Gyroid sphere

Percentage Accurate: 46.7% → 90.6%

Time: 4.9s

Alternatives: 12

Speedup: 8.5×

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: 46.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(30, x, t\_0\right)\right| - 0.2\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1
         (fmax
          (- (hypot (* z 30.0) (* 30.0 x)) 25.0)
          (- (fabs (fma 30.0 x t_0)) 0.2))))
   (if (<= z -8e+93)
     t_1
     (if (<= z 2.6e+38)
       (fmax
        (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
        (-
         (fabs
          (+
           (+
            (* (sin (* x 30.0)) (cos (* y 30.0)))
            (* (sin (* y 30.0)) (cos (* z 30.0))))
           (* t_0 (cos (* x 30.0)))))
         0.2))
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs(fma(30.0, x, t_0)) - 0.2));
	double tmp;
	if (z <= -8e+93) {
		tmp = t_1;
	} else if (z <= 2.6e+38) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (t_0 * cos((x * 30.0))))) - 0.2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(fma(30.0, x, t_0)) - 0.2))
	tmp = 0.0
	if (z <= -8e+93)
		tmp = t_1;
	elseif (z <= 2.6e+38)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 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(t_0 * cos(Float64(x * 30.0))))) - 0.2));
	else
		tmp = 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[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -8e+93], t$95$1, If[LessEqual[z, 2.6e+38], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(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[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000035e93 or 2.5999999999999999e38 < z

   1. Initial program 26.1%

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

   2. 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. Applied rewrites 83.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 83.4%

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

   if -8.00000000000000035e93 < z < 2.5999999999999999e38

   1. Initial program 59.9%

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

   2. 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. Applied rewrites 95.2%

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

Alternative 2: 90.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(30, x, t\_0\right)\right| - 0.2\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1
         (fmax
          (- (hypot (* z 30.0) (* 30.0 x)) 25.0)
          (- (fabs (fma 30.0 x t_0)) 0.2))))
   (if (<= z -8e+93)
     t_1
     (if (<= z 2.6e+38)
       (fmax
        (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
        (- (fabs (fma t_0 (cos (* 30.0 x)) (sin (* 30.0 x)))) 0.2))
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs(fma(30.0, x, t_0)) - 0.2));
	double tmp;
	if (z <= -8e+93) {
		tmp = t_1;
	} else if (z <= 2.6e+38) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs(fma(t_0, cos((30.0 * x)), sin((30.0 * x)))) - 0.2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(fma(30.0, x, t_0)) - 0.2))
	tmp = 0.0
	if (z <= -8e+93)
		tmp = t_1;
	elseif (z <= 2.6e+38)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(fma(t_0, cos(Float64(30.0 * x)), sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = 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[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -8e+93], t$95$1, If[LessEqual[z, 2.6e+38], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000035e93 or 2.5999999999999999e38 < z

   1. Initial program 26.1%

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

   2. 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. Applied rewrites 83.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 83.4%

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

   if -8.00000000000000035e93 < z < 2.5999999999999999e38

   1. Initial program 59.9%

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

   2. 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. Applied rewrites 64.7%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 63.5%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 94.7%

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

Alternative 3: 89.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\\ t_1 := \mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, t\_0\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2))
        (t_1 (fmax (- (hypot (* z 30.0) (* 30.0 x)) 25.0) t_0)))
   (if (<= z -8e+93)
     t_1
     (if (<= z 2.6e+38)
       (fmax (- (hypot (* y 30.0) (* 30.0 x)) 25.0) t_0)
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2;
	double t_1 = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), t_0);
	double tmp;
	if (z <= -8e+93) {
		tmp = t_1;
	} else if (z <= 2.6e+38) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2)
	t_1 = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), t_0)
	tmp = 0.0
	if (z <= -8e+93)
		tmp = t_1;
	elseif (z <= 2.6e+38)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), t_0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$1 = N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]}, If[LessEqual[z, -8e+93], t$95$1, If[LessEqual[z, 2.6e+38], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000035e93 or 2.5999999999999999e38 < z

   1. Initial program 26.1%

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

   2. 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. Applied rewrites 83.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 83.4%

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

   if -8.00000000000000035e93 < z < 2.5999999999999999e38

   1. Initial program 59.9%

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

   2. 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. Applied rewrites 64.7%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 63.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 62.8%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 94.0%

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

Alternative 4: 89.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fmax
          (- (hypot (* z 30.0) (* 30.0 x)) 25.0)
          (- (fabs (* 30.0 x)) 0.2))))
   (if (<= z -8e+93)
     t_0
     (if (<= z 2.6e+38)
       (fmax
        (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
        (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs((30.0 * x)) - 0.2));
	double tmp;
	if (z <= -8e+93) {
		tmp = t_0;
	} else if (z <= 2.6e+38) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2))
	tmp = 0.0
	if (z <= -8e+93)
		tmp = t_0;
	elseif (z <= 2.6e+38)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -8e+93], t$95$0, If[LessEqual[z, 2.6e+38], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000035e93 or 2.5999999999999999e38 < z

   1. Initial program 26.1%

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

   2. 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. Applied rewrites 83.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 83.4%

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

   11. Taylor expanded in x around inf

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

   13. Applied rewrites 83.4%

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

   if -8.00000000000000035e93 < z < 2.5999999999999999e38

   1. Initial program 59.9%

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

   2. 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. Applied rewrites 64.7%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 63.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 62.8%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 94.0%

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

Alternative 5: 88.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(y, 30, 30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, y \cdot 30\right) - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|30 \cdot x\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.1e+123)
   (fmax (* 30.0 x) (- (fabs (fma y 30.0 (* 30.0 x))) 0.2))
   (if (<= x 8.5e+31)
     (fmax
      (- (hypot (* z 30.0) (* y 30.0)) 25.0)
      (- (fabs (sin (* 30.0 x))) 0.2))
     (fmax (- (hypot (* z 30.0) (* 30.0 x)) 25.0) (- (fabs (* 30.0 x)) 0.2)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.1e+123) {
		tmp = fmax((30.0 * x), (fabs(fma(y, 30.0, (30.0 * x))) - 0.2));
	} else if (x <= 8.5e+31) {
		tmp = fmax((hypot((z * 30.0), (y * 30.0)) - 25.0), (fabs(sin((30.0 * x))) - 0.2));
	} else {
		tmp = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.1e+123)
		tmp = fmax(Float64(30.0 * x), Float64(abs(fma(y, 30.0, Float64(30.0 * x))) - 0.2));
	elseif (x <= 8.5e+31)
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(y * 30.0)) - 25.0), Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.1e+123], N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 8.5e+31], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(y * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.09999999999999989e123

   1. Initial program 17.7%

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

   2. 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. Applied rewrites 3.4%

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

   5. 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. Applied rewrites 3.4%

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

   8. 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. Applied rewrites 17.9%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 86.2%

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

   if -4.09999999999999989e123 < x < 8.49999999999999947e31

   1. Initial program 60.2%

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

   2. 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. Applied rewrites 93.2%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 92.5%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 92.1%

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

   if 8.49999999999999947e31 < x

   1. Initial program 29.6%

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

   2. 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. Applied rewrites 82.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 82.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 82.0%

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

   11. Taylor expanded in x around inf

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

   13. Applied rewrites 82.0%

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

Alternative 6: 88.2% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(y, 30, 30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, y \cdot 30\right) - 25, \left|y \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|30 \cdot x\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e+123)
   (fmax (* 30.0 x) (- (fabs (fma y 30.0 (* 30.0 x))) 0.2))
   (if (<= x 8.5e+31)
     (fmax (- (hypot (* z 30.0) (* y 30.0)) 25.0) (- (fabs (* y 30.0)) 0.2))
     (fmax (- (hypot (* z 30.0) (* 30.0 x)) 25.0) (- (fabs (* 30.0 x)) 0.2)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e+123) {
		tmp = fmax((30.0 * x), (fabs(fma(y, 30.0, (30.0 * x))) - 0.2));
	} else if (x <= 8.5e+31) {
		tmp = fmax((hypot((z * 30.0), (y * 30.0)) - 25.0), (fabs((y * 30.0)) - 0.2));
	} else {
		tmp = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e+123)
		tmp = fmax(Float64(30.0 * x), Float64(abs(fma(y, 30.0, Float64(30.0 * x))) - 0.2));
	elseif (x <= 8.5e+31)
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(y * 30.0)) - 25.0), Float64(abs(Float64(y * 30.0)) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e+123], N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 8.5e+31], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(y * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999999e123

   1. Initial program 17.7%

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

   2. 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. Applied rewrites 3.4%

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

   5. 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. Applied rewrites 3.4%

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

   8. 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. Applied rewrites 17.8%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 86.1%

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

   if -1.79999999999999999e123 < x < 8.49999999999999947e31

   1. Initial program 60.2%

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

   2. 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. Applied rewrites 93.2%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 92.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 91.7%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 91.1%

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

   if 8.49999999999999947e31 < x

   1. Initial program 29.6%

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

   2. 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. Applied rewrites 82.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 82.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 82.0%

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

   11. Taylor expanded in x around inf

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

   13. Applied rewrites 82.0%

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

Alternative 7: 86.9% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(y, 30, 30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+99}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* 30.0 x) (- (fabs (fma y 30.0 (* 30.0 x))) 0.2))))
   (if (<= y -1.08e+99)
     t_0
     (if (<= y 1.55e+126)
       (fmax (- (hypot (* z 30.0) (* 30.0 x)) 25.0) (- (fabs (* 30.0 x)) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((30.0 * x), (fabs(fma(y, 30.0, (30.0 * x))) - 0.2));
	double tmp;
	if (y <= -1.08e+99) {
		tmp = t_0;
	} else if (y <= 1.55e+126) {
		tmp = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(30.0 * x), Float64(abs(fma(y, 30.0, Float64(30.0 * x))) - 0.2))
	tmp = 0.0
	if (y <= -1.08e+99)
		tmp = t_0;
	elseif (y <= 1.55e+126)
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -1.08e+99], t$95$0, If[LessEqual[y, 1.55e+126], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08e99 or 1.55e126 < y

   1. Initial program 18.8%

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

   2. 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. Applied rewrites 11.0%

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

   5. 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. Applied rewrites 11.0%

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

   8. 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. Applied rewrites 78.2%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 84.5%

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

   if -1.08e99 < y < 1.55e126

   1. Initial program 59.4%

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

   2. 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. Applied rewrites 90.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 89.2%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 88.6%

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

   11. Taylor expanded in x around inf

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

   13. Applied rewrites 88.0%

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

Alternative 8: 73.3% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-205}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(y, 30, 30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30 - 25, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+94)
   (fmax (* -30.0 x) (- (fabs (* z 30.0)) 0.2))
   (if (<= z 1.45e-205)
     (fmax (* 30.0 x) (- (fabs (fma y 30.0 (* 30.0 x))) 0.2))
     (fmax (- (* z 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 (z <= -1.05e+94) {
		tmp = fmax((-30.0 * x), (fabs((z * 30.0)) - 0.2));
	} else if (z <= 1.45e-205) {
		tmp = fmax((30.0 * x), (fabs(fma(y, 30.0, (30.0 * x))) - 0.2));
	} else {
		tmp = fmax(((z * 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 (z <= -1.05e+94)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(z * 30.0)) - 0.2));
	elseif (z <= 1.45e-205)
		tmp = fmax(Float64(30.0 * x), Float64(abs(fma(y, 30.0, Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(Float64(z * 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[z, -1.05e+94], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1.45e-205], N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(z * 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 3 regimes

2. if z < -1.04999999999999995e94

   1. Initial program 21.7%

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

   2. 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. Applied rewrites 10.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 10.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 10.7%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 76.6%

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

   if -1.04999999999999995e94 < z < 1.45000000000000009e-205

   1. Initial program 59.8%

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

   2. 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. Applied rewrites 22.1%

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

   5. 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. Applied rewrites 21.8%

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

   8. 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. Applied rewrites 55.7%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 72.5%

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

   if 1.45000000000000009e-205 < z

   1. Initial program 44.0%

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

   2. 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. Applied rewrites 73.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 73.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 73.0%

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

   11. Taylor expanded in z around inf

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

   13. Applied rewrites 72.7%

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

Alternative 9: 75.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(y, 30, 30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+94)
   (fmax (* -30.0 x) (- (fabs (* z 30.0)) 0.2))
   (if (<= z 2.6e+38)
     (fmax (* 30.0 x) (- (fabs (fma y 30.0 (* 30.0 x))) 0.2))
     (fmax (* z 30.0) (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+94) {
		tmp = fmax((-30.0 * x), (fabs((z * 30.0)) - 0.2));
	} else if (z <= 2.6e+38) {
		tmp = fmax((30.0 * x), (fabs(fma(y, 30.0, (30.0 * x))) - 0.2));
	} else {
		tmp = fmax((z * 30.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+94)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(z * 30.0)) - 0.2));
	elseif (z <= 2.6e+38)
		tmp = fmax(Float64(30.0 * x), Float64(abs(fma(y, 30.0, Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(z * 30.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+94], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 2.6e+38], N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * 30.0), $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 3 regimes

2. if z < -1.04999999999999995e94

   1. Initial program 21.7%

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

   2. 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. Applied rewrites 10.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 10.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 10.7%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 76.6%

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

   if -1.04999999999999995e94 < z < 2.5999999999999999e38

   1. Initial program 59.9%

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

   2. 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. Applied rewrites 22.1%

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

   5. 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. Applied rewrites 21.8%

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

   8. 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. Applied rewrites 56.1%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 73.0%

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

   if 2.5999999999999999e38 < z

   1. Initial program 29.8%

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

   2. 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. Applied rewrites 82.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 82.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 82.5%

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

   11. Taylor expanded in z around inf

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

   13. Applied rewrites 81.9%

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

Alternative 10: 74.1% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(y, 30, 30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (* z 30.0)) 0.2))))
   (if (<= z -1.05e+94)
     t_0
     (if (<= z 9.2e+108)
       (fmax (* 30.0 x) (- (fabs (fma y 30.0 (* 30.0 x))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs((z * 30.0)) - 0.2));
	double tmp;
	if (z <= -1.05e+94) {
		tmp = t_0;
	} else if (z <= 9.2e+108) {
		tmp = fmax((30.0 * x), (fabs(fma(y, 30.0, (30.0 * x))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(Float64(z * 30.0)) - 0.2))
	tmp = 0.0
	if (z <= -1.05e+94)
		tmp = t_0;
	elseif (z <= 9.2e+108)
		tmp = fmax(Float64(30.0 * x), Float64(abs(fma(y, 30.0, Float64(30.0 * x))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1.05e+94], t$95$0, If[LessEqual[z, 9.2e+108], N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999995e94 or 9.1999999999999996e108 < z

   1. Initial program 20.5%

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

   2. 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. Applied rewrites 11.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 11.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 11.4%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 78.2%

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

   if -1.04999999999999995e94 < z < 9.1999999999999996e108

   1. Initial program 59.8%

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

   2. 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. Applied rewrites 22.0%

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

   5. 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. Applied rewrites 21.7%

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

   8. 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. Applied rewrites 55.3%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 72.1%

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

Alternative 11: 62.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, \left|y \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (* z 30.0)) 0.2))))
   (if (<= z -1e+94)
     t_0
     (if (<= z 3.15e+106) (fmax (* 30.0 x) (- (fabs (* y 30.0)) 0.2)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs((z * 30.0)) - 0.2));
	double tmp;
	if (z <= -1e+94) {
		tmp = t_0;
	} else if (z <= 3.15e+106) {
		tmp = fmax((30.0 * x), (fabs((y * 30.0)) - 0.2));
	} else {
		tmp = 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 = fmax(((-30.0d0) * x), (abs((z * 30.0d0)) - 0.2d0))
    if (z <= (-1d+94)) then
        tmp = t_0
    else if (z <= 3.15d+106) then
        tmp = fmax((30.0d0 * x), (abs((y * 30.0d0)) - 0.2d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (Math.abs((z * 30.0)) - 0.2));
	double tmp;
	if (z <= -1e+94) {
		tmp = t_0;
	} else if (z <= 3.15e+106) {
		tmp = fmax((30.0 * x), (Math.abs((y * 30.0)) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = fmax((-30.0 * x), (math.fabs((z * 30.0)) - 0.2))
	tmp = 0
	if z <= -1e+94:
		tmp = t_0
	elif z <= 3.15e+106:
		tmp = fmax((30.0 * x), (math.fabs((y * 30.0)) - 0.2))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(Float64(z * 30.0)) - 0.2))
	tmp = 0.0
	if (z <= -1e+94)
		tmp = t_0;
	elseif (z <= 3.15e+106)
		tmp = fmax(Float64(30.0 * x), Float64(abs(Float64(y * 30.0)) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = max((-30.0 * x), (abs((z * 30.0)) - 0.2));
	tmp = 0.0;
	if (z <= -1e+94)
		tmp = t_0;
	elseif (z <= 3.15e+106)
		tmp = max((30.0 * x), (abs((y * 30.0)) - 0.2));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1e+94], t$95$0, If[LessEqual[z, 3.15e+106], N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e94 or 3.14999999999999987e106 < z

   1. Initial program 20.8%

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

   2. 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. Applied rewrites 11.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 11.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 11.5%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 78.1%

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

   if -1e94 < z < 3.14999999999999987e106

   1. Initial program 59.8%

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

   2. 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. Applied rewrites 22.1%

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

   5. 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. Applied rewrites 21.7%

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

   8. 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. Applied rewrites 55.4%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 54.9%

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

Alternative 12: 44.9% accurate, 9.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 46.7%

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

2. 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. Applied rewrites 18.8%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 18.4%

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

8. Taylor expanded in x around 0

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

10. Applied rewrites 18.0%

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

11. Taylor expanded in z around 0

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

13. Applied rewrites 44.9%

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

Reproduce

herbie shell --seed 2025101 
(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)))