Gyroid sphere

Percentage Accurate: 46.8% → 90.1%

Time: 9.8s

Alternatives: 6

Speedup: 4.7×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 46.8% 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: 90.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot y\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+75} \lor \neg \left(z \leq 115000000\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(t\_0, 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot y, -30 \cdot x\right) - 25, \left|\mathsf{fma}\left(t\_0, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 y))))
   (if (or (<= z -5.5e+75) (not (<= z 115000000.0)))
     (fmax
      (- (hypot (* -30.0 z) (* -30.0 y)) 25.0)
      (- (fabs (fma t_0 1.0 (* z 30.0))) 0.2))
     (fmax
      (- (hypot (* -30.0 y) (* -30.0 x)) 25.0)
      (- (fabs (fma t_0 1.0 (sin (* 30.0 z)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * y));
	double tmp;
	if ((z <= -5.5e+75) || !(z <= 115000000.0)) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), (fabs(fma(t_0, 1.0, (z * 30.0))) - 0.2));
	} else {
		tmp = fmax((hypot((-30.0 * y), (-30.0 * x)) - 25.0), (fabs(fma(t_0, 1.0, sin((30.0 * z)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * y))
	tmp = 0.0
	if ((z <= -5.5e+75) || !(z <= 115000000.0))
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), Float64(abs(fma(t_0, 1.0, Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * y), Float64(-30.0 * x)) - 25.0), Float64(abs(fma(t_0, 1.0, sin(Float64(30.0 * z)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[z, -5.5e+75], N[Not[LessEqual[z, 115000000.0]], $MachinePrecision]], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * 1.0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * y), $MachinePrecision] ^ 2 + N[(-30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * 1.0 + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000001e75 or 1.15e8 < z

   1. Initial program 39.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 39.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 87.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 87.3%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 87.3%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right) \]

   if -5.5000000000000001e75 < z < 1.15e8

   1. Initial program 59.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 97.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 97.1%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot y, -30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+75} \lor \neg \left(z \leq 115000000\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot y, -30 \cdot x\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot y\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+117} \lor \neg \left(y \leq 2.6 \cdot 10^{-19}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(t\_0, 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, z \cdot 30\right) - 25, \left|\mathsf{fma}\left(t\_0, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 y))))
   (if (or (<= y -6.2e+117) (not (<= y 2.6e-19)))
     (fmax
      (- (hypot (* -30.0 z) (* -30.0 y)) 25.0)
      (- (fabs (fma t_0 1.0 (* z 30.0))) 0.2))
     (fmax
      (- (hypot (* -30.0 x) (* z 30.0)) 25.0)
      (- (fabs (fma t_0 1.0 (sin (* 30.0 z)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * y));
	double tmp;
	if ((y <= -6.2e+117) || !(y <= 2.6e-19)) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), (fabs(fma(t_0, 1.0, (z * 30.0))) - 0.2));
	} else {
		tmp = fmax((hypot((-30.0 * x), (z * 30.0)) - 25.0), (fabs(fma(t_0, 1.0, sin((30.0 * z)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * y))
	tmp = 0.0
	if ((y <= -6.2e+117) || !(y <= 2.6e-19))
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), Float64(abs(fma(t_0, 1.0, Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(hypot(Float64(-30.0 * x), Float64(z * 30.0)) - 25.0), Float64(abs(fma(t_0, 1.0, sin(Float64(30.0 * z)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[y, -6.2e+117], N[Not[LessEqual[y, 2.6e-19]], $MachinePrecision]], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * 1.0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(-30.0 * x), $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * 1.0 + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999995e117 or 2.60000000000000013e-19 < y

   1. Initial program 31.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 31.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 84.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 84.8%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 84.8%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right) \]

   if -6.1999999999999995e117 < y < 2.60000000000000013e-19

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 63.0%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 96.1%

       \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{hypot}\left(-30 \cdot x, z \cdot 30\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+117} \lor \neg \left(y \leq 2.6 \cdot 10^{-19}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot x, z \cdot 30\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot y\right)\\ t_1 := \sin \left(30 \cdot z\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, t\_1\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+164}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(t\_0, 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(t\_0, 1, t\_1\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 y))) (t_1 (sin (* 30.0 z))))
   (if (<= x -1.35e+38)
     (fmax (- (* -30.0 x) 25.0) (- (fabs (fma (* y 30.0) 1.0 t_1)) 0.2))
     (if (<= x 8.5e+164)
       (fmax
        (- (hypot (* -30.0 z) (* -30.0 y)) 25.0)
        (- (fabs (fma t_0 1.0 (* z 30.0))) 0.2))
       (fmax (* 30.0 x) (- (fabs (fma t_0 1.0 t_1)) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * y));
	double t_1 = sin((30.0 * z));
	double tmp;
	if (x <= -1.35e+38) {
		tmp = fmax(((-30.0 * x) - 25.0), (fabs(fma((y * 30.0), 1.0, t_1)) - 0.2));
	} else if (x <= 8.5e+164) {
		tmp = fmax((hypot((-30.0 * z), (-30.0 * y)) - 25.0), (fabs(fma(t_0, 1.0, (z * 30.0))) - 0.2));
	} else {
		tmp = fmax((30.0 * x), (fabs(fma(t_0, 1.0, t_1)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * y))
	t_1 = sin(Float64(30.0 * z))
	tmp = 0.0
	if (x <= -1.35e+38)
		tmp = fmax(Float64(Float64(-30.0 * x) - 25.0), Float64(abs(fma(Float64(y * 30.0), 1.0, t_1)) - 0.2));
	elseif (x <= 8.5e+164)
		tmp = fmax(Float64(hypot(Float64(-30.0 * z), Float64(-30.0 * y)) - 25.0), Float64(abs(fma(t_0, 1.0, Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(30.0 * x), Float64(abs(fma(t_0, 1.0, t_1)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -1.35e+38], N[Max[N[(N[(-30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(y * 30.0), $MachinePrecision] * 1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 8.5e+164], N[Max[N[(N[Sqrt[N[(-30.0 * z), $MachinePrecision] ^ 2 + N[(-30.0 * y), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * 1.0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * x), $MachinePrecision], N[(N[Abs[N[(t$95$0 * 1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.34999999999999998e38

   1. Initial program 36.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 36.1%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 63.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 63.3%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 84.1%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   if -1.34999999999999998e38 < x < 8.50000000000000027e164

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 90.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 90.7%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 90.0%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right) \]

   if 8.50000000000000027e164 < x

   1. Initial program 6.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 6.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 20.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 20.6%

       \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(-30 \cdot z, -30 \cdot y\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 82.6%

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

Alternative 4: 76.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -30 \cdot x - 25\\ t_1 := \sin \left(30 \cdot y\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\mathsf{fma}\left(t\_1, 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot y - 25, \left|\mathsf{fma}\left(t\_1, \cos \left(-30 \cdot z\right), z \cdot 30\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* -30.0 x) 25.0)) (t_1 (sin (* 30.0 y))))
   (if (<= y -9.2e+137)
     (fmax t_0 (- (fabs (fma (* y 30.0) 1.0 (sin (* 30.0 z)))) 0.2))
     (if (<= y 2.6e-19)
       (fmax t_0 (- (fabs (fma t_1 1.0 (* z 30.0))) 0.2))
       (fmax
        (- (* 30.0 y) 25.0)
        (- (fabs (fma t_1 (cos (* -30.0 z)) (* z 30.0))) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = (-30.0 * x) - 25.0;
	double t_1 = sin((30.0 * y));
	double tmp;
	if (y <= -9.2e+137) {
		tmp = fmax(t_0, (fabs(fma((y * 30.0), 1.0, sin((30.0 * z)))) - 0.2));
	} else if (y <= 2.6e-19) {
		tmp = fmax(t_0, (fabs(fma(t_1, 1.0, (z * 30.0))) - 0.2));
	} else {
		tmp = fmax(((30.0 * y) - 25.0), (fabs(fma(t_1, cos((-30.0 * z)), (z * 30.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-30.0 * x) - 25.0)
	t_1 = sin(Float64(30.0 * y))
	tmp = 0.0
	if (y <= -9.2e+137)
		tmp = fmax(t_0, Float64(abs(fma(Float64(y * 30.0), 1.0, sin(Float64(30.0 * z)))) - 0.2));
	elseif (y <= 2.6e-19)
		tmp = fmax(t_0, Float64(abs(fma(t_1, 1.0, Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(Float64(30.0 * y) - 25.0), Float64(abs(fma(t_1, cos(Float64(-30.0 * z)), Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -9.2e+137], N[Max[t$95$0, N[(N[Abs[N[(N[(y * 30.0), $MachinePrecision] * 1.0 + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 2.6e-19], N[Max[t$95$0, N[(N[Abs[N[(t$95$1 * 1.0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$1 * N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.19999999999999997e137

   1. Initial program 21.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 21.8%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 6.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 6.4%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.6%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   if -9.19999999999999997e137 < y < 2.60000000000000013e-19

   1. Initial program 63.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 63.5%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 37.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 37.4%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 78.1%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right) \]

   if 2.60000000000000013e-19 < y

   1. Initial program 35.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 64.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 84.8%

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

Alternative 5: 74.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -30 \cdot x - 25\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+20} \lor \neg \left(z \leq 1.32 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* -30.0 x) 25.0)))
   (if (or (<= z -1.25e+20) (not (<= z 1.32e+16)))
     (fmax t_0 (- (fabs (fma (sin (* 30.0 y)) 1.0 (* z 30.0))) 0.2))
     (fmax t_0 (- (fabs (fma (* y 30.0) 1.0 (sin (* 30.0 z)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = (-30.0 * x) - 25.0;
	double tmp;
	if ((z <= -1.25e+20) || !(z <= 1.32e+16)) {
		tmp = fmax(t_0, (fabs(fma(sin((30.0 * y)), 1.0, (z * 30.0))) - 0.2));
	} else {
		tmp = fmax(t_0, (fabs(fma((y * 30.0), 1.0, sin((30.0 * z)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-30.0 * x) - 25.0)
	tmp = 0.0
	if ((z <= -1.25e+20) || !(z <= 1.32e+16))
		tmp = fmax(t_0, Float64(abs(fma(sin(Float64(30.0 * y)), 1.0, Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(t_0, Float64(abs(fma(Float64(y * 30.0), 1.0, sin(Float64(30.0 * z)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision]}, If[Or[LessEqual[z, -1.25e+20], N[Not[LessEqual[z, 1.32e+16]], $MachinePrecision]], N[Max[t$95$0, N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * 1.0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[t$95$0, N[(N[Abs[N[(N[(y * 30.0), $MachinePrecision] * 1.0 + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e20 or 1.32e16 < z

   1. Initial program 40.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 40.0%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 12.6%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 12.4%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 74.9%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right) \]

   if -1.25e20 < z < 1.32e16

   1. Initial program 59.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.7%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 41.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 41.1%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 77.7%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+20} \lor \neg \left(z \leq 1.32 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (* -30.0 x) 25.0)
  (- (fabs (fma (* y 30.0) 1.0 (sin (* 30.0 z)))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax(((-30.0 * x) - 25.0), (fabs(fma((y * 30.0), 1.0, sin((30.0 * z)))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(Float64(Float64(-30.0 * x) - 25.0), Float64(abs(fma(Float64(y * 30.0), 1.0, sin(Float64(30.0 * z)))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[(-30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(y * 30.0), $MachinePrecision] * 1.0 + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 49.6%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 49.6%

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

6. Taylor expanded in x around -inf

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

8. Applied rewrites 26.5%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 26.4%

    \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

12. Taylor expanded in y around 0

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

14. Applied rewrites 53.8%

    \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2025019 
(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)))