Gyroid sphere

Percentage Accurate: 46.5% → 75.6%

Time: 7.5s

Alternatives: 4

Speedup: 4.1×

Specification

Math

\[\begin{array}{l} \\ \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (-
   (sqrt
    (+ (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0)) (pow (* z 30.0) 2.0)))
   25.0)
  (-
   (fabs
    (+
     (+
      (* (sin (* x 30.0)) (cos (* y 30.0)))
      (* (sin (* y 30.0)) (cos (* z 30.0))))
     (* (sin (* z 30.0)) (cos (* x 30.0)))))
   0.2)))

C

double code(double x, double y, double z) {
	return fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2));
}

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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = fmax((sqrt(((((x * 30.0d0) ** 2.0d0) + ((y * 30.0d0) ** 2.0d0)) + ((z * 30.0d0) ** 2.0d0))) - 25.0d0), (abs((((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))) + (sin((z * 30.0d0)) * cos((x * 30.0d0))))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax((Math.sqrt(((Math.pow((x * 30.0), 2.0) + Math.pow((y * 30.0), 2.0)) + Math.pow((z * 30.0), 2.0))) - 25.0), (Math.abs((((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))) + (Math.sin((z * 30.0)) * Math.cos((x * 30.0))))) - 0.2));
}

Python

def code(x, y, z):
	return fmax((math.sqrt(((math.pow((x * 30.0), 2.0) + math.pow((y * 30.0), 2.0)) + math.pow((z * 30.0), 2.0))) - 25.0), (math.fabs((((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))) + (math.sin((z * 30.0)) * math.cos((x * 30.0))))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((sqrt(((((x * 30.0) ^ 2.0) + ((y * 30.0) ^ 2.0)) + ((z * 30.0) ^ 2.0))) - 25.0), (abs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Initial Program: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (-
   (sqrt
    (+ (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0)) (pow (* z 30.0) 2.0)))
   25.0)
  (-
   (fabs
    (+
     (+
      (* (sin (* x 30.0)) (cos (* y 30.0)))
      (* (sin (* y 30.0)) (cos (* z 30.0))))
     (* (sin (* z 30.0)) (cos (* x 30.0)))))
   0.2)))

C

double code(double x, double y, double z) {
	return fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2));
}

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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = fmax((sqrt(((((x * 30.0d0) ** 2.0d0) + ((y * 30.0d0) ** 2.0d0)) + ((z * 30.0d0) ** 2.0d0))) - 25.0d0), (abs((((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))) + (sin((z * 30.0d0)) * cos((x * 30.0d0))))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax((Math.sqrt(((Math.pow((x * 30.0), 2.0) + Math.pow((y * 30.0), 2.0)) + Math.pow((z * 30.0), 2.0))) - 25.0), (Math.abs((((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))) + (Math.sin((z * 30.0)) * Math.cos((x * 30.0))))) - 0.2));
}

Python

def code(x, y, z):
	return fmax((math.sqrt(((math.pow((x * 30.0), 2.0) + math.pow((y * 30.0), 2.0)) + math.pow((z * 30.0), 2.0))) - 25.0), (math.fabs((((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))) + (math.sin((z * 30.0)) * math.cos((x * 30.0))))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((sqrt(((((x * 30.0) ^ 2.0) + ((y * 30.0) ^ 2.0)) + ((z * 30.0) ^ 2.0))) - 25.0), (abs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Alternative 1: 75.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ t_1 := \left|\sin \left(z \cdot 30\right) + t\_0\right| - 0.2\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_1\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\left(z \cdot 30\right) \cdot 1 + t\_0\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x))) (t_1 (- (fabs (+ (sin (* z 30.0)) t_0)) 0.2)))
   (if (<= y -4.5e+152)
     (fmax (* -30.0 y) t_1)
     (if (<= y 4.5e+152)
       (fmax
        (- (sqrt (* 900.0 (+ (* x x) (* y y)))) 25.0)
        (- (fabs (+ (* (* z 30.0) 1.0) t_0)) 0.2))
       (fmax (* y 30.0) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double t_1 = fabs((sin((z * 30.0)) + t_0)) - 0.2;
	double tmp;
	if (y <= -4.5e+152) {
		tmp = fmax((-30.0 * y), t_1);
	} else if (y <= 4.5e+152) {
		tmp = fmax((sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (fabs((((z * 30.0) * 1.0) + t_0)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), 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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sin((30.0d0 * x))
    t_1 = abs((sin((z * 30.0d0)) + t_0)) - 0.2d0
    if (y <= (-4.5d+152)) then
        tmp = fmax(((-30.0d0) * y), t_1)
    else if (y <= 4.5d+152) then
        tmp = fmax((sqrt((900.0d0 * ((x * x) + (y * y)))) - 25.0d0), (abs((((z * 30.0d0) * 1.0d0) + t_0)) - 0.2d0))
    else
        tmp = fmax((y * 30.0d0), t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin((30.0 * x));
	double t_1 = Math.abs((Math.sin((z * 30.0)) + t_0)) - 0.2;
	double tmp;
	if (y <= -4.5e+152) {
		tmp = fmax((-30.0 * y), t_1);
	} else if (y <= 4.5e+152) {
		tmp = fmax((Math.sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (Math.abs((((z * 30.0) * 1.0) + t_0)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), t_1);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin((30.0 * x))
	t_1 = math.fabs((math.sin((z * 30.0)) + t_0)) - 0.2
	tmp = 0
	if y <= -4.5e+152:
		tmp = fmax((-30.0 * y), t_1)
	elif y <= 4.5e+152:
		tmp = fmax((math.sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (math.fabs((((z * 30.0) * 1.0) + t_0)) - 0.2))
	else:
		tmp = fmax((y * 30.0), t_1)
	return tmp

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	t_1 = Float64(abs(Float64(sin(Float64(z * 30.0)) + t_0)) - 0.2)
	tmp = 0.0
	if (y <= -4.5e+152)
		tmp = fmax(Float64(-30.0 * y), t_1);
	elseif (y <= 4.5e+152)
		tmp = fmax(Float64(sqrt(Float64(900.0 * Float64(Float64(x * x) + Float64(y * y)))) - 25.0), Float64(abs(Float64(Float64(Float64(z * 30.0) * 1.0) + t_0)) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin((30.0 * x));
	t_1 = abs((sin((z * 30.0)) + t_0)) - 0.2;
	tmp = 0.0;
	if (y <= -4.5e+152)
		tmp = max((-30.0 * y), t_1);
	elseif (y <= 4.5e+152)
		tmp = max((sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (abs((((z * 30.0) * 1.0) + t_0)) - 0.2));
	else
		tmp = max((y * 30.0), t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -4.5e+152], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[y, 4.5e+152], N[Max[N[(N[Sqrt[N[(900.0 * N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(z * 30.0), $MachinePrecision] * 1.0), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000001e152

   1. Initial program 9.9%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {x}^{2} + 900 \cdot {y}^{2}}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left({x}^{2} + \color{blue}{{y}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 9.9

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Applied rewrites 9.9%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot \left(x \cdot x + y \cdot y\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 9.9

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   8. Applied rewrites 9.9%

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       3. lift-*.f64 9.9

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   11. Applied rewrites 9.9%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(z \cdot 30\right)}\right| - 0.2\right) \]

   12. Taylor expanded in y around -inf

       \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot y}, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]
   13. Step-by-step derivation

       1. lift-*.f64 76.6

          \[\leadsto \mathsf{max}\left(-30 \cdot \color{blue}{y}, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   14. Applied rewrites 76.6%

       \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot y}, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   if -4.5000000000000001e152 < y < 4.5000000000000001e152

   1. Initial program 67.6%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {x}^{2} + 900 \cdot {y}^{2}}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left({x}^{2} + \color{blue}{{y}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 53.9

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Applied rewrites 53.9%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot \left(x \cdot x + y \cdot y\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 52.9

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   8. Applied rewrites 52.9%

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\left(30 \cdot z\right)} \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot \color{blue}{30}\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lift-*.f64 74.6

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot \color{blue}{30}\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   11. Applied rewrites 74.6%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\left(z \cdot 30\right)} \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot 30\right) \cdot \color{blue}{1}\right| - \frac{1}{5}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 79.3%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot 30\right) \cdot \color{blue}{1}\right| - 0.2\right) \]

   if 4.5000000000000001e152 < y

   1. Initial program 6.8%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {x}^{2} + 900 \cdot {y}^{2}}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left({x}^{2} + \color{blue}{{y}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 6.8

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Applied rewrites 6.8%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot \left(x \cdot x + y \cdot y\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 6.8

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   8. Applied rewrites 6.8%

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       3. lift-*.f64 6.8

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   11. Applied rewrites 6.8%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(z \cdot 30\right)}\right| - 0.2\right) \]

   12. Taylor expanded in y around inf

       \[\leadsto \mathsf{max}\left(\color{blue}{30 \cdot y}, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]
   13. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(y \cdot \color{blue}{30}, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lower-*.f64 79.7

          \[\leadsto \mathsf{max}\left(y \cdot \color{blue}{30}, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   14. Applied rewrites 79.7%

       \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot 30}, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, \left|\sin \left(z \cdot 30\right) + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\left(z \cdot 30\right) \cdot 1 + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, \left|\sin \left(z \cdot 30\right) + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \left|t\_0 + 30 \cdot x\right| - 0.2\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|t\_0 \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))) (t_1 (- (fabs (+ t_0 (* 30.0 x))) 0.2)))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (* t_0 (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))))
          0.2))
        5e+152)
     (fmax (- (sqrt (* 900.0 (+ (* x x) (* y y)))) 25.0) t_1)
     (fmax (* -30.0 x) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fabs((t_0 + (30.0 * x))) - 0.2;
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs(((t_0 * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2)) <= 5e+152) {
		tmp = fmax((sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), t_1);
	} else {
		tmp = fmax((-30.0 * x), 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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sin((z * 30.0d0))
    t_1 = abs((t_0 + (30.0d0 * x))) - 0.2d0
    if (fmax((sqrt(((((x * 30.0d0) ** 2.0d0) + ((y * 30.0d0) ** 2.0d0)) + ((z * 30.0d0) ** 2.0d0))) - 25.0d0), (abs(((t_0 * cos((x * 30.0d0))) + ((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))))) - 0.2d0)) <= 5d+152) then
        tmp = fmax((sqrt((900.0d0 * ((x * x) + (y * y)))) - 25.0d0), t_1)
    else
        tmp = fmax(((-30.0d0) * x), t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin((z * 30.0));
	double t_1 = Math.abs((t_0 + (30.0 * x))) - 0.2;
	double tmp;
	if (fmax((Math.sqrt(((Math.pow((x * 30.0), 2.0) + Math.pow((y * 30.0), 2.0)) + Math.pow((z * 30.0), 2.0))) - 25.0), (Math.abs(((t_0 * Math.cos((x * 30.0))) + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2)) <= 5e+152) {
		tmp = fmax((Math.sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), t_1);
	} else {
		tmp = fmax((-30.0 * x), t_1);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin((z * 30.0))
	t_1 = math.fabs((t_0 + (30.0 * x))) - 0.2
	tmp = 0
	if fmax((math.sqrt(((math.pow((x * 30.0), 2.0) + math.pow((y * 30.0), 2.0)) + math.pow((z * 30.0), 2.0))) - 25.0), (math.fabs(((t_0 * math.cos((x * 30.0))) + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2)) <= 5e+152:
		tmp = fmax((math.sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), t_1)
	else:
		tmp = fmax((-30.0 * x), t_1)
	return tmp

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = Float64(abs(Float64(t_0 + Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(t_0 * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2)) <= 5e+152)
		tmp = fmax(Float64(sqrt(Float64(900.0 * Float64(Float64(x * x) + Float64(y * y)))) - 25.0), t_1);
	else
		tmp = fmax(Float64(-30.0 * x), t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin((z * 30.0));
	t_1 = abs((t_0 + (30.0 * x))) - 0.2;
	tmp = 0.0;
	if (max((sqrt(((((x * 30.0) ^ 2.0) + ((y * 30.0) ^ 2.0)) + ((z * 30.0) ^ 2.0))) - 25.0), (abs(((t_0 * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2)) <= 5e+152)
		tmp = max((sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), t_1);
	else
		tmp = max((-30.0 * x), t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[N[(t$95$0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 5e+152], N[Max[N[(N[Sqrt[N[(900.0 * N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$1], $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 5e152

   1. Initial program 99.9%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {x}^{2} + 900 \cdot {y}^{2}}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left({x}^{2} + \color{blue}{{y}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 78.9

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Applied rewrites 78.9%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot \left(x \cdot x + y \cdot y\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 77.4

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   8. Applied rewrites 77.4%

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       3. lift-*.f64 77.0

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   11. Applied rewrites 77.0%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(z \cdot 30\right)}\right| - 0.2\right) \]

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]
   13. Step-by-step derivation

       1. lift-*.f64 75.8

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|30 \cdot x + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   14. Applied rewrites 75.8%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   if 5e152 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 9.4%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. lower-*.f64 18.2

         \[\leadsto \mathsf{max}\left(-30 \cdot \color{blue}{x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Applied rewrites 18.2%

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 18.0

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   8. Applied rewrites 18.0%

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       3. lift-*.f64 18.0

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   11. Applied rewrites 18.0%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(z \cdot 30\right)}\right| - 0.2\right) \]

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]
   13. Step-by-step derivation

       1. lift-*.f64 34.2

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   14. Applied rewrites 34.2%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(z \cdot 30\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\sin \left(z \cdot 30\right) + 30 \cdot x\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+145} \lor \neg \left(x \leq 5.3 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\sin \left(z \cdot 30\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\left(z \cdot 30\right) \cdot 1 + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.2e+145) (not (<= x 5.3e+96)))
   (fmax (* -30.0 x) (- (fabs (+ (sin (* z 30.0)) (* 30.0 x))) 0.2))
   (fmax
    (- (sqrt (* 900.0 (+ (* x x) (* y y)))) 25.0)
    (- (fabs (+ (* (* z 30.0) 1.0) (sin (* 30.0 x)))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+145) || !(x <= 5.3e+96)) {
		tmp = fmax((-30.0 * x), (fabs((sin((z * 30.0)) + (30.0 * x))) - 0.2));
	} else {
		tmp = fmax((sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (fabs((((z * 30.0) * 1.0) + sin((30.0 * x)))) - 0.2));
	}
	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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6.2d+145)) .or. (.not. (x <= 5.3d+96))) then
        tmp = fmax(((-30.0d0) * x), (abs((sin((z * 30.0d0)) + (30.0d0 * x))) - 0.2d0))
    else
        tmp = fmax((sqrt((900.0d0 * ((x * x) + (y * y)))) - 25.0d0), (abs((((z * 30.0d0) * 1.0d0) + sin((30.0d0 * x)))) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+145) || !(x <= 5.3e+96)) {
		tmp = fmax((-30.0 * x), (Math.abs((Math.sin((z * 30.0)) + (30.0 * x))) - 0.2));
	} else {
		tmp = fmax((Math.sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (Math.abs((((z * 30.0) * 1.0) + Math.sin((30.0 * x)))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.2e+145) or not (x <= 5.3e+96):
		tmp = fmax((-30.0 * x), (math.fabs((math.sin((z * 30.0)) + (30.0 * x))) - 0.2))
	else:
		tmp = fmax((math.sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (math.fabs((((z * 30.0) * 1.0) + math.sin((30.0 * x)))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.2e+145) || !(x <= 5.3e+96))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(sin(Float64(z * 30.0)) + Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(sqrt(Float64(900.0 * Float64(Float64(x * x) + Float64(y * y)))) - 25.0), Float64(abs(Float64(Float64(Float64(z * 30.0) * 1.0) + sin(Float64(30.0 * x)))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.2e+145) || ~((x <= 5.3e+96)))
		tmp = max((-30.0 * x), (abs((sin((z * 30.0)) + (30.0 * x))) - 0.2));
	else
		tmp = max((sqrt((900.0 * ((x * x) + (y * y)))) - 25.0), (abs((((z * 30.0) * 1.0) + sin((30.0 * x)))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e+145], N[Not[LessEqual[x, 5.3e+96]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(900.0 * N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(z * 30.0), $MachinePrecision] * 1.0), $MachinePrecision] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.19999999999999977e145 or 5.29999999999999971e96 < x

   1. Initial program 19.4%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. lower-*.f64 36.4

         \[\leadsto \mathsf{max}\left(-30 \cdot \color{blue}{x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Applied rewrites 36.4%

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 36.4

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   8. Applied rewrites 36.4%

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

       3. lift-*.f64 36.2

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   11. Applied rewrites 36.2%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(z \cdot 30\right)}\right| - 0.2\right) \]

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]
   13. Step-by-step derivation

       1. lift-*.f64 75.0

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   14. Applied rewrites 75.0%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

   if -6.19999999999999977e145 < x < 5.29999999999999971e96

   1. Initial program 63.6%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {x}^{2} + 900 \cdot {y}^{2}}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \color{blue}{\left({x}^{2} + {y}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left({x}^{2} + \color{blue}{{y}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + {\color{blue}{y}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 49.9

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot \color{blue}{y}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Applied rewrites 49.9%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot \left(x \cdot x + y \cdot y\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 49.0

         \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   8. Applied rewrites 49.0%

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\left(30 \cdot z\right)} \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot \color{blue}{30}\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

       2. lift-*.f64 70.5

          \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot \color{blue}{30}\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   11. Applied rewrites 70.5%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\left(z \cdot 30\right)} \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot 30\right) \cdot \color{blue}{1}\right| - \frac{1}{5}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 75.2%

       \[\leadsto \mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\sin \left(30 \cdot x\right) + \left(z \cdot 30\right) \cdot \color{blue}{1}\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+145} \lor \neg \left(x \leq 5.3 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\sin \left(z \cdot 30\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \left(x \cdot x + y \cdot y\right)} - 25, \left|\left(z \cdot 30\right) \cdot 1 + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 32.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(-30 \cdot x, \left|\sin \left(z \cdot 30\right) + 30 \cdot x\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax (* -30.0 x) (- (fabs (+ (sin (* z 30.0)) (* 30.0 x))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((-30.0 * x), (fabs((sin((z * 30.0)) + (30.0 * x))) - 0.2));
}

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(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = fmax(((-30.0d0) * x), (abs((sin((z * 30.0d0)) + (30.0d0 * x))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax((-30.0 * x), (Math.abs((Math.sin((z * 30.0)) + (30.0 * x))) - 0.2));
}

Python

def code(x, y, z):
	return fmax((-30.0 * x), (math.fabs((math.sin((z * 30.0)) + (30.0 * x))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(-30.0 * x), Float64(abs(Float64(sin(Float64(z * 30.0)) + Float64(30.0 * x))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((-30.0 * x), (abs((sin((z * 30.0)) + (30.0 * x))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 52.2%

   \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
2. Add Preprocessing

3. Taylor expanded in x around -inf

   \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
4. Step-by-step derivation

   1. lower-*.f64 18.6

      \[\leadsto \mathsf{max}\left(-30 \cdot \color{blue}{x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

5. Applied rewrites 18.6%

   \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

6. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
7. Step-by-step derivation

   1. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   2. lift-*.f64 17.9

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

8. Applied rewrites 17.9%

   \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot x\right)} + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

9. Taylor expanded in x around 0

   \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
10. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

    2. lift-sin.f64 N/A

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]

    3. lift-*.f64 17.8

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

11. Applied rewrites 17.8%

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{\sin \left(z \cdot 30\right)}\right| - 0.2\right) \]

12. Taylor expanded in x around 0

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - \frac{1}{5}\right) \]
13. Step-by-step derivation

    1. lift-*.f64 30.1

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

14. Applied rewrites 30.1%

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot \color{blue}{x} + \sin \left(z \cdot 30\right)\right| - 0.2\right) \]

15. Final simplification 30.1%

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(z \cdot 30\right) + 30 \cdot x\right| - 0.2\right) \]
16. Add Preprocessing

Reproduce

herbie shell --seed 2025058 
(FPCore (x y z)
  :name "Gyroid sphere"
  :precision binary64
  (fmax (- (sqrt (+ (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0)) (pow (* z 30.0) 2.0))) 25.0) (- (fabs (+ (+ (* (sin (* x 30.0)) (cos (* y 30.0))) (* (sin (* y 30.0)) (cos (* z 30.0)))) (* (sin (* z 30.0)) (cos (* x 30.0))))) 0.2)))