Gyroid sphere

Percentage Accurate: 46.0% → 89.3%

Time: 9.9s

Alternatives: 16

Speedup: 4.8×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 46.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \sin \left(30 \cdot x\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot x\right) - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(-30 \cdot x\right), t\_1\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|t\_0 \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|t\_1\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))) (t_1 (sin (* 30.0 x))))
   (if (<= x -8e+37)
     (fmax
      (- (hypot (* -30.0 z) (* -30.0 x)) 25.0)
      (- (fabs (fma t_0 (cos (* -30.0 x)) t_1)) 0.2))
     (if (<= x 9e+154)
       (fmax
        (- (hypot (* -30.0 z) (* -30.0 y)) 25.0)
        (-
         (fabs
          (+
           (* t_0 (cos (* x 30.0)))
           (+
            (* (sin (* x 30.0)) (cos (* y 30.0)))
            (* (sin (* y 30.0)) (cos (* z 30.0))))))
         0.2))
       (fmax (- (hypot (* -30.0 x) (* -30.0 y)) 25.0) (- (fabs 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 (x <= -8e+37) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * x)) - 25.0), (fabs(fma(t_0, cos((-30.0 * x)), t_1)) - 0.2));
	} else if (x <= 9e+154) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), (fabs(((t_0 * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
	} else {
		tmp = fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (fabs(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 (x <= -8e+37)
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * x)) - 25.0), Float64(abs(fma(t_0, cos(Float64(-30.0 * x)), t_1)) - 0.2));
	elseif (x <= 9e+154)
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), Float64(abs(Float64(Float64(t_0 * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), Float64(abs(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[LessEqual[x, -8e+37], N[Max[N[(N[Sqrt[N[(-30.0 * z), $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], If[LessEqual[x, 9e+154], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$1], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.99999999999999963e37

   1. Initial program 28.6%

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

   3. Taylor expanded in 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 86.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.3%

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

   if -7.99999999999999963e37 < x < 9.00000000000000018e154

   1. Initial program 56.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.6%

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

   if 9.00000000000000018e154 < x

   1. Initial program 7.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 97.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 97.2%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(-30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 43.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 50000000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (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))
      50000000.0)
   (fmax (- (* -30.0 x) 25.0) (- (fabs (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 (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)) <= 50000000.0) {
		tmp = fmax(((-30.0 * x) - 25.0), (fabs(sin((30.0 * x))) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (fmax((sqrt(((((x * 30.0d0) ** 2.0d0) + ((y * 30.0d0) ** 2.0d0)) + ((z * 30.0d0) ** 2.0d0))) - 25.0d0), (abs(((sin((z * 30.0d0)) * cos((x * 30.0d0))) + ((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))))) - 0.2d0)) <= 50000000.0d0) then
        tmp = fmax((((-30.0d0) * x) - 25.0d0), (abs(sin((30.0d0 * x))) - 0.2d0))
    else
        tmp = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (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((z * 30.0)) * Math.cos((x * 30.0))) + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2)) <= 50000000.0) {
		tmp = fmax(((-30.0 * x) - 25.0), (Math.abs(Math.sin((30.0 * x))) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if fmax((math.sqrt(((math.pow((x * 30.0), 2.0) + math.pow((y * 30.0), 2.0)) + math.pow((z * 30.0), 2.0))) - 25.0), (math.fabs(((math.sin((z * 30.0)) * math.cos((x * 30.0))) + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2)) <= 50000000.0:
		tmp = fmax(((-30.0 * x) - 25.0), (math.fabs(math.sin((30.0 * x))) - 0.2))
	else:
		tmp = fmax((-30.0 * x), (math.fabs((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)) <= 50000000.0)
		tmp = fmax(Float64(Float64(-30.0 * x) - 25.0), Float64(abs(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

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (max((sqrt(((((x * 30.0) ^ 2.0) + ((y * 30.0) ^ 2.0)) + ((z * 30.0) ^ 2.0))) - 25.0), (abs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2)) <= 50000000.0)
		tmp = max(((-30.0 * x) - 25.0), (abs(sin((30.0 * x))) - 0.2));
	else
		tmp = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	end
	tmp_2 = 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], 50000000.0], N[Max[N[(N[(-30.0 * x), $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[(30.0 * x), $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))) < 5e7

   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

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

   5. Applied rewrites 97.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 94.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 91.8%

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

   12. Taylor expanded in x around -inf

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

   14. Applied rewrites 89.5%

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

   if 5e7 < (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 34.4%

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

   3. Taylor expanded in x around -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 19.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 18.7%

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

   9. Taylor expanded in y 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 18.2%

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

   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 32.9%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \leq 50000000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|t\_0\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|t\_0 \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot x\right) - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(-30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))))
   (if (<= z -3.2e+15)
     (fmax (- (hypot (* -30.0 z) (* -30.0 y)) 25.0) (- (fabs t_0) 0.2))
     (if (<= z 2.25e+65)
       (fmax
        (- (hypot (* -30.0 x) (* -30.0 y)) 25.0)
        (-
         (fabs
          (+
           (* t_0 (cos (* x 30.0)))
           (+
            (* (sin (* x 30.0)) (cos (* y 30.0)))
            (* (sin (* y 30.0)) (cos (* z 30.0))))))
         0.2))
       (fmax
        (- (hypot (* -30.0 z) (* -30.0 x)) 25.0)
        (- (fabs (fma t_0 (cos (* -30.0 x)) (sin (* 30.0 x)))) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double tmp;
	if (z <= -3.2e+15) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), (fabs(t_0) - 0.2));
	} else if (z <= 2.25e+65) {
		tmp = fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (fabs(((t_0 * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
	} else {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * x)) - 25.0), (fabs(fma(t_0, cos((-30.0 * x)), sin((30.0 * x)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	tmp = 0.0
	if (z <= -3.2e+15)
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), Float64(abs(t_0) - 0.2));
	elseif (z <= 2.25e+65)
		tmp = fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), Float64(abs(Float64(Float64(t_0 * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * x)) - 25.0), Float64(abs(fma(t_0, cos(Float64(-30.0 * x)), sin(Float64(30.0 * x)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -3.2e+15], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 2.25e+65], N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * z), $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] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e15

   1. Initial program 42.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 89.7%

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

   if -3.2e15 < z < 2.25e65

   1. Initial program 53.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   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 98.6%

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

   if 2.25e65 < z

   1. Initial program 22.9%

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

   3. Taylor expanded in 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 86.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(-30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+15} \lor \neg \left(z \leq 6.5 \cdot 10^{+83}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|t\_0\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(-30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))))
   (if (or (<= z -3.2e+15) (not (<= z 6.5e+83)))
     (fmax (- (hypot (* -30.0 z) (* -30.0 y)) 25.0) (- (fabs t_0) 0.2))
     (fmax
      (- (hypot (* -30.0 x) (* -30.0 y)) 25.0)
      (- (fabs (fma t_0 (cos (* -30.0 x)) (sin (* 30.0 x)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double tmp;
	if ((z <= -3.2e+15) || !(z <= 6.5e+83)) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), (fabs(t_0) - 0.2));
	} else {
		tmp = fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (fabs(fma(t_0, cos((-30.0 * x)), sin((30.0 * x)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	tmp = 0.0
	if ((z <= -3.2e+15) || !(z <= 6.5e+83))
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), Float64(abs(t_0) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), Float64(abs(fma(t_0, cos(Float64(-30.0 * x)), sin(Float64(30.0 * x)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[z, -3.2e+15], N[Not[LessEqual[z, 6.5e+83]], $MachinePrecision]], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e15 or 6.5000000000000003e83 < z

   1. Initial program 32.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 88.1%

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

   if -3.2e15 < z < 6.5000000000000003e83

   1. Initial program 53.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 96.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+15} \lor \neg \left(z \leq 6.5 \cdot 10^{+83}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(-30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ t_1 := \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(-30 \cdot x\right), t\_0\right)\right| - 0.2\\ \mathbf{if}\;x \leq -8 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot x\right) - 25, t\_1\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|t\_0\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x)))
        (t_1 (- (fabs (fma (sin (* z 30.0)) (cos (* -30.0 x)) t_0)) 0.2)))
   (if (<= x -8e+37)
     (fmax (- (hypot (* -30.0 z) (* -30.0 x)) 25.0) t_1)
     (if (<= x 9e+154)
       (fmax (- (hypot (* -30.0 z) (* -30.0 y)) 25.0) t_1)
       (fmax (- (hypot (* -30.0 x) (* -30.0 y)) 25.0) (- (fabs t_0) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double t_1 = fabs(fma(sin((z * 30.0)), cos((-30.0 * x)), t_0)) - 0.2;
	double tmp;
	if (x <= -8e+37) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * x)) - 25.0), t_1);
	} else if (x <= 9e+154) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), t_1);
	} else {
		tmp = fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (fabs(t_0) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	t_1 = Float64(abs(fma(sin(Float64(z * 30.0)), cos(Float64(-30.0 * x)), t_0)) - 0.2)
	tmp = 0.0
	if (x <= -8e+37)
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * x)) - 25.0), t_1);
	elseif (x <= 9e+154)
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), t_1);
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), Float64(abs(t_0) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[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]}, If[LessEqual[x, -8e+37], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[x, 9e+154], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.99999999999999963e37

   1. Initial program 28.6%

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

   3. Taylor expanded in 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 86.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.3%

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

   if -7.99999999999999963e37 < x < 9.00000000000000018e154

   1. Initial program 56.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 94.9%

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

   if 9.00000000000000018e154 < x

   1. Initial program 7.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 97.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 97.2%

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

Alternative 6: 90.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \left|\mathsf{fma}\left(t\_0, \cos \left(-30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|t\_0\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot x\right) - 25, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1 (- (fabs (fma t_0 (cos (* -30.0 x)) (sin (* 30.0 x)))) 0.2)))
   (if (<= z -3.2e+15)
     (fmax (- (hypot (* -30.0 z) (* -30.0 y)) 25.0) (- (fabs t_0) 0.2))
     (if (<= z 2.25e+65)
       (fmax (- (hypot (* -30.0 x) (* -30.0 y)) 25.0) t_1)
       (fmax (- (hypot (* -30.0 z) (* -30.0 x)) 25.0) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fabs(fma(t_0, cos((-30.0 * x)), sin((30.0 * x)))) - 0.2;
	double tmp;
	if (z <= -3.2e+15) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), (fabs(t_0) - 0.2));
	} else if (z <= 2.25e+65) {
		tmp = fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), t_1);
	} else {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * x)) - 25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = Float64(abs(fma(t_0, cos(Float64(-30.0 * x)), sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (z <= -3.2e+15)
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), Float64(abs(t_0) - 0.2));
	elseif (z <= 2.25e+65)
		tmp = fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), t_1);
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * x)) - 25.0), t_1);
	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[(N[Abs[N[(t$95$0 * N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -3.2e+15], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 2.25e+65], N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e15

   1. Initial program 42.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 89.7%

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

   if -3.2e15 < z < 2.25e65

   1. Initial program 53.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   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 98.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 97.6%

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

   if 2.25e65 < z

   1. Initial program 22.9%

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

   3. Taylor expanded in 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 86.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.0%

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

Alternative 7: 90.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(z \cdot 30\right)\right| - 0.2\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+15} \lor \neg \left(z \leq 6.5 \cdot 10^{+83}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* z 30.0))) 0.2)))
   (if (or (<= z -3.2e+15) (not (<= z 6.5e+83)))
     (fmax (- (hypot (* -30.0 z) (* -30.0 y)) 25.0) t_0)
     (fmax (- (hypot (* -30.0 x) (* -30.0 y)) 25.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((z * 30.0))) - 0.2;
	double tmp;
	if ((z <= -3.2e+15) || !(z <= 6.5e+83)) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), t_0);
	} else {
		tmp = fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), t_0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((z * 30.0))) - 0.2;
	double tmp;
	if ((z <= -3.2e+15) || !(z <= 6.5e+83)) {
		tmp = fmax((Math.hypot((-30.0 * z), (-30.0 * y)) - 25.0), t_0);
	} else {
		tmp = fmax((Math.hypot((-30.0 * x), (-30.0 * y)) - 25.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((z * 30.0))) - 0.2
	tmp = 0
	if (z <= -3.2e+15) or not (z <= 6.5e+83):
		tmp = fmax((math.hypot((-30.0 * z), (-30.0 * y)) - 25.0), t_0)
	else:
		tmp = fmax((math.hypot((-30.0 * x), (-30.0 * y)) - 25.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(z * 30.0))) - 0.2)
	tmp = 0.0
	if ((z <= -3.2e+15) || !(z <= 6.5e+83))
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), t_0);
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((z * 30.0))) - 0.2;
	tmp = 0.0;
	if ((z <= -3.2e+15) || ~((z <= 6.5e+83)))
		tmp = max((hypot((-30.0 * z), (-30.0 * y)) - 25.0), t_0);
	else
		tmp = max((hypot((-30.0 * x), (-30.0 * y)) - 25.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[Or[LessEqual[z, -3.2e+15], N[Not[LessEqual[z, 6.5e+83]], $MachinePrecision]], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e15 or 6.5000000000000003e83 < z

   1. Initial program 32.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 88.1%

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

   if -3.2e15 < z < 6.5000000000000003e83

   1. Initial program 53.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 96.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 96.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+15} \lor \neg \left(z \leq 6.5 \cdot 10^{+83}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, -30 \cdot y\right) - 25, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.4% accurate, 3.4× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (hypot (* -30.0 x) (* -30.0 y)) 25.0)
  (- (fabs (sin (* z 30.0))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (fabs(sin((z * 30.0))) - 0.2));
}

Java

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

Python

def code(x, y, z):
	return fmax((math.hypot((-30.0 * x), (-30.0 * y)) - 25.0), (math.fabs(math.sin((z * 30.0))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), Float64(abs(sin(Float64(z * 30.0))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (abs(sin((z * 30.0))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 43.8%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 68.9%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 68.4%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 68.1%

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

Alternative 9: 71.0% accurate, 3.4× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (hypot (* -30.0 x) (* -30.0 y)) 25.0)
  (- (fabs (sin (* 30.0 x))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (fabs(sin((30.0 * x))) - 0.2));
}

Java

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

Python

def code(x, y, z):
	return fmax((math.hypot((-30.0 * x), (-30.0 * y)) - 25.0), (math.fabs(math.sin((30.0 * x))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), Float64(abs(sin(Float64(30.0 * x))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (abs(sin((30.0 * x))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 43.8%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 68.9%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 68.4%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 67.6%

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

Alternative 10: 56.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ t_1 := \left|t\_0\right| - 0.2\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, t\_0\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, t\_1\right)\\ \mathbf{elif}\;x \leq 0.00295:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30 - 25, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x - 25, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x))) (t_1 (- (fabs t_0) 0.2)))
   (if (<= x -9.2e-74)
     (fmax (* -30.0 x) (- (fabs (fma y 30.0 t_0)) 0.2))
     (if (<= x -3.7e-292)
       (fmax (- (* -30.0 y) 25.0) t_1)
       (if (<= x 0.00295)
         (fmax (- (* y 30.0) 25.0) (- (fabs (sin (* z 30.0))) 0.2))
         (fmax (- (* 30.0 x) 25.0) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double t_1 = fabs(t_0) - 0.2;
	double tmp;
	if (x <= -9.2e-74) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, t_0)) - 0.2));
	} else if (x <= -3.7e-292) {
		tmp = fmax(((-30.0 * y) - 25.0), t_1);
	} else if (x <= 0.00295) {
		tmp = fmax(((y * 30.0) - 25.0), (fabs(sin((z * 30.0))) - 0.2));
	} else {
		tmp = fmax(((30.0 * x) - 25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	t_1 = Float64(abs(t_0) - 0.2)
	tmp = 0.0
	if (x <= -9.2e-74)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, t_0)) - 0.2));
	elseif (x <= -3.7e-292)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), t_1);
	elseif (x <= 0.00295)
		tmp = fmax(Float64(Float64(y * 30.0) - 25.0), Float64(abs(sin(Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(Float64(30.0 * x) - 25.0), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -9.2e-74], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, -3.7e-292], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[x, 0.00295], N[Max[N[(N[(y * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.19999999999999922e-74

   1. Initial program 34.0%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   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 42.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 64.1%

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

   if -9.19999999999999922e-74 < x < -3.69999999999999997e-292

   1. Initial program 68.9%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   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 72.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 71.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 69.8%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 57.2%

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

   if -3.69999999999999997e-292 < x < 0.00294999999999999993

   1. Initial program 63.4%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   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 61.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 60.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 49.1%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 49.1%

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

   if 0.00294999999999999993 < x

   1. Initial program 18.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 75.0%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 58.7%

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

Alternative 11: 52.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, t\_0\right)\\ \mathbf{elif}\;x \leq 0.00295:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30 - 25, \left|\sin \left(z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= x -1.7e+22)
     (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))
     (if (<= x -3.7e-292)
       (fmax (- (* -30.0 y) 25.0) t_0)
       (if (<= x 0.00295)
         (fmax (- (* y 30.0) 25.0) (- (fabs (sin (* z 30.0))) 0.2))
         (fmax (- (* 30.0 x) 25.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (x <= -1.7e+22) {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	} else if (x <= -3.7e-292) {
		tmp = fmax(((-30.0 * y) - 25.0), t_0);
	} else if (x <= 0.00295) {
		tmp = fmax(((y * 30.0) - 25.0), (fabs(sin((z * 30.0))) - 0.2));
	} else {
		tmp = fmax(((30.0 * x) - 25.0), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((30.0d0 * x))) - 0.2d0
    if (x <= (-1.7d+22)) then
        tmp = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    else if (x <= (-3.7d-292)) then
        tmp = fmax((((-30.0d0) * y) - 25.0d0), t_0)
    else if (x <= 0.00295d0) then
        tmp = fmax(((y * 30.0d0) - 25.0d0), (abs(sin((z * 30.0d0))) - 0.2d0))
    else
        tmp = fmax(((30.0d0 * x) - 25.0d0), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * x))) - 0.2;
	double tmp;
	if (x <= -1.7e+22) {
		tmp = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	} else if (x <= -3.7e-292) {
		tmp = fmax(((-30.0 * y) - 25.0), t_0);
	} else if (x <= 0.00295) {
		tmp = fmax(((y * 30.0) - 25.0), (Math.abs(Math.sin((z * 30.0))) - 0.2));
	} else {
		tmp = fmax(((30.0 * x) - 25.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if x <= -1.7e+22:
		tmp = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	elif x <= -3.7e-292:
		tmp = fmax(((-30.0 * y) - 25.0), t_0)
	elif x <= 0.00295:
		tmp = fmax(((y * 30.0) - 25.0), (math.fabs(math.sin((z * 30.0))) - 0.2))
	else:
		tmp = fmax(((30.0 * x) - 25.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (x <= -1.7e+22)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2));
	elseif (x <= -3.7e-292)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), t_0);
	elseif (x <= 0.00295)
		tmp = fmax(Float64(Float64(y * 30.0) - 25.0), Float64(abs(sin(Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(Float64(30.0 * x) - 25.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (x <= -1.7e+22)
		tmp = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	elseif (x <= -3.7e-292)
		tmp = max(((-30.0 * y) - 25.0), t_0);
	elseif (x <= 0.00295)
		tmp = max(((y * 30.0) - 25.0), (abs(sin((z * 30.0))) - 0.2));
	else
		tmp = max(((30.0 * x) - 25.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.7e+22], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, -3.7e-292], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 0.00295], N[Max[N[(N[(y * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.7e22

   1. Initial program 29.1%

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

   3. Taylor expanded in x around -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 54.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 54.9%

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

   9. Taylor expanded in y 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 54.9%

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

   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 54.9%

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

   if -1.7e22 < x < -3.69999999999999997e-292

   1. Initial program 62.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 71.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 68.4%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 52.9%

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

   if -3.69999999999999997e-292 < x < 0.00294999999999999993

   1. Initial program 63.4%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   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 61.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 60.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 49.1%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 49.1%

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

   if 0.00294999999999999993 < x

   1. Initial program 18.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 75.0%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 58.7%

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

Alternative 12: 52.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+22} \lor \neg \left(x \leq 700000\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e+22) (not (<= x 700000.0)))
   (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))
   (fmax (- (* -30.0 y) 25.0) (- (fabs (sin (* 30.0 x))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+22) || !(x <= 700000.0)) {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs(sin((30.0 * x))) - 0.2));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.7d+22)) .or. (.not. (x <= 700000.0d0))) then
        tmp = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    else
        tmp = fmax((((-30.0d0) * y) - 25.0d0), (abs(sin((30.0d0 * x))) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+22) || !(x <= 700000.0)) {
		tmp = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (Math.abs(Math.sin((30.0 * x))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e+22) or not (x <= 700000.0):
		tmp = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	else:
		tmp = fmax(((-30.0 * y) - 25.0), (math.fabs(math.sin((30.0 * x))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e+22) || !(x <= 700000.0))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.7e+22) || ~((x <= 700000.0)))
		tmp = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	else
		tmp = max(((-30.0 * y) - 25.0), (abs(sin((30.0 * x))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e+22], N[Not[LessEqual[x, 700000.0]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e22 or 7e5 < x

   1. Initial program 23.9%

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

   3. Taylor expanded in 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 30.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 30.3%

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

   9. Taylor expanded in y 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 30.4%

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

   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 56.8%

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

   if -1.7e22 < x < 7e5

   1. Initial program 62.2%

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

   3. Taylor expanded in 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 66.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 64.3%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 47.7%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+22} \lor \neg \left(x \leq 700000\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 82000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= x -1.7e+22)
     (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))
     (if (<= x 82000.0)
       (fmax (- (* -30.0 y) 25.0) t_0)
       (fmax (- (* 30.0 x) 25.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (x <= -1.7e+22) {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	} else if (x <= 82000.0) {
		tmp = fmax(((-30.0 * y) - 25.0), t_0);
	} else {
		tmp = fmax(((30.0 * x) - 25.0), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((30.0d0 * x))) - 0.2d0
    if (x <= (-1.7d+22)) then
        tmp = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    else if (x <= 82000.0d0) then
        tmp = fmax((((-30.0d0) * y) - 25.0d0), t_0)
    else
        tmp = fmax(((30.0d0 * x) - 25.0d0), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * x))) - 0.2;
	double tmp;
	if (x <= -1.7e+22) {
		tmp = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	} else if (x <= 82000.0) {
		tmp = fmax(((-30.0 * y) - 25.0), t_0);
	} else {
		tmp = fmax(((30.0 * x) - 25.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if x <= -1.7e+22:
		tmp = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	elif x <= 82000.0:
		tmp = fmax(((-30.0 * y) - 25.0), t_0)
	else:
		tmp = fmax(((30.0 * x) - 25.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (x <= -1.7e+22)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2));
	elseif (x <= 82000.0)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), t_0);
	else
		tmp = fmax(Float64(Float64(30.0 * x) - 25.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (x <= -1.7e+22)
		tmp = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	elseif (x <= 82000.0)
		tmp = max(((-30.0 * y) - 25.0), t_0);
	else
		tmp = max(((30.0 * x) - 25.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.7e+22], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 82000.0], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e22

   1. Initial program 29.1%

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

   3. Taylor expanded in x around -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 54.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 54.9%

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

   9. Taylor expanded in y 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 54.9%

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

   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 54.9%

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

   if -1.7e22 < x < 82000

   1. Initial program 62.2%

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

   3. Taylor expanded in 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 66.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 64.3%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 47.7%

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

   if 82000 < x

   1. Initial program 18.3%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. 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 74.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 74.5%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 59.7%

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

Alternative 14: 68.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30 - 25, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+22)
   (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* 30.0 x)))) 0.2))
   (fmax (- (* y 30.0) 25.0) (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+22) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax(((y * 30.0) - 25.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+22)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = fmax(Float64(Float64(y * 30.0) - 25.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+22], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(y * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e22

   1. Initial program 31.6%

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

   3. Taylor expanded in 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 11.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 10.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 70.6%

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

   if -1.4e22 < y

   1. Initial program 47.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 65.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 64.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 35.2%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 63.1%

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

Alternative 15: 70.6% accurate, 4.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax (- (hypot (* -30.0 x) (* -30.0 y)) 25.0) (- (fabs (* 30.0 x)) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (fabs((30.0 * x)) - 0.2));
}

Java

public static double code(double x, double y, double z) {
	return fmax((Math.hypot((-30.0 * x), (-30.0 * y)) - 25.0), (Math.abs((30.0 * x)) - 0.2));
}

Python

def code(x, y, z):
	return fmax((math.hypot((-30.0 * x), (-30.0 * y)) - 25.0), (math.fabs((30.0 * x)) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(hypot(Float64(-30.0 * x), Float64(-30.0 * y)) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((hypot((-30.0 * x), (-30.0 * y)) - 25.0), (abs((30.0 * x)) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 43.8%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 68.9%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 68.4%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 67.6%

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

12. Taylor expanded in x around 0

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

14. Applied rewrites 67.2%

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

Alternative 16: 32.0% 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 43.8%

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

3. Taylor expanded in x around -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 17.2%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 16.8%

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

9. Taylor expanded in y 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 16.3%

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

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 29.0%

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

Reproduce

herbie shell --seed 2025018 
(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)))