Gyroid sphere

Percentage Accurate: 47.0% → 90.0%

Time: 7.6s

Alternatives: 10

Speedup: 7.4×

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: 47.0% 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: 90.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 30 \cdot \mathsf{hypot}\left(x, y\right) - 25\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 11200:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(y, z\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* 30.0 (hypot x y)) 25.0)))
   (if (<= x -2.6e+49)
     (fmax t_0 (- (fabs (* 30.0 x)) 0.2))
     (if (<= x 11200.0)
       (fmax
        (- (* 30.0 (hypot y z)) 25.0)
        (-
         (fabs
          (+
           (* (sin (* z 30.0)) (cos (* x 30.0)))
           (+
            (* (sin (* x 30.0)) (cos (* y 30.0)))
            (* (sin (* y 30.0)) (cos (* z 30.0))))))
         0.2))
       (fmax t_0 (- (fabs (sin (* 30.0 x))) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = (30.0 * hypot(x, y)) - 25.0;
	double tmp;
	if (x <= -2.6e+49) {
		tmp = fmax(t_0, (fabs((30.0 * x)) - 0.2));
	} else if (x <= 11200.0) {
		tmp = fmax(((30.0 * hypot(y, z)) - 25.0), (fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
	} else {
		tmp = fmax(t_0, (fabs(sin((30.0 * x))) - 0.2));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (30.0 * Math.hypot(x, y)) - 25.0;
	double tmp;
	if (x <= -2.6e+49) {
		tmp = fmax(t_0, (Math.abs((30.0 * x)) - 0.2));
	} else if (x <= 11200.0) {
		tmp = fmax(((30.0 * Math.hypot(y, z)) - 25.0), (Math.abs(((Math.sin((z * 30.0)) * 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));
	} else {
		tmp = fmax(t_0, (Math.abs(Math.sin((30.0 * x))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (30.0 * math.hypot(x, y)) - 25.0
	tmp = 0
	if x <= -2.6e+49:
		tmp = fmax(t_0, (math.fabs((30.0 * x)) - 0.2))
	elif x <= 11200.0:
		tmp = fmax(((30.0 * math.hypot(y, z)) - 25.0), (math.fabs(((math.sin((z * 30.0)) * 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))
	else:
		tmp = fmax(t_0, (math.fabs(math.sin((30.0 * x))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(30.0 * hypot(x, y)) - 25.0)
	tmp = 0.0
	if (x <= -2.6e+49)
		tmp = fmax(t_0, Float64(abs(Float64(30.0 * x)) - 0.2));
	elseif (x <= 11200.0)
		tmp = fmax(Float64(Float64(30.0 * hypot(y, z)) - 25.0), Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * 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));
	else
		tmp = fmax(t_0, Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (30.0 * hypot(x, y)) - 25.0;
	tmp = 0.0;
	if (x <= -2.6e+49)
		tmp = max(t_0, (abs((30.0 * x)) - 0.2));
	elseif (x <= 11200.0)
		tmp = max(((30.0 * hypot(y, z)) - 25.0), (abs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
	else
		tmp = max(t_0, (abs(sin((30.0 * x))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(30.0 * N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision]}, If[LessEqual[x, -2.6e+49], N[Max[t$95$0, N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 11200.0], N[Max[N[(N[(30.0 * N[Sqrt[y ^ 2 + z ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * 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], N[Max[t$95$0, N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.59999999999999989e49

   1. Initial program 37.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 89.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - \frac{1}{5}\right) \]

   14. Applied rewrites 89.9%

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - 0.2\right) \]

   if -2.59999999999999989e49 < x < 11200

   1. Initial program 55.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   if 11200 < x

   1. Initial program 39.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 85.8%

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 11200:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(y, z\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ t_1 := 30 \cdot \mathsf{hypot}\left(x, y\right) - 25\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{max}\left(t\_1, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 11200:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, z \cdot 30\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(30 \cdot x\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_1, \left|t\_0\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x))) (t_1 (- (* 30.0 (hypot x y)) 25.0)))
   (if (<= x -2.6e+49)
     (fmax t_1 (- (fabs (* 30.0 x)) 0.2))
     (if (<= x 11200.0)
       (fmax
        (- (hypot (* y 30.0) (* z 30.0)) 25.0)
        (- (fabs (fma (sin (* z 30.0)) (cos (* 30.0 x)) t_0)) 0.2))
       (fmax t_1 (- (fabs t_0) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double t_1 = (30.0 * hypot(x, y)) - 25.0;
	double tmp;
	if (x <= -2.6e+49) {
		tmp = fmax(t_1, (fabs((30.0 * x)) - 0.2));
	} else if (x <= 11200.0) {
		tmp = fmax((hypot((y * 30.0), (z * 30.0)) - 25.0), (fabs(fma(sin((z * 30.0)), cos((30.0 * x)), t_0)) - 0.2));
	} else {
		tmp = fmax(t_1, (fabs(t_0) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	t_1 = Float64(Float64(30.0 * hypot(x, y)) - 25.0)
	tmp = 0.0
	if (x <= -2.6e+49)
		tmp = fmax(t_1, Float64(abs(Float64(30.0 * x)) - 0.2));
	elseif (x <= 11200.0)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(z * 30.0)) - 25.0), Float64(abs(fma(sin(Float64(z * 30.0)), cos(Float64(30.0 * x)), t_0)) - 0.2));
	else
		tmp = fmax(t_1, Float64(abs(t_0) - 0.2));
	end
	return 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[(30.0 * N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision]}, If[LessEqual[x, -2.6e+49], N[Max[t$95$1, N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 11200.0], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[t$95$1, N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.59999999999999989e49

   1. Initial program 37.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 89.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - \frac{1}{5}\right) \]

   14. Applied rewrites 89.9%

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - 0.2\right) \]

   if -2.59999999999999989e49 < x < 11200

   1. Initial program 55.5%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 60.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 99.6%

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

   if 11200 < x

   1. Initial program 39.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 85.8%

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 30 \cdot \mathsf{hypot}\left(x, y\right) - 25\\ t_1 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 11200:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, z \cdot 30\right) - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_0, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* 30.0 (hypot x y)) 25.0))
        (t_1 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= x -2.6e+49)
     (fmax t_0 (- (fabs (* 30.0 x)) 0.2))
     (if (<= x 11200.0)
       (fmax (- (hypot (* y 30.0) (* z 30.0)) 25.0) t_1)
       (fmax t_0 t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = (30.0 * hypot(x, y)) - 25.0;
	double t_1 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (x <= -2.6e+49) {
		tmp = fmax(t_0, (fabs((30.0 * x)) - 0.2));
	} else if (x <= 11200.0) {
		tmp = fmax((hypot((y * 30.0), (z * 30.0)) - 25.0), t_1);
	} else {
		tmp = fmax(t_0, t_1);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (30.0 * Math.hypot(x, y)) - 25.0;
	double t_1 = Math.abs(Math.sin((30.0 * x))) - 0.2;
	double tmp;
	if (x <= -2.6e+49) {
		tmp = fmax(t_0, (Math.abs((30.0 * x)) - 0.2));
	} else if (x <= 11200.0) {
		tmp = fmax((Math.hypot((y * 30.0), (z * 30.0)) - 25.0), t_1);
	} else {
		tmp = fmax(t_0, t_1);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (30.0 * math.hypot(x, y)) - 25.0
	t_1 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if x <= -2.6e+49:
		tmp = fmax(t_0, (math.fabs((30.0 * x)) - 0.2))
	elif x <= 11200.0:
		tmp = fmax((math.hypot((y * 30.0), (z * 30.0)) - 25.0), t_1)
	else:
		tmp = fmax(t_0, t_1)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(30.0 * hypot(x, y)) - 25.0)
	t_1 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (x <= -2.6e+49)
		tmp = fmax(t_0, Float64(abs(Float64(30.0 * x)) - 0.2));
	elseif (x <= 11200.0)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(z * 30.0)) - 25.0), t_1);
	else
		tmp = fmax(t_0, t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (30.0 * hypot(x, y)) - 25.0;
	t_1 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (x <= -2.6e+49)
		tmp = max(t_0, (abs((30.0 * x)) - 0.2));
	elseif (x <= 11200.0)
		tmp = max((hypot((y * 30.0), (z * 30.0)) - 25.0), t_1);
	else
		tmp = max(t_0, t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(30.0 * N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -2.6e+49], N[Max[t$95$0, N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 11200.0], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[t$95$0, t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.59999999999999989e49

   1. Initial program 37.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 89.9%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - \frac{1}{5}\right) \]

   14. Applied rewrites 89.9%

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - 0.2\right) \]

   if -2.59999999999999989e49 < x < 11200

   1. Initial program 55.5%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 60.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 60.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 59.0%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 99.5%

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

   if 11200 < x

   1. Initial program 39.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 85.8%

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;z \leq -3 \cdot 10^{+186}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, t\_0\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30 - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= z -3e+186)
     (fmax (* -30.0 z) t_0)
     (if (<= z 1.3e+84)
       (fmax (- (* 30.0 (hypot x y)) 25.0) t_0)
       (fmax (- (* z 30.0) 25.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -3e+186) {
		tmp = fmax((-30.0 * z), t_0);
	} else if (z <= 1.3e+84) {
		tmp = fmax(((30.0 * hypot(x, y)) - 25.0), t_0);
	} else {
		tmp = fmax(((z * 30.0) - 25.0), t_0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -3e+186) {
		tmp = fmax((-30.0 * z), t_0);
	} else if (z <= 1.3e+84) {
		tmp = fmax(((30.0 * Math.hypot(x, y)) - 25.0), t_0);
	} else {
		tmp = fmax(((z * 30.0) - 25.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if z <= -3e+186:
		tmp = fmax((-30.0 * z), t_0)
	elif z <= 1.3e+84:
		tmp = fmax(((30.0 * math.hypot(x, y)) - 25.0), t_0)
	else:
		tmp = fmax(((z * 30.0) - 25.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (z <= -3e+186)
		tmp = fmax(Float64(-30.0 * z), t_0);
	elseif (z <= 1.3e+84)
		tmp = fmax(Float64(Float64(30.0 * hypot(x, y)) - 25.0), t_0);
	else
		tmp = fmax(Float64(Float64(z * 30.0) - 25.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (z <= -3e+186)
		tmp = max((-30.0 * z), t_0);
	elseif (z <= 1.3e+84)
		tmp = max(((30.0 * hypot(x, y)) - 25.0), t_0);
	else
		tmp = max(((z * 30.0) - 25.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -3e+186], N[Max[N[(-30.0 * z), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 1.3e+84], N[Max[N[(N[(30.0 * N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(z * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999982e186

   1. Initial program 7.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 8.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 8.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 7.6%

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

   12. Taylor expanded in z around -inf

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

   14. Applied rewrites 95.4%

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

   if -2.99999999999999982e186 < z < 1.3000000000000001e84

   1. Initial program 56.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 90.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 90.4%

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

   if 1.3000000000000001e84 < z

   1. Initial program 27.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 26.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 26.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 25.5%

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

   12. Taylor expanded in z around inf

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

   14. Applied rewrites 78.3%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot 30} - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 82.4% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;z \leq -3 \cdot 10^{+186}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, t\_0\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30 - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= z -3e+186)
     (fmax (* -30.0 z) t_0)
     (if (<= z 1.3e+84)
       (fmax (- (* 30.0 (hypot x y)) 25.0) (- (fabs (* 30.0 x)) 0.2))
       (fmax (- (* z 30.0) 25.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -3e+186) {
		tmp = fmax((-30.0 * z), t_0);
	} else if (z <= 1.3e+84) {
		tmp = fmax(((30.0 * hypot(x, y)) - 25.0), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax(((z * 30.0) - 25.0), t_0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -3e+186) {
		tmp = fmax((-30.0 * z), t_0);
	} else if (z <= 1.3e+84) {
		tmp = fmax(((30.0 * Math.hypot(x, y)) - 25.0), (Math.abs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax(((z * 30.0) - 25.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if z <= -3e+186:
		tmp = fmax((-30.0 * z), t_0)
	elif z <= 1.3e+84:
		tmp = fmax(((30.0 * math.hypot(x, y)) - 25.0), (math.fabs((30.0 * x)) - 0.2))
	else:
		tmp = fmax(((z * 30.0) - 25.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (z <= -3e+186)
		tmp = fmax(Float64(-30.0 * z), t_0);
	elseif (z <= 1.3e+84)
		tmp = fmax(Float64(Float64(30.0 * hypot(x, y)) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(Float64(z * 30.0) - 25.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (z <= -3e+186)
		tmp = max((-30.0 * z), t_0);
	elseif (z <= 1.3e+84)
		tmp = max(((30.0 * hypot(x, y)) - 25.0), (abs((30.0 * x)) - 0.2));
	else
		tmp = max(((z * 30.0) - 25.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -3e+186], N[Max[N[(-30.0 * z), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 1.3e+84], N[Max[N[(N[(30.0 * N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(z * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999982e186

   1. Initial program 7.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 8.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 8.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 7.6%

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

   12. Taylor expanded in z around -inf

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

   14. Applied rewrites 95.4%

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

   if -2.99999999999999982e186 < z < 1.3000000000000001e84

   1. Initial program 56.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 90.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 90.4%

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

   12. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - \frac{1}{5}\right) \]

   14. Applied rewrites 90.1%

       \[\leadsto \mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, y\right) - 25, \left|30 \cdot x\right| - 0.2\right) \]

   if 1.3000000000000001e84 < z

   1. Initial program 27.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 26.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 26.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 25.5%

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

   12. Taylor expanded in z around inf

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

   14. Applied rewrites 78.3%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot 30} - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 68.7% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_0\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= y -5.6e+91)
     (fmax (* -30.0 y) t_0)
     (if (<= y 7.5e+76)
       (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* z 30.0)) 0.2))
       (fmax (* y 30.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (y <= -5.6e+91) {
		tmp = fmax((-30.0 * y), t_0);
	} else if (y <= 7.5e+76) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((z * 30.0)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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) :: tmp
    t_0 = abs(sin((30.0d0 * x))) - 0.2d0
    if (y <= (-5.6d+91)) then
        tmp = fmax(((-30.0d0) * y), t_0)
    else if (y <= 7.5d+76) then
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((z * 30.0d0)) - 0.2d0))
    else
        tmp = fmax((y * 30.0d0), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * x))) - 0.2;
	double tmp;
	if (y <= -5.6e+91) {
		tmp = fmax((-30.0 * y), t_0);
	} else if (y <= 7.5e+76) {
		tmp = fmax((Math.sqrt(((x * x) * 900.0)) - 25.0), (Math.abs((z * 30.0)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if y <= -5.6e+91:
		tmp = fmax((-30.0 * y), t_0)
	elif y <= 7.5e+76:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((z * 30.0)) - 0.2))
	else:
		tmp = fmax((y * 30.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (y <= -5.6e+91)
		tmp = fmax(Float64(-30.0 * y), t_0);
	elseif (y <= 7.5e+76)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(z * 30.0)) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (y <= -5.6e+91)
		tmp = max((-30.0 * y), t_0);
	elseif (y <= 7.5e+76)
		tmp = max((sqrt(((x * x) * 900.0)) - 25.0), (abs((z * 30.0)) - 0.2));
	else
		tmp = max((y * 30.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -5.6e+91], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 7.5e+76], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5999999999999997e91

   1. Initial program 31.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 91.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 91.4%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 80.0%

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

   if -5.5999999999999997e91 < y < 7.4999999999999995e76

   1. Initial program 57.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.2%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 37.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 71.9%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.3%

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

   if 7.4999999999999995e76 < y

   1. Initial program 31.5%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 92.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 92.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 92.0%

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

   12. Taylor expanded in y around inf

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

   14. Applied rewrites 76.6%

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

Alternative 7: 67.9% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\left(x \cdot x\right) \cdot 900} - 25\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|y \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (sqrt (* (* x x) 900.0)) 25.0)))
   (if (<= y -5.6e+91)
     (fmax (* -30.0 y) (- (fabs (sin (* 30.0 x))) 0.2))
     (if (<= y 8.2e+70)
       (fmax t_0 (- (fabs (* z 30.0)) 0.2))
       (fmax t_0 (- (fabs (* y 30.0)) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sqrt(((x * x) * 900.0)) - 25.0;
	double tmp;
	if (y <= -5.6e+91) {
		tmp = fmax((-30.0 * y), (fabs(sin((30.0 * x))) - 0.2));
	} else if (y <= 8.2e+70) {
		tmp = fmax(t_0, (fabs((z * 30.0)) - 0.2));
	} else {
		tmp = fmax(t_0, (fabs((y * 30.0)) - 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) :: t_0
    real(8) :: tmp
    t_0 = sqrt(((x * x) * 900.0d0)) - 25.0d0
    if (y <= (-5.6d+91)) then
        tmp = fmax(((-30.0d0) * y), (abs(sin((30.0d0 * x))) - 0.2d0))
    else if (y <= 8.2d+70) then
        tmp = fmax(t_0, (abs((z * 30.0d0)) - 0.2d0))
    else
        tmp = fmax(t_0, (abs((y * 30.0d0)) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sqrt(((x * x) * 900.0)) - 25.0;
	double tmp;
	if (y <= -5.6e+91) {
		tmp = fmax((-30.0 * y), (Math.abs(Math.sin((30.0 * x))) - 0.2));
	} else if (y <= 8.2e+70) {
		tmp = fmax(t_0, (Math.abs((z * 30.0)) - 0.2));
	} else {
		tmp = fmax(t_0, (Math.abs((y * 30.0)) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sqrt(((x * x) * 900.0)) - 25.0
	tmp = 0
	if y <= -5.6e+91:
		tmp = fmax((-30.0 * y), (math.fabs(math.sin((30.0 * x))) - 0.2))
	elif y <= 8.2e+70:
		tmp = fmax(t_0, (math.fabs((z * 30.0)) - 0.2))
	else:
		tmp = fmax(t_0, (math.fabs((y * 30.0)) - 0.2))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0)
	tmp = 0.0
	if (y <= -5.6e+91)
		tmp = fmax(Float64(-30.0 * y), Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	elseif (y <= 8.2e+70)
		tmp = fmax(t_0, Float64(abs(Float64(z * 30.0)) - 0.2));
	else
		tmp = fmax(t_0, Float64(abs(Float64(y * 30.0)) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sqrt(((x * x) * 900.0)) - 25.0;
	tmp = 0.0;
	if (y <= -5.6e+91)
		tmp = max((-30.0 * y), (abs(sin((30.0 * x))) - 0.2));
	elseif (y <= 8.2e+70)
		tmp = max(t_0, (abs((z * 30.0)) - 0.2));
	else
		tmp = max(t_0, (abs((y * 30.0)) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision]}, If[LessEqual[y, -5.6e+91], N[Max[N[(-30.0 * y), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 8.2e+70], N[Max[t$95$0, N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[t$95$0, N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5999999999999997e91

   1. Initial program 31.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 91.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 91.4%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 80.0%

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

   if -5.5999999999999997e91 < y < 8.2000000000000004e70

   1. Initial program 57.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.5%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 37.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 72.4%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.7%

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

   if 8.2000000000000004e70 < y

   1. Initial program 31.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 31.1%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 6.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 6.9%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.9%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|y \cdot 30\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 67.0% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\left(x \cdot x\right) \cdot 900} - 25\\ \mathbf{if}\;y \leq -7 \cdot 10^{+41} \lor \neg \left(y \leq 8.2 \cdot 10^{+70}\right):\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|y \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (sqrt (* (* x x) 900.0)) 25.0)))
   (if (or (<= y -7e+41) (not (<= y 8.2e+70)))
     (fmax t_0 (- (fabs (* y 30.0)) 0.2))
     (fmax t_0 (- (fabs (* z 30.0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sqrt(((x * x) * 900.0)) - 25.0;
	double tmp;
	if ((y <= -7e+41) || !(y <= 8.2e+70)) {
		tmp = fmax(t_0, (fabs((y * 30.0)) - 0.2));
	} else {
		tmp = fmax(t_0, (fabs((z * 30.0)) - 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) :: t_0
    real(8) :: tmp
    t_0 = sqrt(((x * x) * 900.0d0)) - 25.0d0
    if ((y <= (-7d+41)) .or. (.not. (y <= 8.2d+70))) then
        tmp = fmax(t_0, (abs((y * 30.0d0)) - 0.2d0))
    else
        tmp = fmax(t_0, (abs((z * 30.0d0)) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sqrt(((x * x) * 900.0)) - 25.0;
	double tmp;
	if ((y <= -7e+41) || !(y <= 8.2e+70)) {
		tmp = fmax(t_0, (Math.abs((y * 30.0)) - 0.2));
	} else {
		tmp = fmax(t_0, (Math.abs((z * 30.0)) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sqrt(((x * x) * 900.0)) - 25.0
	tmp = 0
	if (y <= -7e+41) or not (y <= 8.2e+70):
		tmp = fmax(t_0, (math.fabs((y * 30.0)) - 0.2))
	else:
		tmp = fmax(t_0, (math.fabs((z * 30.0)) - 0.2))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0)
	tmp = 0.0
	if ((y <= -7e+41) || !(y <= 8.2e+70))
		tmp = fmax(t_0, Float64(abs(Float64(y * 30.0)) - 0.2));
	else
		tmp = fmax(t_0, Float64(abs(Float64(z * 30.0)) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sqrt(((x * x) * 900.0)) - 25.0;
	tmp = 0.0;
	if ((y <= -7e+41) || ~((y <= 8.2e+70)))
		tmp = max(t_0, (abs((y * 30.0)) - 0.2));
	else
		tmp = max(t_0, (abs((z * 30.0)) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision]}, If[Or[LessEqual[y, -7e+41], N[Not[LessEqual[y, 8.2e+70]], $MachinePrecision]], N[Max[t$95$0, N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[t$95$0, N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999998e41 or 8.2000000000000004e70 < y

   1. Initial program 34.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 34.4%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 8.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 8.9%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.8%

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

   if -6.9999999999999998e41 < y < 8.2000000000000004e70

   1. Initial program 57.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.1%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 38.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 74.5%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 74.0%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+41} \lor \neg \left(y \leq 8.2 \cdot 10^{+70}\right):\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|y \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.7% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+152} \lor \neg \left(x \leq 4.5 \cdot 10^{+152}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|y \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.5e+152) (not (<= x 4.5e+152)))
   (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))
   (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* y 30.0)) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.5e+152) || !(x <= 4.5e+152)) {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((y * 30.0)) - 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 <= (-4.5d+152)) .or. (.not. (x <= 4.5d+152))) then
        tmp = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    else
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((y * 30.0d0)) - 0.2d0))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.5e+152) or not (x <= 4.5e+152):
		tmp = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	else:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((y * 30.0)) - 0.2))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.5e+152], N[Not[LessEqual[x, 4.5e+152]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000001e152 or 4.5000000000000001e152 < x

   1. Initial program 9.2%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 38.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 38.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 38.7%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 79.3%

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

   if -4.5000000000000001e152 < x < 4.5000000000000001e152

   1. Initial program 58.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 58.6%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 30.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 29.7%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 66.8%

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

4. Final simplification 69.7%

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

Alternative 10: 30.5% accurate, 9.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 47.5%

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

3. Taylor expanded in x around -inf

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

5. Applied rewrites 17.4%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 17.1%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 16.5%

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

12. Taylor expanded in x around 0

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

14. Applied rewrites 33.1%

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

Reproduce

herbie shell --seed 2025042 -o generate:proofs
(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)))