Gyroid sphere

Percentage Accurate: 46.2% → 90.3%

Time: 6.3s

Alternatives: 12

Speedup: 4.7×

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: 46.2% 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: 90.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ t_1 := \sin \left(y \cdot 30\right)\\ t_2 := \cos \left(y \cdot 30\right)\\ t_3 := \sin \left(z \cdot 30\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y, x\right) \cdot 30 - 25, \left|\mathsf{fma}\left(t\_0, t\_2, t\_1\right)\right| - 0.2\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|t\_3 \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot t\_2 + t\_1 \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(t\_3, \cos \left(30 \cdot x\right), t\_0\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x)))
        (t_1 (sin (* y 30.0)))
        (t_2 (cos (* y 30.0)))
        (t_3 (sin (* z 30.0))))
   (if (<= y -2.3e+33)
     (fmax (- (* (hypot y x) 30.0) 25.0) (- (fabs (fma t_0 t_2 t_1)) 0.2))
     (if (<= y 1.4e+97)
       (fmax
        (- (hypot (* z 30.0) (* 30.0 x)) 25.0)
        (-
         (fabs
          (+
           (* t_3 (cos (* x 30.0)))
           (+ (* (sin (* x 30.0)) t_2) (* t_1 (cos (* z 30.0))))))
         0.2))
       (fmax
        (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
        (- (fabs (fma t_3 (cos (* 30.0 x)) t_0)) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double t_1 = sin((y * 30.0));
	double t_2 = cos((y * 30.0));
	double t_3 = sin((z * 30.0));
	double tmp;
	if (y <= -2.3e+33) {
		tmp = fmax(((hypot(y, x) * 30.0) - 25.0), (fabs(fma(t_0, t_2, t_1)) - 0.2));
	} else if (y <= 1.4e+97) {
		tmp = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs(((t_3 * cos((x * 30.0))) + ((sin((x * 30.0)) * t_2) + (t_1 * cos((z * 30.0)))))) - 0.2));
	} else {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs(fma(t_3, cos((30.0 * x)), t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	t_1 = sin(Float64(y * 30.0))
	t_2 = cos(Float64(y * 30.0))
	t_3 = sin(Float64(z * 30.0))
	tmp = 0.0
	if (y <= -2.3e+33)
		tmp = fmax(Float64(Float64(hypot(y, x) * 30.0) - 25.0), Float64(abs(fma(t_0, t_2, t_1)) - 0.2));
	elseif (y <= 1.4e+97)
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(Float64(t_3 * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * t_2) + Float64(t_1 * cos(Float64(z * 30.0)))))) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(fma(t_3, cos(Float64(30.0 * x)), 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[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -2.3e+33], N[Max[N[(N[(N[Sqrt[y ^ 2 + x ^ 2], $MachinePrecision] * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * t$95$2 + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 1.4e+97], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(t$95$3 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision] + N[(t$95$1 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$3 * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000011e33

   1. Initial program 43.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 43.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. +-commutative N/A

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

      10. unpow2 N/A

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

      11. unpow-prod-down N/A

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

      12. metadata-eval N/A

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

      13. unpow-prod-down N/A

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

      14. metadata-eval N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

   7. Applied rewrites 43.1%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 92.2%

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

   if -2.30000000000000011e33 < y < 1.4e97

   1. Initial program 51.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 95.2%

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

   if 1.4e97 < y

   1. Initial program 17.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 93.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 93.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y, x\right) \cdot 30 - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 70.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ t_1 := \sin \left(y \cdot 30\right)\\ t_2 := \cos \left(y \cdot 30\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot t\_2 + t\_1 \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot 30, z \cdot 30, 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, \left|\mathsf{fma}\left(t\_0, t\_2, t\_1\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, t\_0\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x))) (t_1 (sin (* y 30.0))) (t_2 (cos (* y 30.0))))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (* (sin (* z 30.0)) (cos (* x 30.0)))
            (+ (* (sin (* x 30.0)) t_2) (* t_1 (cos (* z 30.0))))))
          0.2))
        1e+154)
     (fmax
      (- (sqrt (fma (* z 30.0) (* z 30.0) (* 900.0 (fma x x (* y y))))) 25.0)
      (- (fabs (fma t_0 t_2 t_1)) 0.2))
     (fmax (* -30.0 x) (- (fabs (fma (* z 30.0) 1.0 t_0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double t_1 = sin((y * 30.0));
	double t_2 = cos((y * 30.0));
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * t_2) + (t_1 * cos((z * 30.0)))))) - 0.2)) <= 1e+154) {
		tmp = fmax((sqrt(fma((z * 30.0), (z * 30.0), (900.0 * fma(x, x, (y * y))))) - 25.0), (fabs(fma(t_0, t_2, t_1)) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (fabs(fma((z * 30.0), 1.0, t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	t_1 = sin(Float64(y * 30.0))
	t_2 = cos(Float64(y * 30.0))
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * t_2) + Float64(t_1 * cos(Float64(z * 30.0)))))) - 0.2)) <= 1e+154)
		tmp = fmax(Float64(sqrt(fma(Float64(z * 30.0), Float64(z * 30.0), Float64(900.0 * fma(x, x, Float64(y * y))))) - 25.0), Float64(abs(fma(t_0, t_2, t_1)) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(Float64(z * 30.0), 1.0, 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[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(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] * t$95$2), $MachinePrecision] + N[(t$95$1 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 1e+154], N[Max[N[(N[Sqrt[N[(N[(z * 30.0), $MachinePrecision] * N[(z * 30.0), $MachinePrecision] + N[(900.0 * N[(x * x + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * t$95$2 + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[(z * 30.0), $MachinePrecision] * 1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 1.00000000000000004e154

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. +-commutative N/A

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

      10. unpow2 N/A

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

      11. unpow-prod-down N/A

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

      12. metadata-eval N/A

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

      13. unpow-prod-down N/A

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

      14. metadata-eval N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

   7. Applied rewrites 98.0%

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

   if 1.00000000000000004e154 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 9.0%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 21.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 21.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 38.6%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 50.6%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot 30, z \cdot 30, 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(y \cdot 30\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + t\_0 \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot 30, z \cdot 30, 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, \left|t\_0\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* y 30.0))))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (* (sin (* z 30.0)) (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* t_0 (cos (* z 30.0))))))
          0.2))
        1e+154)
     (fmax
      (- (sqrt (fma (* z 30.0) (* z 30.0) (* 900.0 (fma x x (* y y))))) 25.0)
      (- (fabs t_0) 0.2))
     (fmax (* -30.0 x) (- (fabs (fma (* z 30.0) 1.0 (sin (* 30.0 x)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((y * 30.0));
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (t_0 * cos((z * 30.0)))))) - 0.2)) <= 1e+154) {
		tmp = fmax((sqrt(fma((z * 30.0), (z * 30.0), (900.0 * fma(x, x, (y * y))))) - 25.0), (fabs(t_0) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (fabs(fma((z * 30.0), 1.0, sin((30.0 * x)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(y * 30.0))
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(t_0 * cos(Float64(z * 30.0)))))) - 0.2)) <= 1e+154)
		tmp = fmax(Float64(sqrt(fma(Float64(z * 30.0), Float64(z * 30.0), Float64(900.0 * fma(x, x, Float64(y * y))))) - 25.0), Float64(abs(t_0) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(Float64(z * 30.0), 1.0, sin(Float64(30.0 * x)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(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[(t$95$0 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 1e+154], N[Max[N[(N[Sqrt[N[(N[(z * 30.0), $MachinePrecision] * N[(z * 30.0), $MachinePrecision] + N[(900.0 * N[(x * x + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[(z * 30.0), $MachinePrecision] * 1.0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 1.00000000000000004e154

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. +-commutative N/A

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

      10. unpow2 N/A

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

      11. unpow-prod-down N/A

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

      12. metadata-eval N/A

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

      13. unpow-prod-down N/A

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

      14. metadata-eval N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

   7. Applied rewrites 98.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 97.4%

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

   if 1.00000000000000004e154 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 9.0%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 21.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 21.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 38.6%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 50.6%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot 30, z \cdot 30, 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, \left|\sin \left(y \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(y \cdot 30\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + t\_0 \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 20:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(y \cdot y\right) \cdot 900} - 25, \left|t\_0\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, \cos \left(30 \cdot x\right), 30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* y 30.0))))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (* (sin (* z 30.0)) (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* t_0 (cos (* z 30.0))))))
          0.2))
        20.0)
     (fmax (- (sqrt (* (* y y) 900.0)) 25.0) (- (fabs t_0) 0.2))
     (fmax
      (* -30.0 x)
      (- (fabs (fma (* z 30.0) (cos (* 30.0 x)) (* 30.0 x))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((y * 30.0));
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (t_0 * cos((z * 30.0)))))) - 0.2)) <= 20.0) {
		tmp = fmax((sqrt(((y * y) * 900.0)) - 25.0), (fabs(t_0) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (fabs(fma((z * 30.0), cos((30.0 * x)), (30.0 * x))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(y * 30.0))
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(t_0 * cos(Float64(z * 30.0)))))) - 0.2)) <= 20.0)
		tmp = fmax(Float64(sqrt(Float64(Float64(y * y) * 900.0)) - 25.0), Float64(abs(t_0) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(Float64(z * 30.0), cos(Float64(30.0 * x)), Float64(30.0 * x))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(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[(t$95$0 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 20.0], N[Max[N[(N[Sqrt[N[(N[(y * y), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[(z * 30.0), $MachinePrecision] * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 20

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 92.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 92.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 90.2%

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

   if 20 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 37.4%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 22.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 21.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 40.6%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 51.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 20:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(y \cdot y\right) \cdot 900} - 25, \left|\sin \left(y \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, \cos \left(30 \cdot x\right), 30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 20:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(y \cdot y\right) \cdot 900} - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, \cos \left(30 \cdot x\right), 30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (fmax
       (-
        (sqrt
         (+
          (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
          (pow (* z 30.0) 2.0)))
        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))
      20.0)
   (fmax (- (sqrt (* (* y y) 900.0)) 25.0) (- (fabs (sin (* 30.0 x))) 0.2))
   (fmax
    (* -30.0 x)
    (- (fabs (fma (* z 30.0) (cos (* 30.0 x)) (* 30.0 x))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs(((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)) <= 20.0) {
		tmp = fmax((sqrt(((y * y) * 900.0)) - 25.0), (fabs(sin((30.0 * x))) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (fabs(fma((z * 30.0), cos((30.0 * x)), (30.0 * x))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(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)) <= 20.0)
		tmp = fmax(Float64(sqrt(Float64(Float64(y * y) * 900.0)) - 25.0), Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(Float64(z * 30.0), cos(Float64(30.0 * x)), Float64(30.0 * x))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(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], 20.0], N[Max[N[(N[Sqrt[N[(N[(y * y), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[(z * 30.0), $MachinePrecision] * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 20

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 92.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 92.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 88.8%

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

   if 20 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 37.4%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 22.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 21.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 40.6%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 51.9%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 20:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(y \cdot y\right) \cdot 900} - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, \cos \left(30 \cdot x\right), 30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|t\_0 + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|t\_0 + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin (* z 30.0)) (cos (* x 30.0)))))
   (if (or (<= z -1.15e+30) (not (<= z 1.3e+69)))
     (fmax
      (- (hypot (* z 30.0) (* 30.0 x)) 25.0)
      (- (fabs (+ t_0 (sin (* 30.0 x)))) 0.2))
     (fmax
      (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
      (-
       (fabs
        (+
         t_0
         (+
          (* (sin (* x 30.0)) (cos (* y 30.0)))
          (* (sin (* y 30.0)) (cos (* z 30.0))))))
       0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0)) * cos((x * 30.0));
	double tmp;
	if ((z <= -1.15e+30) || !(z <= 1.3e+69)) {
		tmp = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs((t_0 + sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs((t_0 + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin((z * 30.0)) * Math.cos((x * 30.0));
	double tmp;
	if ((z <= -1.15e+30) || !(z <= 1.3e+69)) {
		tmp = fmax((Math.hypot((z * 30.0), (30.0 * x)) - 25.0), (Math.abs((t_0 + Math.sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax((Math.hypot((y * 30.0), (30.0 * x)) - 25.0), (Math.abs((t_0 + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin((z * 30.0)) * math.cos((x * 30.0))
	tmp = 0
	if (z <= -1.15e+30) or not (z <= 1.3e+69):
		tmp = fmax((math.hypot((z * 30.0), (30.0 * x)) - 25.0), (math.fabs((t_0 + math.sin((30.0 * x)))) - 0.2))
	else:
		tmp = fmax((math.hypot((y * 30.0), (30.0 * x)) - 25.0), (math.fabs((t_0 + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0)))
	tmp = 0.0
	if ((z <= -1.15e+30) || !(z <= 1.3e+69))
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(t_0 + sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(t_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));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin((z * 30.0)) * cos((x * 30.0));
	tmp = 0.0;
	if ((z <= -1.15e+30) || ~((z <= 1.3e+69)))
		tmp = max((hypot((z * 30.0), (30.0 * x)) - 25.0), (abs((t_0 + sin((30.0 * x)))) - 0.2));
	else
		tmp = max((hypot((y * 30.0), (30.0 * x)) - 25.0), (abs((t_0 + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.15e+30], N[Not[LessEqual[z, 1.3e+69]], $MachinePrecision]], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 + 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]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e30 or 1.3000000000000001e69 < z

   1. Initial program 32.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.9%

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

   if -1.15e30 < z < 1.3000000000000001e69

   1. Initial program 50.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 97.0%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \sin \left(30 \cdot x\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|t\_0 \cdot \cos \left(x \cdot 30\right) + t\_1\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(30 \cdot x\right), t\_1\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))) (t_1 (sin (* 30.0 x))))
   (if (or (<= z -1.15e+30) (not (<= z 1.3e+69)))
     (fmax
      (- (hypot (* z 30.0) (* 30.0 x)) 25.0)
      (- (fabs (+ (* t_0 (cos (* x 30.0))) t_1)) 0.2))
     (fmax
      (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
      (- (fabs (fma t_0 (cos (* 30.0 x)) t_1)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = sin((30.0 * x));
	double tmp;
	if ((z <= -1.15e+30) || !(z <= 1.3e+69)) {
		tmp = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs(((t_0 * cos((x * 30.0))) + t_1)) - 0.2));
	} else {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs(fma(t_0, cos((30.0 * x)), t_1)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = sin(Float64(30.0 * x))
	tmp = 0.0
	if ((z <= -1.15e+30) || !(z <= 1.3e+69))
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(Float64(t_0 * cos(Float64(x * 30.0))) + t_1)) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(fma(t_0, cos(Float64(30.0 * x)), t_1)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[z, -1.15e+30], N[Not[LessEqual[z, 1.3e+69]], $MachinePrecision]], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e30 or 1.3000000000000001e69 < z

   1. Initial program 32.1%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.9%

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

   if -1.15e30 < z < 1.3000000000000001e69

   1. Initial program 50.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 97.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 96.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+102} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(30 \cdot x\right), t\_0\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x))))
   (if (or (<= z -1.4e+102) (not (<= z 1.3e+69)))
     (fmax (* -30.0 x) (- (fabs (fma (* z 30.0) 1.0 t_0)) 0.2))
     (fmax
      (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
      (- (fabs (fma (sin (* z 30.0)) (cos (* 30.0 x)) t_0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double tmp;
	if ((z <= -1.4e+102) || !(z <= 1.3e+69)) {
		tmp = fmax((-30.0 * x), (fabs(fma((z * 30.0), 1.0, t_0)) - 0.2));
	} else {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs(fma(sin((z * 30.0)), cos((30.0 * x)), t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	tmp = 0.0
	if ((z <= -1.4e+102) || !(z <= 1.3e+69))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(Float64(z * 30.0), 1.0, t_0)) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(fma(sin(Float64(z * 30.0)), cos(Float64(30.0 * x)), 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]}, If[Or[LessEqual[z, -1.4e+102], N[Not[LessEqual[z, 1.3e+69]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[(z * 30.0), $MachinePrecision] * 1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $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]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000009e102 or 1.3000000000000001e69 < z

   1. Initial program 28.0%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 16.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 16.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 58.0%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 82.5%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   if -1.40000000000000009e102 < z < 1.3000000000000001e69

   1. Initial program 52.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 95.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+102} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+101} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y, x\right) \cdot 30 - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x))))
   (if (or (<= z -9.8e+101) (not (<= z 1.3e+69)))
     (fmax (* -30.0 x) (- (fabs (fma (* z 30.0) 1.0 t_0)) 0.2))
     (fmax
      (- (* (hypot y x) 30.0) 25.0)
      (- (fabs (fma t_0 (cos (* y 30.0)) (sin (* y 30.0)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double tmp;
	if ((z <= -9.8e+101) || !(z <= 1.3e+69)) {
		tmp = fmax((-30.0 * x), (fabs(fma((z * 30.0), 1.0, t_0)) - 0.2));
	} else {
		tmp = fmax(((hypot(y, x) * 30.0) - 25.0), (fabs(fma(t_0, cos((y * 30.0)), sin((y * 30.0)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	tmp = 0.0
	if ((z <= -9.8e+101) || !(z <= 1.3e+69))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(Float64(z * 30.0), 1.0, t_0)) - 0.2));
	else
		tmp = fmax(Float64(Float64(hypot(y, x) * 30.0) - 25.0), Float64(abs(fma(t_0, cos(Float64(y * 30.0)), sin(Float64(y * 30.0)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[z, -9.8e+101], N[Not[LessEqual[z, 1.3e+69]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[(z * 30.0), $MachinePrecision] * 1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(N[Sqrt[y ^ 2 + x ^ 2], $MachinePrecision] * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999965e101 or 1.3000000000000001e69 < z

   1. Initial program 28.0%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 16.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 16.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 58.0%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 82.5%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   if -9.79999999999999965e101 < z < 1.3000000000000001e69

   1. Initial program 52.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 51.4%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. +-commutative N/A

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

      10. unpow2 N/A

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

      11. unpow-prod-down N/A

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

      12. metadata-eval N/A

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

      13. unpow-prod-down N/A

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

      14. metadata-eval N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. lift-*.f64 N/A

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 94.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+101} \lor \neg \left(z \leq 1.3 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y, x\right) \cdot 30 - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 3.2e+161)
   (fmax (* -30.0 x) (- (fabs (fma (* z 30.0) 1.0 (sin (* 30.0 x)))) 0.2))
   (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.2e+161) {
		tmp = fmax((-30.0 * x), (fabs(fma((z * 30.0), 1.0, sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.2e+161)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(Float64(z * 30.0), 1.0, sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.2e+161], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[(z * 30.0), $MachinePrecision] * 1.0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.20000000000000002e161

   1. Initial program 47.4%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 23.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 22.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 41.3%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 50.8%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(z \cdot 30, 1, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   if 3.20000000000000002e161 < x

   1. Initial program 13.5%

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

   3. Taylor expanded in x around -inf

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

   5. Applied rewrites 3.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 3.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 3.4%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 73.1%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 31.3% accurate, 4.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 43.5%

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

3. Taylor expanded in x around -inf

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

5. Applied rewrites 20.8%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 20.5%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 31.8%

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

Alternative 12: 30.8% 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 43.5%

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

3. Taylor expanded in x around -inf

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

5. Applied rewrites 20.8%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 20.5%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 19.6%

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

12. Taylor expanded in x around 0

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

14. Applied rewrites 30.9%

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

Reproduce

herbie shell --seed 2025026 
(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)))