2 - 1.0) * t_2))
	t_7 = (z0 + z1) + z2
	t_8 = t_7 + z2
	tmp = 0
	if t_6 <= -1e-194:
		tmp = ((((z0 + z2) * z2) + (z1 * z0)) * (z0 + z2)) * (z2 / ((t_4 - 1.0) * t_4))
	elif t_6 <= 4e-11:
		tmp = (((z0 * z1) + (t_7 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / (z0 + z1))
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(Float64(z0 + z2) + z2)
	t_4 = Float64(t_3 * t_3)
	t_5 = Float64(t_0 * z2)
	t_6 = Float64(Float64(t_5 + Float64(z1 * z0)) * Float64(t_5 / Float64(Float64(t_2 - 1.0) * t_2)))
	t_7 = Float64(Float64(z0 + z1) + z2)
	t_8 = Float64(t_7 + z2)
	tmp = 0.0
	if (t_6 <= -1e-194)
		tmp = Float64(Float64(Float64(Float64(Float64(z0 + z2) * z2) + Float64(z1 * z0)) * Float64(z0 + z2)) * Float64(z2 / Float64(Float64(t_4 - 1.0) * t_4)));
	elseif (t_6 <= 4e-11)
		tmp = Float64(Float64(Float64(Float64(z0 * z1) + Float64(t_7 * z2)) / Float64(Float64(t_8 * t_8) - 1.0)) * Float64(z2 / Float64(z0 + z1)));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = (z0 + z2) + z2;
	t_4 = t_3 * t_3;
	t_5 = t_0 * z2;
	t_6 = (t_5 + (z1 * z0)) * (t_5 / ((t_2 - 1.0) * t_2));
	t_7 = (z0 + z1) + z2;
	t_8 = t_7 + z2;
	tmp = 0.0;
	if (t_6 <= -1e-194)
		tmp = ((((z0 + z2) * z2) + (z1 * z0)) * (z0 + z2)) * (z2 / ((t_4 - 1.0) * t_4));
	elseif (t_6 <= 4e-11)
		tmp = (((z0 * z1) + (t_7 * z2)) / ((t_8 * t_8) - 1.0)) * (z2 / (z0 + z1));
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z0 + z2), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$5 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$5 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 + z2), $MachinePrecision]}, If[LessEqual[t$95$6, -1e-194], N[(N[(N[(N[(N[(z0 + z2), $MachinePrecision] * z2), $MachinePrecision] + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(z0 + z2), $MachinePrecision]), $MachinePrecision] * N[(z2 / N[(N[(t$95$4 - 1.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$6, 4e-11], N[(N[(N[(N[(z0 * z1), $MachinePrecision] + N[(t$95$7 * z2), $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$8 * t$95$8), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] * N[(z2 / N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -1e-194

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   2. Taylor expanded in z1 around 0

      \[\leadsto \left(\left(z2 + \color{blue}{z0}\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   3. Step-by-step derivation

   4. Applied rewrites 44.7%

      \[\leadsto \left(\left(z2 + \color{blue}{z0}\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   5. Taylor expanded in z1 around 0

      \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \color{blue}{z0}\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 44.3%

      \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \color{blue}{z0}\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   8. Taylor expanded in z1 around 0

      \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + \color{blue}{z0}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 44.8%

       \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + \color{blue}{z0}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   11. Taylor expanded in z1 around 0

       \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + \color{blue}{z0}\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 44.3%

       \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + \color{blue}{z0}\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   14. Taylor expanded in z1 around 0

       \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \color{blue}{z0}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   15. Step-by-step derivation

   16. Applied rewrites 40.9%

       \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \color{blue}{z0}\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   17. Taylor expanded in z1 around 0

       \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + \color{blue}{z0}\right) + z2\right)\right)} \]
   18. Step-by-step derivation

   19. Applied rewrites 30.8%

       \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + \color{blue}{z0}\right) + z2\right)\right)} \]
   20. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right)\right)}} \]

       2. lift-/.f64 N/A

          \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + z0\right) \cdot z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right)\right)}} \]

       3. lift-*.f64 N/A

          \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\color{blue}{\left(z2 + z0\right) \cdot z2}}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right)\right)} \]

       4. associate-/l* N/A

          \[\leadsto \left(\left(z2 + z0\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\left(\left(z2 + z0\right) \cdot \frac{z2}{\left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + z0\right) + z2\right) \cdot \left(\left(z2 + z0\right) + z2\right)\right)}\right)} \]

   21. Applied rewrites 20.0%

       \[\leadsto \color{blue}{\left(\left(\left(z0 + z2\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(z0 + z2\right)\right) \cdot \frac{z2}{\left(\left(\left(z0 + z2\right) + z2\right) \cdot \left(\left(z0 + z2\right) + z2\right) - 1\right) \cdot \left(\left(\left(z0 + z2\right) + z2\right) \cdot \left(\left(z0 + z2\right) + z2\right)\right)}} \]

   if -1e-194 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      5. times-frac N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}} \]

   3. Applied rewrites 57.8%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{\left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2}{z0 + z1}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2}{\color{blue}{z0 + z1}} \]

      2. lower-+.f64 45.8%

         \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2}{z0 + \color{blue}{z1}} \]

   6. Applied rewrites 45.8%

      \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2}{z0 + z1}} \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 78.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ t_4 := \left(t\_3 + z1 \cdot z0\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2}\\ t_5 := \left(z0 + z1\right) + z2\\ t_6 := t\_5 + z2\\ t_7 := t\_6 \cdot t\_6 - 1\\ \mathbf{if}\;t\_4 \leq -2 \cdot 10^{-120}:\\ \;\;\;\;\frac{t\_5}{t\_7} \cdot \left(0.25 \cdot z2\right)\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{z0 \cdot z1 + t\_5 \cdot z2}{t\_7} \cdot \frac{z2}{z0 + z1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2))
       (t_4 (* (+ t_3 (* z1 z0)) (/ t_3 (* (- t_2 1.0) t_2))))
       (t_5 (+ (+ z0 z1) z2))
       (t_6 (+ t_5 z2))
       (t_7 (- (* t_6 t_6) 1.0)))
  (if (<= t_4 -2e-120)
    (* (/ t_5 t_7) (* 0.25 z2))
    (if (<= t_4 4e-11)
      (* (/ (+ (* z0 z1) (* t_5 z2)) t_7) (/ z2 (+ z0 z1)))
      (/
       (-
        (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
        (* 0.125 (+ z0 z1)))
       z2)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2));
	double t_5 = (z0 + z1) + z2;
	double t_6 = t_5 + z2;
	double t_7 = (t_6 * t_6) - 1.0;
	double tmp;
	if (t_4 <= -2e-120) {
		tmp = (t_5 / t_7) * (0.25 * z2);
	} else if (t_4 <= 4e-11) {
		tmp = (((z0 * z1) + (t_5 * z2)) / t_7) * (z2 / (z0 + z1));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0d0) * t_2))
    t_5 = (z0 + z1) + z2
    t_6 = t_5 + z2
    t_7 = (t_6 * t_6) - 1.0d0
    if (t_4 <= (-2d-120)) then
        tmp = (t_5 / t_7) * (0.25d0 * z2)
    else if (t_4 <= 4d-11) then
        tmp = (((z0 * z1) + (t_5 * z2)) / t_7) * (z2 / (z0 + z1))
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2));
	double t_5 = (z0 + z1) + z2;
	double t_6 = t_5 + z2;
	double t_7 = (t_6 * t_6) - 1.0;
	double tmp;
	if (t_4 <= -2e-120) {
		tmp = (t_5 / t_7) * (0.25 * z2);
	} else if (t_4 <= 4e-11) {
		tmp = (((z0 * z1) + (t_5 * z2)) / t_7) * (z2 / (z0 + z1));
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))
	t_5 = (z0 + z1) + z2
	t_6 = t_5 + z2
	t_7 = (t_6 * t_6) - 1.0
	tmp = 0
	if t_4 <= -2e-120:
		tmp = (t_5 / t_7) * (0.25 * z2)
	elif t_4 <= 4e-11:
		tmp = (((z0 * z1) + (t_5 * z2)) / t_7) * (z2 / (z0 + z1))
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	t_4 = Float64(Float64(t_3 + Float64(z1 * z0)) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2)))
	t_5 = Float64(Float64(z0 + z1) + z2)
	t_6 = Float64(t_5 + z2)
	t_7 = Float64(Float64(t_6 * t_6) - 1.0)
	tmp = 0.0
	if (t_4 <= -2e-120)
		tmp = Float64(Float64(t_5 / t_7) * Float64(0.25 * z2));
	elseif (t_4 <= 4e-11)
		tmp = Float64(Float64(Float64(Float64(z0 * z1) + Float64(t_5 * z2)) / t_7) * Float64(z2 / Float64(z0 + z1)));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	t_4 = (t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2));
	t_5 = (z0 + z1) + z2;
	t_6 = t_5 + z2;
	t_7 = (t_6 * t_6) - 1.0;
	tmp = 0.0;
	if (t_4 <= -2e-120)
		tmp = (t_5 / t_7) * (0.25 * z2);
	elseif (t_4 <= 4e-11)
		tmp = (((z0 * z1) + (t_5 * z2)) / t_7) * (z2 / (z0 + z1));
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 + z2), $MachinePrecision]}, Block[{t$95$7 = N[(N[(t$95$6 * t$95$6), $MachinePrecision] - 1.0), $MachinePrecision]}, If[LessEqual[t$95$4, -2e-120], N[(N[(t$95$5 / t$95$7), $MachinePrecision] * N[(0.25 * z2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 4e-11], N[(N[(N[(N[(z0 * z1), $MachinePrecision] + N[(t$95$5 * z2), $MachinePrecision]), $MachinePrecision] / t$95$7), $MachinePrecision] * N[(z2 / N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -2e-120

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]

   4. Taylor expanded in z2 around inf

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\left(\frac{1}{4} \cdot z2\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 49.3%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(0.25 \cdot \color{blue}{z2}\right) \]

   6. Applied rewrites 49.3%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\left(0.25 \cdot z2\right)} \]

   if -2e-120 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < 3.9999999999999998e-11

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2\right)}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      5. times-frac N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}} \]

   3. Applied rewrites 57.8%

      \[\leadsto \color{blue}{\frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{\left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \]

   4. Taylor expanded in z2 around 0

      \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2}{z0 + z1}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2}{\color{blue}{z0 + z1}} \]

      2. lower-+.f64 45.8%

         \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2}{z0 + \color{blue}{z1}} \]

   6. Applied rewrites 45.8%

      \[\leadsto \frac{z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2}{z0 + z1}} \]

   if 3.9999999999999998e-11 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := z2 + \left(z1 + z0\right)\\ t_1 := t\_0 + z2\\ t_2 := t\_1 \cdot t\_1\\ t_3 := t\_0 \cdot z2\\ t_4 := \left(z0 + z1\right) + z2\\ t_5 := t\_4 + z2\\ \mathbf{if}\;\left(t\_3 + z1 \cdot z0\right) \cdot \frac{t\_3}{\left(t\_2 - 1\right) \cdot t\_2} \leq -1 \cdot 10^{-282}:\\ \;\;\;\;\frac{t\_4}{t\_5 \cdot t\_5 - 1} \cdot \left(0.25 \cdot z2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2}\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ z2 (+ z1 z0)))
       (t_1 (+ t_0 z2))
       (t_2 (* t_1 t_1))
       (t_3 (* t_0 z2))
       (t_4 (+ (+ z0 z1) z2))
       (t_5 (+ t_4 z2)))
  (if (<= (* (+ t_3 (* z1 z0)) (/ t_3 (* (- t_2 1.0) t_2))) -1e-282)
    (* (/ t_4 (- (* t_5 t_5) 1.0)) (* 0.25 z2))
    (/
     (-
      (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
      (* 0.125 (+ z0 z1)))
     z2))))

C

double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (z0 + z1) + z2;
	double t_5 = t_4 + z2;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= -1e-282) {
		tmp = (t_4 / ((t_5 * t_5) - 1.0)) * (0.25 * z2);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = z2 + (z1 + z0)
    t_1 = t_0 + z2
    t_2 = t_1 * t_1
    t_3 = t_0 * z2
    t_4 = (z0 + z1) + z2
    t_5 = t_4 + z2
    if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0d0) * t_2))) <= (-1d-282)) then
        tmp = (t_4 / ((t_5 * t_5) - 1.0d0)) * (0.25d0 * z2)
    else
        tmp = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = z2 + (z1 + z0);
	double t_1 = t_0 + z2;
	double t_2 = t_1 * t_1;
	double t_3 = t_0 * z2;
	double t_4 = (z0 + z1) + z2;
	double t_5 = t_4 + z2;
	double tmp;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= -1e-282) {
		tmp = (t_4 / ((t_5 * t_5) - 1.0)) * (0.25 * z2);
	} else {
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = z2 + (z1 + z0)
	t_1 = t_0 + z2
	t_2 = t_1 * t_1
	t_3 = t_0 * z2
	t_4 = (z0 + z1) + z2
	t_5 = t_4 + z2
	tmp = 0
	if ((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= -1e-282:
		tmp = (t_4 / ((t_5 * t_5) - 1.0)) * (0.25 * z2)
	else:
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(z2 + Float64(z1 + z0))
	t_1 = Float64(t_0 + z2)
	t_2 = Float64(t_1 * t_1)
	t_3 = Float64(t_0 * z2)
	t_4 = Float64(Float64(z0 + z1) + z2)
	t_5 = Float64(t_4 + z2)
	tmp = 0.0
	if (Float64(Float64(t_3 + Float64(z1 * z0)) * Float64(t_3 / Float64(Float64(t_2 - 1.0) * t_2))) <= -1e-282)
		tmp = Float64(Float64(t_4 / Float64(Float64(t_5 * t_5) - 1.0)) * Float64(0.25 * z2));
	else
		tmp = Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = z2 + (z1 + z0);
	t_1 = t_0 + z2;
	t_2 = t_1 * t_1;
	t_3 = t_0 * z2;
	t_4 = (z0 + z1) + z2;
	t_5 = t_4 + z2;
	tmp = 0.0;
	if (((t_3 + (z1 * z0)) * (t_3 / ((t_2 - 1.0) * t_2))) <= -1e-282)
		tmp = (t_4 / ((t_5 * t_5) - 1.0)) * (0.25 * z2);
	else
		tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(z2 + N[(z1 + z0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + z2), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * z2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z0 + z1), $MachinePrecision] + z2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + z2), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 + N[(z1 * z0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 / N[(N[(t$95$2 - 1.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e-282], N[(N[(t$95$4 / N[(N[(t$95$5 * t$95$5), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] * N[(0.25 * z2), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2))))) < -1e-282

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]

   4. Taylor expanded in z2 around inf

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\left(\frac{1}{4} \cdot z2\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 49.3%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(0.25 \cdot \color{blue}{z2}\right) \]

   6. Applied rewrites 49.3%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\left(0.25 \cdot z2\right)} \]

   if -1e-282 < (*.f64 (+.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 z1 z0)) (/.f64 (*.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (*.f64 (-.f64 (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2) (+.f64 (+.f64 z2 (+.f64 z1 z0)) z2)))))

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       10. lower-+.f64 71.4%

           \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 71.4%

       \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 71.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(z1, z0\right) + \mathsf{min}\left(z1, z0\right)\\ t_1 := \left(0.0625 + 0.125 \cdot \frac{\mathsf{max}\left(z1, z0\right)}{z2}\right) - 0.125 \cdot \frac{t\_0}{z2}\\ \mathbf{if}\;z2 \leq -225:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z2 \leq 6.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{0.0625 \cdot \left(2 \cdot \mathsf{max}\left(z1, z0\right) + 2 \cdot \mathsf{min}\left(z1, z0\right)\right) - 0.125 \cdot t\_0}{z2}\\ \mathbf{elif}\;z2 \leq 2.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{1}{\mathsf{max}\left(z1, z0\right)} \cdot \frac{z2 \cdot \left(\mathsf{min}\left(z1, z0\right) + z2\right)}{\mathsf{max}\left(z1, z0\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (let* ((t_0 (+ (fmax z1 z0) (fmin z1 z0)))
       (t_1
        (-
         (+ 0.0625 (* 0.125 (/ (fmax z1 z0) z2)))
         (* 0.125 (/ t_0 z2)))))
  (if (<= z2 -225.0)
    t_1
    (if (<= z2 6.4e+19)
      (/
       (-
        (* 0.0625 (+ (* 2.0 (fmax z1 z0)) (* 2.0 (fmin z1 z0))))
        (* 0.125 t_0))
       z2)
      (if (<= z2 2.8e+87)
        (*
         (/ 1.0 (fmax z1 z0))
         (/ (* z2 (+ (fmin z1 z0) z2)) (fmax z1 z0)))
        t_1)))))

C

double code(double z2, double z1, double z0) {
	double t_0 = fmax(z1, z0) + fmin(z1, z0);
	double t_1 = (0.0625 + (0.125 * (fmax(z1, z0) / z2))) - (0.125 * (t_0 / z2));
	double tmp;
	if (z2 <= -225.0) {
		tmp = t_1;
	} else if (z2 <= 6.4e+19) {
		tmp = ((0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0)))) - (0.125 * t_0)) / z2;
	} else if (z2 <= 2.8e+87) {
		tmp = (1.0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0));
	} 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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = fmax(z1, z0) + fmin(z1, z0)
    t_1 = (0.0625d0 + (0.125d0 * (fmax(z1, z0) / z2))) - (0.125d0 * (t_0 / z2))
    if (z2 <= (-225.0d0)) then
        tmp = t_1
    else if (z2 <= 6.4d+19) then
        tmp = ((0.0625d0 * ((2.0d0 * fmax(z1, z0)) + (2.0d0 * fmin(z1, z0)))) - (0.125d0 * t_0)) / z2
    else if (z2 <= 2.8d+87) then
        tmp = (1.0d0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double t_0 = fmax(z1, z0) + fmin(z1, z0);
	double t_1 = (0.0625 + (0.125 * (fmax(z1, z0) / z2))) - (0.125 * (t_0 / z2));
	double tmp;
	if (z2 <= -225.0) {
		tmp = t_1;
	} else if (z2 <= 6.4e+19) {
		tmp = ((0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0)))) - (0.125 * t_0)) / z2;
	} else if (z2 <= 2.8e+87) {
		tmp = (1.0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	t_0 = fmax(z1, z0) + fmin(z1, z0)
	t_1 = (0.0625 + (0.125 * (fmax(z1, z0) / z2))) - (0.125 * (t_0 / z2))
	tmp = 0
	if z2 <= -225.0:
		tmp = t_1
	elif z2 <= 6.4e+19:
		tmp = ((0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0)))) - (0.125 * t_0)) / z2
	elif z2 <= 2.8e+87:
		tmp = (1.0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0))
	else:
		tmp = t_1
	return tmp

Julia

function code(z2, z1, z0)
	t_0 = Float64(fmax(z1, z0) + fmin(z1, z0))
	t_1 = Float64(Float64(0.0625 + Float64(0.125 * Float64(fmax(z1, z0) / z2))) - Float64(0.125 * Float64(t_0 / z2)))
	tmp = 0.0
	if (z2 <= -225.0)
		tmp = t_1;
	elseif (z2 <= 6.4e+19)
		tmp = Float64(Float64(Float64(0.0625 * Float64(Float64(2.0 * fmax(z1, z0)) + Float64(2.0 * fmin(z1, z0)))) - Float64(0.125 * t_0)) / z2);
	elseif (z2 <= 2.8e+87)
		tmp = Float64(Float64(1.0 / fmax(z1, z0)) * Float64(Float64(z2 * Float64(fmin(z1, z0) + z2)) / fmax(z1, z0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	t_0 = max(z1, z0) + min(z1, z0);
	t_1 = (0.0625 + (0.125 * (max(z1, z0) / z2))) - (0.125 * (t_0 / z2));
	tmp = 0.0;
	if (z2 <= -225.0)
		tmp = t_1;
	elseif (z2 <= 6.4e+19)
		tmp = ((0.0625 * ((2.0 * max(z1, z0)) + (2.0 * min(z1, z0)))) - (0.125 * t_0)) / z2;
	elseif (z2 <= 2.8e+87)
		tmp = (1.0 / max(z1, z0)) * ((z2 * (min(z1, z0) + z2)) / max(z1, z0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := Block[{t$95$0 = N[(N[Max[z1, z0], $MachinePrecision] + N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.0625 + N[(0.125 * N[(N[Max[z1, z0], $MachinePrecision] / z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(t$95$0 / z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z2, -225.0], t$95$1, If[LessEqual[z2, 6.4e+19], N[(N[(N[(0.0625 * N[(N[(2.0 * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * t$95$0), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision], If[LessEqual[z2, 2.8e+87], N[(N[(1.0 / N[Max[z1, z0], $MachinePrecision]), $MachinePrecision] * N[(N[(z2 * N[(N[Min[z1, z0], $MachinePrecision] + z2), $MachinePrecision]), $MachinePrecision] / N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z2 < -225 or 2.8000000000000002e87 < z2

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z1 around 0

      \[\leadsto \left(0.0625 + \frac{1}{8} \cdot \frac{z0}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \left(\frac{1}{16} + \frac{1}{8} \cdot \frac{z0}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

       2. lower-/.f64 39.7%

          \[\leadsto \left(0.0625 + 0.125 \cdot \frac{z0}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   11. Applied rewrites 39.7%

       \[\leadsto \left(0.0625 + 0.125 \cdot \frac{z0}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   if -225 < z2 < 6.4e19

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-+.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-+.f64 44.3%

          \[\leadsto \frac{0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 44.3%

       \[\leadsto \frac{0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]

   if 6.4e19 < z2 < 2.8000000000000002e87

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]

   4. Taylor expanded in z0 around inf

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{\color{blue}{z0}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

      3. lower-+.f64 38.2%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   6. Applied rewrites 38.2%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]
   8. Step-by-step derivation

      1. lower-/.f64 32.4%

         \[\leadsto \frac{1}{\color{blue}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   9. Applied rewrites 32.4%

      \[\leadsto \color{blue}{\frac{1}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 68.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z2 \leq -0.9:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;z2 \leq 6.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{0.0625 \cdot \left(2 \cdot \mathsf{max}\left(z1, z0\right) + 2 \cdot \mathsf{min}\left(z1, z0\right)\right) - 0.125 \cdot \left(\mathsf{max}\left(z1, z0\right) + \mathsf{min}\left(z1, z0\right)\right)}{z2}\\ \mathbf{elif}\;z2 \leq 2.35 \cdot 10^{+140}:\\ \;\;\;\;\frac{1}{\mathsf{max}\left(z1, z0\right)} \cdot \frac{z2 \cdot \left(\mathsf{min}\left(z1, z0\right) + z2\right)}{\mathsf{max}\left(z1, z0\right)}\\ \mathbf{else}:\\ \;\;\;\;0.0625\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (if (<= z2 -0.9)
  0.0625
  (if (<= z2 6.4e+19)
    (/
     (-
      (* 0.0625 (+ (* 2.0 (fmax z1 z0)) (* 2.0 (fmin z1 z0))))
      (* 0.125 (+ (fmax z1 z0) (fmin z1 z0))))
     z2)
    (if (<= z2 2.35e+140)
      (*
       (/ 1.0 (fmax z1 z0))
       (/ (* z2 (+ (fmin z1 z0) z2)) (fmax z1 z0)))
      0.0625))))

C

double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -0.9) {
		tmp = 0.0625;
	} else if (z2 <= 6.4e+19) {
		tmp = ((0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0)))) - (0.125 * (fmax(z1, z0) + fmin(z1, z0)))) / z2;
	} else if (z2 <= 2.35e+140) {
		tmp = (1.0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0));
	} else {
		tmp = 0.0625;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if (z2 <= (-0.9d0)) then
        tmp = 0.0625d0
    else if (z2 <= 6.4d+19) then
        tmp = ((0.0625d0 * ((2.0d0 * fmax(z1, z0)) + (2.0d0 * fmin(z1, z0)))) - (0.125d0 * (fmax(z1, z0) + fmin(z1, z0)))) / z2
    else if (z2 <= 2.35d+140) then
        tmp = (1.0d0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0))
    else
        tmp = 0.0625d0
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -0.9) {
		tmp = 0.0625;
	} else if (z2 <= 6.4e+19) {
		tmp = ((0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0)))) - (0.125 * (fmax(z1, z0) + fmin(z1, z0)))) / z2;
	} else if (z2 <= 2.35e+140) {
		tmp = (1.0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0));
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	tmp = 0
	if z2 <= -0.9:
		tmp = 0.0625
	elif z2 <= 6.4e+19:
		tmp = ((0.0625 * ((2.0 * fmax(z1, z0)) + (2.0 * fmin(z1, z0)))) - (0.125 * (fmax(z1, z0) + fmin(z1, z0)))) / z2
	elif z2 <= 2.35e+140:
		tmp = (1.0 / fmax(z1, z0)) * ((z2 * (fmin(z1, z0) + z2)) / fmax(z1, z0))
	else:
		tmp = 0.0625
	return tmp

Julia

function code(z2, z1, z0)
	tmp = 0.0
	if (z2 <= -0.9)
		tmp = 0.0625;
	elseif (z2 <= 6.4e+19)
		tmp = Float64(Float64(Float64(0.0625 * Float64(Float64(2.0 * fmax(z1, z0)) + Float64(2.0 * fmin(z1, z0)))) - Float64(0.125 * Float64(fmax(z1, z0) + fmin(z1, z0)))) / z2);
	elseif (z2 <= 2.35e+140)
		tmp = Float64(Float64(1.0 / fmax(z1, z0)) * Float64(Float64(z2 * Float64(fmin(z1, z0) + z2)) / fmax(z1, z0)));
	else
		tmp = 0.0625;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	tmp = 0.0;
	if (z2 <= -0.9)
		tmp = 0.0625;
	elseif (z2 <= 6.4e+19)
		tmp = ((0.0625 * ((2.0 * max(z1, z0)) + (2.0 * min(z1, z0)))) - (0.125 * (max(z1, z0) + min(z1, z0)))) / z2;
	elseif (z2 <= 2.35e+140)
		tmp = (1.0 / max(z1, z0)) * ((z2 * (min(z1, z0) + z2)) / max(z1, z0));
	else
		tmp = 0.0625;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := If[LessEqual[z2, -0.9], 0.0625, If[LessEqual[z2, 6.4e+19], N[(N[(N[(0.0625 * N[(N[(2.0 * N[Max[z1, z0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(N[Max[z1, z0], $MachinePrecision] + N[Min[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision], If[LessEqual[z2, 2.35e+140], N[(N[(1.0 / N[Max[z1, z0], $MachinePrecision]), $MachinePrecision] * N[(N[(z2 * N[(N[Min[z1, z0], $MachinePrecision] + z2), $MachinePrecision]), $MachinePrecision] / N[Max[z1, z0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0625]]]

Derivation

1. Split input into 3 regimes

2. if z2 < -0.90000000000000002 or 2.3500000000000001e140 < z2

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   2. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\frac{1}{16}} \]
   3. Step-by-step derivation

   4. Applied rewrites 31.2%

      \[\leadsto \color{blue}{0.0625} \]

   if -0.90000000000000002 < z2 < 6.4e19

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

      10. lower-+.f64 50.3%

          \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

   8. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

   9. Taylor expanded in z2 around 0

      \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       3. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       4. lower-+.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       6. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{\frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

       8. lower-+.f64 44.3%

          \[\leadsto \frac{0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

   11. Applied rewrites 44.3%

       \[\leadsto \frac{0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]

   if 6.4e19 < z2 < 2.3500000000000001e140

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]

   4. Taylor expanded in z0 around inf

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{\color{blue}{z0}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

      3. lower-+.f64 38.2%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   6. Applied rewrites 38.2%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]
   8. Step-by-step derivation

      1. lower-/.f64 32.4%

         \[\leadsto \frac{1}{\color{blue}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   9. Applied rewrites 32.4%

      \[\leadsto \color{blue}{\frac{1}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 66.7% accurate, 2.1× speedup

Math

\[\frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (/
 (-
  (+ (* 0.0625 z2) (* 0.0625 (+ (* 2.0 z0) (* 2.0 z1))))
  (* 0.125 (+ z0 z1)))
 z2))

C

double code(double z2, double z1, double z0) {
	return (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
}

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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    code = (((0.0625d0 * z2) + (0.0625d0 * ((2.0d0 * z0) + (2.0d0 * z1)))) - (0.125d0 * (z0 + z1))) / z2
end function

Java

public static double code(double z2, double z1, double z0) {
	return (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
}

Python

def code(z2, z1, z0):
	return (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2

Julia

function code(z2, z1, z0)
	return Float64(Float64(Float64(Float64(0.0625 * z2) + Float64(0.0625 * Float64(Float64(2.0 * z0) + Float64(2.0 * z1)))) - Float64(0.125 * Float64(z0 + z1))) / z2)
end

MATLAB

function tmp = code(z2, z1, z0)
	tmp = (((0.0625 * z2) + (0.0625 * ((2.0 * z0) + (2.0 * z1)))) - (0.125 * (z0 + z1))) / z2;
end

Wolfram

code[z2_, z1_, z0_] := N[(N[(N[(N[(0.0625 * z2), $MachinePrecision] + N[(0.0625 * N[(N[(2.0 * z0), $MachinePrecision] + N[(2.0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.125 * N[(z0 + z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]

Derivation

1. Initial program 47.4%

   \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

   3. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   6. times-frac N/A

      \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

3. Applied rewrites 57.3%

   \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
4. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   3. associate-/r* N/A

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. lower-/.f64 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. lift-+.f64 N/A

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   7. +-commutative N/A

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   8. lower-+.f64 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   9. lift-+.f64 N/A

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   10. +-commutative N/A

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   11. lower-+.f64 58.8%

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   12. lift-+.f64 N/A

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   13. +-commutative N/A

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   14. lower-+.f64 58.8%

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   15. lift-+.f64 N/A

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   16. +-commutative N/A

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   17. lower-+.f64 58.8%

       \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

5. Applied rewrites 58.8%

   \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

6. Taylor expanded in z2 around inf

   \[\leadsto \color{blue}{\left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]
7. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8} \cdot \frac{z0 + z1}{z2}} \]

   2. lower-+.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \color{blue}{\frac{1}{8}} \cdot \frac{z0 + z1}{z2} \]

   3. lower-*.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

   4. lower-/.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

   5. lower-+.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

   7. lower-*.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{z2} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \color{blue}{\frac{z0 + z1}{z2}} \]

   9. lower-/.f64 N/A

      \[\leadsto \left(\frac{1}{16} + \frac{1}{16} \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - \frac{1}{8} \cdot \frac{z0 + z1}{\color{blue}{z2}} \]

   10. lower-+.f64 50.3%

       \[\leadsto \left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2} \]

8. Applied rewrites 50.3%

   \[\leadsto \color{blue}{\left(0.0625 + 0.0625 \cdot \frac{2 \cdot z0 + 2 \cdot z1}{z2}\right) - 0.125 \cdot \frac{z0 + z1}{z2}} \]

9. Taylor expanded in z2 around 0

   \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
10. Step-by-step derivation

    1. lower-/.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    2. lower--.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    3. lower-+.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    4. lower-*.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    5. lower-*.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    6. lower-+.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    7. lower-*.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    8. lower-*.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    9. lower-*.f64 N/A

       \[\leadsto \frac{\left(\frac{1}{16} \cdot z2 + \frac{1}{16} \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - \frac{1}{8} \cdot \left(z0 + z1\right)}{z2} \]

    10. lower-+.f64 71.4%

        \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{z2} \]

11. Applied rewrites 71.4%

    \[\leadsto \frac{\left(0.0625 \cdot z2 + 0.0625 \cdot \left(2 \cdot z0 + 2 \cdot z1\right)\right) - 0.125 \cdot \left(z0 + z1\right)}{\color{blue}{z2}} \]
12. Add Preprocessing

Alternative 16: 52.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z2 \leq -8.5 \cdot 10^{-26}:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;z2 \leq 2.35 \cdot 10^{+140}:\\ \;\;\;\;\frac{1}{z0} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0}\\ \mathbf{else}:\\ \;\;\;\;0.0625\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (if (<= z2 -8.5e-26)
  0.0625
  (if (<= z2 2.35e+140)
    (* (/ 1.0 z0) (/ (* z2 (+ z1 z2)) z0))
    0.0625)))

C

double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -8.5e-26) {
		tmp = 0.0625;
	} else if (z2 <= 2.35e+140) {
		tmp = (1.0 / z0) * ((z2 * (z1 + z2)) / z0);
	} else {
		tmp = 0.0625;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if (z2 <= (-8.5d-26)) then
        tmp = 0.0625d0
    else if (z2 <= 2.35d+140) then
        tmp = (1.0d0 / z0) * ((z2 * (z1 + z2)) / z0)
    else
        tmp = 0.0625d0
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -8.5e-26) {
		tmp = 0.0625;
	} else if (z2 <= 2.35e+140) {
		tmp = (1.0 / z0) * ((z2 * (z1 + z2)) / z0);
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	tmp = 0
	if z2 <= -8.5e-26:
		tmp = 0.0625
	elif z2 <= 2.35e+140:
		tmp = (1.0 / z0) * ((z2 * (z1 + z2)) / z0)
	else:
		tmp = 0.0625
	return tmp

Julia

function code(z2, z1, z0)
	tmp = 0.0
	if (z2 <= -8.5e-26)
		tmp = 0.0625;
	elseif (z2 <= 2.35e+140)
		tmp = Float64(Float64(1.0 / z0) * Float64(Float64(z2 * Float64(z1 + z2)) / z0));
	else
		tmp = 0.0625;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	tmp = 0.0;
	if (z2 <= -8.5e-26)
		tmp = 0.0625;
	elseif (z2 <= 2.35e+140)
		tmp = (1.0 / z0) * ((z2 * (z1 + z2)) / z0);
	else
		tmp = 0.0625;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := If[LessEqual[z2, -8.5e-26], 0.0625, If[LessEqual[z2, 2.35e+140], N[(N[(1.0 / z0), $MachinePrecision] * N[(N[(z2 * N[(z1 + z2), $MachinePrecision]), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision], 0.0625]]

Derivation

1. Split input into 2 regimes

2. if z2 < -8.5e-26 or 2.3500000000000001e140 < z2

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   2. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\frac{1}{16}} \]
   3. Step-by-step derivation

   4. Applied rewrites 31.2%

      \[\leadsto \color{blue}{0.0625} \]

   if -8.5e-26 < z2 < 2.3500000000000001e140

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]

   4. Taylor expanded in z0 around inf

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{\color{blue}{z0}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

      3. lower-+.f64 38.2%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   6. Applied rewrites 38.2%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \color{blue}{\frac{1}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]
   8. Step-by-step derivation

      1. lower-/.f64 32.4%

         \[\leadsto \frac{1}{\color{blue}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   9. Applied rewrites 32.4%

      \[\leadsto \color{blue}{\frac{1}{z0}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 45.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z2 \leq -0.106:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;z2 \leq 2 \cdot 10^{-28}:\\ \;\;\;\;\frac{0.25}{z2} \cdot \frac{z2 \cdot z1}{z0}\\ \mathbf{else}:\\ \;\;\;\;0.0625\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (if (<= z2 -0.106)
  0.0625
  (if (<= z2 2e-28) (* (/ 0.25 z2) (/ (* z2 z1) z0)) 0.0625)))

C

double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -0.106) {
		tmp = 0.0625;
	} else if (z2 <= 2e-28) {
		tmp = (0.25 / z2) * ((z2 * z1) / z0);
	} else {
		tmp = 0.0625;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if (z2 <= (-0.106d0)) then
        tmp = 0.0625d0
    else if (z2 <= 2d-28) then
        tmp = (0.25d0 / z2) * ((z2 * z1) / z0)
    else
        tmp = 0.0625d0
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -0.106) {
		tmp = 0.0625;
	} else if (z2 <= 2e-28) {
		tmp = (0.25 / z2) * ((z2 * z1) / z0);
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	tmp = 0
	if z2 <= -0.106:
		tmp = 0.0625
	elif z2 <= 2e-28:
		tmp = (0.25 / z2) * ((z2 * z1) / z0)
	else:
		tmp = 0.0625
	return tmp

Julia

function code(z2, z1, z0)
	tmp = 0.0
	if (z2 <= -0.106)
		tmp = 0.0625;
	elseif (z2 <= 2e-28)
		tmp = Float64(Float64(0.25 / z2) * Float64(Float64(z2 * z1) / z0));
	else
		tmp = 0.0625;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	tmp = 0.0;
	if (z2 <= -0.106)
		tmp = 0.0625;
	elseif (z2 <= 2e-28)
		tmp = (0.25 / z2) * ((z2 * z1) / z0);
	else
		tmp = 0.0625;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := If[LessEqual[z2, -0.106], 0.0625, If[LessEqual[z2, 2e-28], N[(N[(0.25 / z2), $MachinePrecision] * N[(N[(z2 * z1), $MachinePrecision] / z0), $MachinePrecision]), $MachinePrecision], 0.0625]]

Derivation

1. Split input into 2 regimes

2. if z2 < -0.106 or 1.9999999999999999e-28 < z2

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   2. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\frac{1}{16}} \]
   3. Step-by-step derivation

   4. Applied rewrites 31.2%

      \[\leadsto \color{blue}{0.0625} \]

   if -0.106 < z2 < 1.9999999999999999e-28

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]

   4. Taylor expanded in z0 around inf

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{\color{blue}{z0}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

      3. lower-+.f64 38.2%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   6. Applied rewrites 38.2%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \color{blue}{\frac{z2 \cdot \left(z1 + z2\right)}{z0}} \]

   7. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\frac{\frac{1}{4}}{z2}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]
   8. Step-by-step derivation

      1. lower-/.f64 16.2%

         \[\leadsto \frac{0.25}{\color{blue}{z2}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   9. Applied rewrites 16.2%

      \[\leadsto \color{blue}{\frac{0.25}{z2}} \cdot \frac{z2 \cdot \left(z1 + z2\right)}{z0} \]

   10. Taylor expanded in z2 around 0

       \[\leadsto \frac{0.25}{z2} \cdot \frac{z2 \cdot z1}{z0} \]
   11. Step-by-step derivation

   12. Applied rewrites 19.1%

       \[\leadsto \frac{0.25}{z2} \cdot \frac{z2 \cdot z1}{z0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z2 \leq -0.0023:\\ \;\;\;\;0.0625\\ \mathbf{elif}\;z2 \leq 6.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{\mathsf{min}\left(z1, z0\right)} \cdot \left(0.25 \cdot z2\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625\\ \end{array} \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  (if (<= z2 -0.0023)
  0.0625
  (if (<= z2 6.5e+19) (* (/ 1.0 (fmin z1 z0)) (* 0.25 z2)) 0.0625)))

C

double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -0.0023) {
		tmp = 0.0625;
	} else if (z2 <= 6.5e+19) {
		tmp = (1.0 / fmin(z1, z0)) * (0.25 * z2);
	} else {
		tmp = 0.0625;
	}
	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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    real(8) :: tmp
    if (z2 <= (-0.0023d0)) then
        tmp = 0.0625d0
    else if (z2 <= 6.5d+19) then
        tmp = (1.0d0 / fmin(z1, z0)) * (0.25d0 * z2)
    else
        tmp = 0.0625d0
    end if
    code = tmp
end function

Java

public static double code(double z2, double z1, double z0) {
	double tmp;
	if (z2 <= -0.0023) {
		tmp = 0.0625;
	} else if (z2 <= 6.5e+19) {
		tmp = (1.0 / fmin(z1, z0)) * (0.25 * z2);
	} else {
		tmp = 0.0625;
	}
	return tmp;
}

Python

def code(z2, z1, z0):
	tmp = 0
	if z2 <= -0.0023:
		tmp = 0.0625
	elif z2 <= 6.5e+19:
		tmp = (1.0 / fmin(z1, z0)) * (0.25 * z2)
	else:
		tmp = 0.0625
	return tmp

Julia

function code(z2, z1, z0)
	tmp = 0.0
	if (z2 <= -0.0023)
		tmp = 0.0625;
	elseif (z2 <= 6.5e+19)
		tmp = Float64(Float64(1.0 / fmin(z1, z0)) * Float64(0.25 * z2));
	else
		tmp = 0.0625;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z2, z1, z0)
	tmp = 0.0;
	if (z2 <= -0.0023)
		tmp = 0.0625;
	elseif (z2 <= 6.5e+19)
		tmp = (1.0 / min(z1, z0)) * (0.25 * z2);
	else
		tmp = 0.0625;
	end
	tmp_2 = tmp;
end

Wolfram

code[z2_, z1_, z0_] := If[LessEqual[z2, -0.0023], 0.0625, If[LessEqual[z2, 6.5e+19], N[(N[(1.0 / N[Min[z1, z0], $MachinePrecision]), $MachinePrecision] * N[(0.25 * z2), $MachinePrecision]), $MachinePrecision], 0.0625]]

Derivation

1. Split input into 2 regimes

2. if z2 < -0.0023 or 6.5e19 < z2

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

   2. Taylor expanded in z2 around inf

      \[\leadsto \color{blue}{\frac{1}{16}} \]
   3. Step-by-step derivation

   4. Applied rewrites 31.2%

      \[\leadsto \color{blue}{0.0625} \]

   if -0.0023 < z2 < 6.5e19

   1. Initial program 47.4%

      \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right)} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\color{blue}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)}} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

      6. times-frac N/A

         \[\leadsto \color{blue}{\left(\frac{z2 + \left(z1 + z0\right)}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1} \cdot \frac{z2}{\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)}\right)} \cdot \left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \]

   3. Applied rewrites 57.3%

      \[\leadsto \color{blue}{\frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right)} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{z2}{\color{blue}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right)}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      5. lower-/.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\color{blue}{\frac{z2}{\left(\left(z0 + z1\right) + z2\right) + z2}}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      8. lower-+.f64 58.8%

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      9. lift-+.f64 N/A

         \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      11. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2}}{\left(\left(z0 + z1\right) + z2\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(\left(z0 + z1\right) + z2\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      14. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\color{blue}{\left(z2 + \left(z0 + z1\right)\right)} + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z0 + z1\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

      17. lower-+.f64 58.8%

          \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \color{blue}{\left(z1 + z0\right)}\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   5. Applied rewrites 58.8%

      \[\leadsto \frac{\left(z0 + z1\right) + z2}{\left(\left(\left(z0 + z1\right) + z2\right) + z2\right) \cdot \left(\left(\left(z0 + z1\right) + z2\right) + z2\right) - 1} \cdot \left(\color{blue}{\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2}} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   6. Taylor expanded in z1 around inf

      \[\leadsto \color{blue}{\frac{1}{z1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 37.6%

         \[\leadsto \frac{1}{\color{blue}{z1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   8. Applied rewrites 37.6%

      \[\leadsto \color{blue}{\frac{1}{z1}} \cdot \left(\frac{\frac{z2}{\left(z2 + \left(z1 + z0\right)\right) + z2}}{\left(z2 + \left(z1 + z0\right)\right) + z2} \cdot \left(z0 \cdot z1 + \left(\left(z0 + z1\right) + z2\right) \cdot z2\right)\right) \]

   9. Taylor expanded in z2 around inf

      \[\leadsto \frac{1}{z1} \cdot \color{blue}{\left(\frac{1}{4} \cdot z2\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 16.0%

          \[\leadsto \frac{1}{z1} \cdot \left(0.25 \cdot \color{blue}{z2}\right) \]

   11. Applied rewrites 16.0%

       \[\leadsto \frac{1}{z1} \cdot \color{blue}{\left(0.25 \cdot z2\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 31.2% accurate, 101.0× speedup

Math

\[0.0625 \]

FPCore

(FPCore (z2 z1 z0)
  :precision binary64
  0.0625)

C

double code(double z2, double z1, double z0) {
	return 0.0625;
}

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(z2, z1, z0)
use fmin_fmax_functions
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8), intent (in) :: z0
    code = 0.0625d0
end function

Java

public static double code(double z2, double z1, double z0) {
	return 0.0625;
}

Python

def code(z2, z1, z0):
	return 0.0625

Julia

function code(z2, z1, z0)
	return 0.0625
end

MATLAB

function tmp = code(z2, z1, z0)
	tmp = 0.0625;
end

Wolfram

code[z2_, z1_, z0_] := 0.0625

Derivation

1. Initial program 47.4%

   \[\left(\left(z2 + \left(z1 + z0\right)\right) \cdot z2 + z1 \cdot z0\right) \cdot \frac{\left(z2 + \left(z1 + z0\right)\right) \cdot z2}{\left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) - 1\right) \cdot \left(\left(\left(z2 + \left(z1 + z0\right)\right) + z2\right) \cdot \left(\left(z2 + \left(z1 + z0\right)\right) + z2\right)\right)} \]

2. Taylor expanded in z2 around inf

   \[\leadsto \color{blue}{\frac{1}{16}} \]
3. Step-by-step derivation

4. Applied rewrites 31.2%

   \[\leadsto \color{blue}{0.0625} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (z2 z1 z0)
  :name "(* (+ (* (+ z2 (+ z1 z0)) z2) (* z1 z0)) (/ (* (+ z2 (+ z1 z0)) z2) (* (- (* (+ (+ z2 (+ z1 z0)) z2) (+ (+ z2 (+ z1 z0)) z2)) 1) (* (+ (+ z2 (+ z1 z0)) z2) (+ (+ z2 (+ z1 z0)) z2)))))"
  :precision binary64
  (* (+ (* (+ z2 (+ z1 z0)) z2) (* z1 z0)) (/ (* (+ z2 (+ z1 z0)) z2) (* (- (* (+ (+ z2 (+ z1 z0)) z2) (+ (+ z2 (+ z1 z0)) z2)) 1.0) (* (+ (+ z2 (+ z1 z0)) z2) (+ (+ z2 (+ z1 z0)) z2))))))