Gyroid sphere

Percentage Accurate: 46.3% → 86.4%

Time: 4.8s

Alternatives: 7

Speedup: 5.8×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 46.3% 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: 86.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right) + 30 \cdot y\right| - 0.2\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_0\right)\\ \mathbf{elif}\;y \leq 10^{+67}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(x, z\right) - 25, \left|\sin \left(y \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (+ (sin (* 30.0 x)) (* 30.0 y))) 0.2)))
   (if (<= y -4.2e+119)
     (fmax (* -30.0 x) t_0)
     (if (<= y 1e+67)
       (fmax (- (* 30.0 (hypot x z)) 25.0) (- (fabs (sin (* y 30.0))) 0.2))
       (fmax (- (* (+ (/ 25.0 x) 30.0) x)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((sin((30.0 * x)) + (30.0 * y))) - 0.2;
	double tmp;
	if (y <= -4.2e+119) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (y <= 1e+67) {
		tmp = fmax(((30.0 * hypot(x, z)) - 25.0), (fabs(sin((y * 30.0))) - 0.2));
	} else {
		tmp = fmax(-(((25.0 / x) + 30.0) * x), 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)) + (30.0 * y))) - 0.2;
	double tmp;
	if (y <= -4.2e+119) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (y <= 1e+67) {
		tmp = fmax(((30.0 * Math.hypot(x, z)) - 25.0), (Math.abs(Math.sin((y * 30.0))) - 0.2));
	} else {
		tmp = fmax(-(((25.0 / x) + 30.0) * x), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((math.sin((30.0 * x)) + (30.0 * y))) - 0.2
	tmp = 0
	if y <= -4.2e+119:
		tmp = fmax((-30.0 * x), t_0)
	elif y <= 1e+67:
		tmp = fmax(((30.0 * math.hypot(x, z)) - 25.0), (math.fabs(math.sin((y * 30.0))) - 0.2))
	else:
		tmp = fmax(-(((25.0 / x) + 30.0) * x), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(sin(Float64(30.0 * x)) + Float64(30.0 * y))) - 0.2)
	tmp = 0.0
	if (y <= -4.2e+119)
		tmp = fmax(Float64(-30.0 * x), t_0);
	elseif (y <= 1e+67)
		tmp = fmax(Float64(Float64(30.0 * hypot(x, z)) - 25.0), Float64(abs(sin(Float64(y * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(-Float64(Float64(Float64(25.0 / x) + 30.0) * x)), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((sin((30.0 * x)) + (30.0 * y))) - 0.2;
	tmp = 0.0;
	if (y <= -4.2e+119)
		tmp = max((-30.0 * x), t_0);
	elseif (y <= 1e+67)
		tmp = max(((30.0 * hypot(x, z)) - 25.0), (abs(sin((y * 30.0))) - 0.2));
	else
		tmp = max(-(((25.0 / x) + 30.0) * x), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(30.0 * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -4.2e+119], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 1e+67], N[Max[N[(N[(30.0 * N[Sqrt[x ^ 2 + z ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[(-N[(N[(N[(25.0 / x), $MachinePrecision] + 30.0), $MachinePrecision] * x), $MachinePrecision]), t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999966e119

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in x around -inf

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

   10. Applied rewrites 17.3%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 45.6%

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

   if -4.19999999999999966e119 < y < 9.99999999999999983e66

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 35.9%

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

   12. Applied rewrites 70.8%

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

   if 9.99999999999999983e66 < y

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in x around -inf

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

   10. Applied rewrites 28.0%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.6%

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

Alternative 2: 70.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+188}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z - 25, \left|\sin \left(y \cdot 30\right)\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, \left|\sin \left(30 \cdot x\right) + 30 \cdot y\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - 25 \cdot \frac{1}{z}\right), \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.65e+188)
   (fmax (- (* -30.0 z) 25.0) (- (fabs (sin (* y 30.0))) 0.2))
   (if (<= z 7.2e+24)
     (fmax
      (- (* (+ (/ 25.0 x) 30.0) x))
      (- (fabs (+ (sin (* 30.0 x)) (* 30.0 y))) 0.2))
     (fmax
      (* z (- 30.0 (* 25.0 (/ 1.0 z))))
      (- (fabs (sin (* z 30.0))) 0.2)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.65e+188) {
		tmp = fmax(((-30.0 * z) - 25.0), (fabs(sin((y * 30.0))) - 0.2));
	} else if (z <= 7.2e+24) {
		tmp = fmax(-(((25.0 / x) + 30.0) * x), (fabs((sin((30.0 * x)) + (30.0 * y))) - 0.2));
	} else {
		tmp = fmax((z * (30.0 - (25.0 * (1.0 / z)))), (fabs(sin((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) :: tmp
    if (z <= (-1.65d+188)) then
        tmp = fmax((((-30.0d0) * z) - 25.0d0), (abs(sin((y * 30.0d0))) - 0.2d0))
    else if (z <= 7.2d+24) then
        tmp = fmax(-(((25.0d0 / x) + 30.0d0) * x), (abs((sin((30.0d0 * x)) + (30.0d0 * y))) - 0.2d0))
    else
        tmp = fmax((z * (30.0d0 - (25.0d0 * (1.0d0 / z)))), (abs(sin((z * 30.0d0))) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.65e+188) {
		tmp = fmax(((-30.0 * z) - 25.0), (Math.abs(Math.sin((y * 30.0))) - 0.2));
	} else if (z <= 7.2e+24) {
		tmp = fmax(-(((25.0 / x) + 30.0) * x), (Math.abs((Math.sin((30.0 * x)) + (30.0 * y))) - 0.2));
	} else {
		tmp = fmax((z * (30.0 - (25.0 * (1.0 / z)))), (Math.abs(Math.sin((z * 30.0))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.65e+188:
		tmp = fmax(((-30.0 * z) - 25.0), (math.fabs(math.sin((y * 30.0))) - 0.2))
	elif z <= 7.2e+24:
		tmp = fmax(-(((25.0 / x) + 30.0) * x), (math.fabs((math.sin((30.0 * x)) + (30.0 * y))) - 0.2))
	else:
		tmp = fmax((z * (30.0 - (25.0 * (1.0 / z)))), (math.fabs(math.sin((z * 30.0))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.65e+188)
		tmp = fmax(Float64(Float64(-30.0 * z) - 25.0), Float64(abs(sin(Float64(y * 30.0))) - 0.2));
	elseif (z <= 7.2e+24)
		tmp = fmax(Float64(-Float64(Float64(Float64(25.0 / x) + 30.0) * x)), Float64(abs(Float64(sin(Float64(30.0 * x)) + Float64(30.0 * y))) - 0.2));
	else
		tmp = fmax(Float64(z * Float64(30.0 - Float64(25.0 * Float64(1.0 / z)))), Float64(abs(sin(Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.65e+188)
		tmp = max(((-30.0 * z) - 25.0), (abs(sin((y * 30.0))) - 0.2));
	elseif (z <= 7.2e+24)
		tmp = max(-(((25.0 / x) + 30.0) * x), (abs((sin((30.0 * x)) + (30.0 * y))) - 0.2));
	else
		tmp = max((z * (30.0 - (25.0 * (1.0 / z)))), (abs(sin((z * 30.0))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.65e+188], N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 7.2e+24], N[Max[(-N[(N[(N[(25.0 / x), $MachinePrecision] + 30.0), $MachinePrecision] * x), $MachinePrecision]), N[(N[Abs[N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(30.0 * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * N[(30.0 - N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999991e188

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in z around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-1 \cdot \left(z \cdot \left(30 + \frac{1}{60} \cdot \frac{900 \cdot {x}^{2} + 900 \cdot {y}^{2}}{{z}^{2}}\right)\right)} - 25, \left|\sin \left(y \cdot 30\right)\right| - \frac{1}{5}\right) \]

   10. Applied rewrites 24.1%

       \[\leadsto \mathsf{max}\left(\color{blue}{\left(-\mathsf{fma}\left(\frac{\mathsf{fma}\left(x, x, y \cdot y\right) \cdot 900}{z \cdot z}, 0.016666666666666666, 30\right) \cdot z\right)} - 25, \left|\sin \left(y \cdot 30\right)\right| - 0.2\right) \]

   11. Taylor expanded in z around inf

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

   13. Applied rewrites 28.6%

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

   if -1.64999999999999991e188 < z < 7.19999999999999966e24

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in x around -inf

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

   10. Applied rewrites 28.0%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.6%

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

   if 7.19999999999999966e24 < z

   1. Initial program 46.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 27.6%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 63.3% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + 30 \cdot y\right| - 0.2\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 15500000000:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \sqrt{\mathsf{fma}\left(x, x, z \cdot z\right)} - 25, \left|y \cdot \left(30 + -4500 \cdot {y}^{2}\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fmax (* -30.0 x) (- (fabs (+ (sin (* 30.0 x)) (* 30.0 y))) 0.2))))
   (if (<= y -9.5e+39)
     t_0
     (if (<= y 15500000000.0)
       (fmax
        (- (* 30.0 (sqrt (fma x x (* z z)))) 25.0)
        (- (fabs (* y (+ 30.0 (* -4500.0 (pow y 2.0))))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs((sin((30.0 * x)) + (30.0 * y))) - 0.2));
	double tmp;
	if (y <= -9.5e+39) {
		tmp = t_0;
	} else if (y <= 15500000000.0) {
		tmp = fmax(((30.0 * sqrt(fma(x, x, (z * z)))) - 25.0), (fabs((y * (30.0 + (-4500.0 * pow(y, 2.0))))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(Float64(sin(Float64(30.0 * x)) + Float64(30.0 * y))) - 0.2))
	tmp = 0.0
	if (y <= -9.5e+39)
		tmp = t_0;
	elseif (y <= 15500000000.0)
		tmp = fmax(Float64(Float64(30.0 * sqrt(fma(x, x, Float64(z * z)))) - 25.0), Float64(abs(Float64(y * Float64(30.0 + Float64(-4500.0 * (y ^ 2.0))))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(30.0 * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -9.5e+39], t$95$0, If[LessEqual[y, 15500000000.0], N[Max[N[(N[(30.0 * N[Sqrt[N[(x * x + N[(z * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(y * N[(30.0 + N[(-4500.0 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000011e39 or 1.55e10 < y

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in x around -inf

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

   10. Applied rewrites 17.3%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 45.6%

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

   if -9.50000000000000011e39 < y < 1.55e10

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 35.9%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(30 \cdot \sqrt{\mathsf{fma}\left(x, x, z \cdot z\right)} - 25, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - \frac{1}{5}\right) \]

   13. Applied rewrites 33.9%

       \[\leadsto \mathsf{max}\left(30 \cdot \sqrt{\mathsf{fma}\left(x, x, z \cdot z\right)} - 25, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 46.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \sqrt{\mathsf{fma}\left(x, x, z \cdot z\right)} - 25, \left|y \cdot \left(30 + -4500 \cdot {y}^{2}\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.22e+41)
   (fmax (* -30.0 y) (- (fabs (sin (* z 30.0))) 0.2))
   (fmax
    (- (* 30.0 (sqrt (fma x x (* z z)))) 25.0)
    (- (fabs (* y (+ 30.0 (* -4500.0 (pow y 2.0))))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.22e+41) {
		tmp = fmax((-30.0 * y), (fabs(sin((z * 30.0))) - 0.2));
	} else {
		tmp = fmax(((30.0 * sqrt(fma(x, x, (z * z)))) - 25.0), (fabs((y * (30.0 + (-4500.0 * pow(y, 2.0))))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.22e+41)
		tmp = fmax(Float64(-30.0 * y), Float64(abs(sin(Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(Float64(30.0 * sqrt(fma(x, x, Float64(z * z)))) - 25.0), Float64(abs(Float64(y * Float64(30.0 + Float64(-4500.0 * (y ^ 2.0))))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.22e+41], N[Max[N[(-30.0 * y), $MachinePrecision], N[(N[Abs[N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 * N[Sqrt[N[(x * x + N[(z * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(y * N[(30.0 + N[(-4500.0 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22e41

   1. Initial program 46.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in y around -inf

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

   10. Applied rewrites 18.3%

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

   if -1.22e41 < y

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 35.9%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(30 \cdot \sqrt{\mathsf{fma}\left(x, x, z \cdot z\right)} - 25, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - \frac{1}{5}\right) \]

   13. Applied rewrites 33.9%

       \[\leadsto \mathsf{max}\left(30 \cdot \sqrt{\mathsf{fma}\left(x, x, z \cdot z\right)} - 25, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 39.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, \left|y \cdot \left(30 + -4500 \cdot {y}^{2}\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+41)
   (fmax (* -30.0 y) (- (fabs (sin (* z 30.0))) 0.2))
   (fmax
    (- (* (+ (/ 25.0 x) 30.0) x))
    (- (fabs (* y (+ 30.0 (* -4500.0 (pow y 2.0))))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+41) {
		tmp = fmax((-30.0 * y), (fabs(sin((z * 30.0))) - 0.2));
	} else {
		tmp = fmax(-(((25.0 / x) + 30.0) * x), (fabs((y * (30.0 + (-4500.0 * pow(y, 2.0))))) - 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 (y <= (-2.7d+41)) then
        tmp = fmax(((-30.0d0) * y), (abs(sin((z * 30.0d0))) - 0.2d0))
    else
        tmp = fmax(-(((25.0d0 / x) + 30.0d0) * x), (abs((y * (30.0d0 + ((-4500.0d0) * (y ** 2.0d0))))) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+41) {
		tmp = fmax((-30.0 * y), (Math.abs(Math.sin((z * 30.0))) - 0.2));
	} else {
		tmp = fmax(-(((25.0 / x) + 30.0) * x), (Math.abs((y * (30.0 + (-4500.0 * Math.pow(y, 2.0))))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+41:
		tmp = fmax((-30.0 * y), (math.fabs(math.sin((z * 30.0))) - 0.2))
	else:
		tmp = fmax(-(((25.0 / x) + 30.0) * x), (math.fabs((y * (30.0 + (-4500.0 * math.pow(y, 2.0))))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+41)
		tmp = fmax(Float64(-30.0 * y), Float64(abs(sin(Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(-Float64(Float64(Float64(25.0 / x) + 30.0) * x)), Float64(abs(Float64(y * Float64(30.0 + Float64(-4500.0 * (y ^ 2.0))))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+41)
		tmp = max((-30.0 * y), (abs(sin((z * 30.0))) - 0.2));
	else
		tmp = max(-(((25.0 / x) + 30.0) * x), (abs((y * (30.0 + (-4500.0 * (y ^ 2.0))))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+41], N[Max[N[(-30.0 * y), $MachinePrecision], N[(N[Abs[N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[(-N[(N[(N[(25.0 / x), $MachinePrecision] + 30.0), $MachinePrecision] * x), $MachinePrecision]), N[(N[Abs[N[(y * N[(30.0 + N[(-4500.0 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e41

   1. Initial program 46.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 46.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in y around -inf

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

   10. Applied rewrites 18.3%

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

   if -2.7e41 < y

   1. Initial program 46.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.7%

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

   8. Taylor expanded in x around -inf

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

   10. Applied rewrites 28.0%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - \frac{1}{5}\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto \mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 26.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, \left|y \cdot \left(30 + -4500 \cdot {y}^{2}\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (* (+ (/ 25.0 x) 30.0) x))
  (- (fabs (* y (+ 30.0 (* -4500.0 (pow y 2.0))))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax(-(((25.0 / x) + 30.0) * x), (fabs((y * (30.0 + (-4500.0 * pow(y, 2.0))))) - 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(-(((25.0d0 / x) + 30.0d0) * x), (abs((y * (30.0d0 + ((-4500.0d0) * (y ** 2.0d0))))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax(-(((25.0 / x) + 30.0) * x), (Math.abs((y * (30.0 + (-4500.0 * Math.pow(y, 2.0))))) - 0.2));
}

Python

def code(x, y, z):
	return fmax(-(((25.0 / x) + 30.0) * x), (math.fabs((y * (30.0 + (-4500.0 * math.pow(y, 2.0))))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(-Float64(Float64(Float64(25.0 / x) + 30.0) * x)), Float64(abs(Float64(y * Float64(30.0 + Float64(-4500.0 * (y ^ 2.0))))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max(-(((25.0 / x) + 30.0) * x), (abs((y * (30.0 + (-4500.0 * (y ^ 2.0))))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[(-N[(N[(N[(25.0 / x), $MachinePrecision] + 30.0), $MachinePrecision] * x), $MachinePrecision]), N[(N[Abs[N[(y * N[(30.0 + N[(-4500.0 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 46.3%

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

2. Taylor expanded in z around 0

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

4. Applied rewrites 45.9%

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

5. Taylor expanded in x around 0

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

7. Applied rewrites 45.7%

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

8. Taylor expanded in x around -inf

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

10. Applied rewrites 28.0%

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

11. Taylor expanded in y around 0

    \[\leadsto \mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - \frac{1}{5}\right) \]

13. Applied rewrites 26.2%

    \[\leadsto \mathsf{max}\left(-\left(\frac{25}{x} + 30\right) \cdot x, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - 0.2\right) \]
14. Add Preprocessing

Alternative 7: 15.4% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(-30 \cdot x, \left|y \cdot \left(30 + -4500 \cdot {y}^{2}\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax (* -30.0 x) (- (fabs (* y (+ 30.0 (* -4500.0 (pow y 2.0))))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((-30.0 * x), (fabs((y * (30.0 + (-4500.0 * pow(y, 2.0))))) - 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(((-30.0d0) * x), (abs((y * (30.0d0 + ((-4500.0d0) * (y ** 2.0d0))))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax((-30.0 * x), (Math.abs((y * (30.0 + (-4500.0 * Math.pow(y, 2.0))))) - 0.2));
}

Python

def code(x, y, z):
	return fmax((-30.0 * x), (math.fabs((y * (30.0 + (-4500.0 * math.pow(y, 2.0))))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(-30.0 * x), Float64(abs(Float64(y * Float64(30.0 + Float64(-4500.0 * (y ^ 2.0))))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((-30.0 * x), (abs((y * (30.0 + (-4500.0 * (y ^ 2.0))))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * N[(30.0 + N[(-4500.0 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 46.3%

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

2. Taylor expanded in z around 0

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

4. Applied rewrites 45.9%

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

5. Taylor expanded in x around 0

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

7. Applied rewrites 45.7%

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

8. Taylor expanded in x around -inf

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

10. Applied rewrites 17.3%

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

11. Taylor expanded in y around 0

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - \frac{1}{5}\right) \]

13. Applied rewrites 15.4%

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|y \cdot \left(30 + \color{blue}{-4500 \cdot {y}^{2}}\right)\right| - 0.2\right) \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025141 
(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)))