Gyroid sphere

Percentage Accurate: 45.7% → 99.9%

Time: 4.8s

Alternatives: 9

Speedup: 18.1×

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: 45.7% 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: 99.9% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (hypot (* z 30.0) (hypot (* y 30.0) (* x 30.0))) 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((hypot((z * 30.0), hypot((y * 30.0), (x * 30.0))) - 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));
}

Java

public static double code(double x, double y, double z) {
	return fmax((Math.hypot((z * 30.0), Math.hypot((y * 30.0), (x * 30.0))) - 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.hypot((z * 30.0), math.hypot((y * 30.0), (x * 30.0))) - 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(hypot(Float64(z * 30.0), hypot(Float64(y * 30.0), Float64(x * 30.0))) - 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((hypot((z * 30.0), hypot((y * 30.0), (x * 30.0))) - 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[(z * 30.0), $MachinePrecision] ^ 2 + N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(x * 30.0), $MachinePrecision] ^ 2], $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[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 45.7%

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

   1. lift-sqrt.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-pow.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift-pow.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-pow.f64 N/A

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

   10. +-commutative N/A

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

   11. unpow2 N/A

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

   12. unpow-prod-down N/A

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

   13. metadata-eval N/A

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

   14. *-commutative N/A

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

   15. unpow-prod-down N/A

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

   16. metadata-eval N/A

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

   17. *-commutative N/A

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

   18. unpow1 N/A

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

   19. metadata-eval N/A

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

3. Applied rewrites 58.9%

   \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{hypot}\left(z \cdot 30, \sqrt{900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
4. Step-by-step derivation

   1. lift-sqrt.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-fma.f64 N/A

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

   5. pow2 N/A

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

   6. pow2 N/A

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

   7. distribute-rgt-in N/A

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

   8. metadata-eval N/A

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

   9. unpow-prod-down N/A

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

   10. metadata-eval N/A

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

   11. unpow-prod-down N/A

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

   12. lift-*.f64 N/A

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

   13. lift-pow.f64 N/A

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

   14. +-commutative N/A

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

   15. lift-pow.f64 N/A

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

   16. unpow2 N/A

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

   17. lift-*.f64 N/A

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

   18. *-commutative N/A

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

   19. lift-*.f64 N/A

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

   20. *-commutative N/A

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

   21. unpow2 N/A

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

   22. *-commutative N/A

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

   23. *-commutative N/A

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

5. Applied rewrites 99.9%

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

Alternative 2: 99.6% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 45.7%

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

   1. lift-sqrt.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-pow.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift-pow.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-pow.f64 N/A

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

   10. +-commutative N/A

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

   11. unpow2 N/A

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

   12. unpow-prod-down N/A

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

   13. metadata-eval N/A

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

   14. *-commutative N/A

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

   15. unpow-prod-down N/A

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

   16. metadata-eval N/A

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

   17. *-commutative N/A

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

   18. unpow1 N/A

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

   19. metadata-eval N/A

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

3. Applied rewrites 58.9%

   \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{hypot}\left(z \cdot 30, \sqrt{900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
4. Step-by-step derivation

   1. lift-sqrt.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-fma.f64 N/A

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

   5. pow2 N/A

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

   6. pow2 N/A

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

   7. distribute-rgt-in N/A

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

   8. metadata-eval N/A

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

   9. unpow-prod-down N/A

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

   10. metadata-eval N/A

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

   11. unpow-prod-down N/A

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

   12. lift-*.f64 N/A

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

   13. lift-pow.f64 N/A

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

   14. +-commutative N/A

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

   15. lift-pow.f64 N/A

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

   16. unpow2 N/A

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

   17. lift-*.f64 N/A

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

   18. *-commutative N/A

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

   19. lift-*.f64 N/A

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

   20. *-commutative N/A

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

   21. unpow2 N/A

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

   22. *-commutative N/A

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

   23. *-commutative N/A

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

5. Applied rewrites 99.9%

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

6. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-sin.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-sin.f64 N/A

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

   12. lift-*.f64 99.6

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

8. Applied rewrites 99.6%

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

Alternative 3: 99.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 45.7%

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

   1. lift-sqrt.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-pow.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift-pow.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-pow.f64 N/A

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

   10. +-commutative N/A

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

   11. unpow2 N/A

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

   12. unpow-prod-down N/A

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

   13. metadata-eval N/A

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

   14. *-commutative N/A

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

   15. unpow-prod-down N/A

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

   16. metadata-eval N/A

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

   17. *-commutative N/A

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

   18. unpow1 N/A

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

   19. metadata-eval N/A

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

3. Applied rewrites 58.9%

   \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{hypot}\left(z \cdot 30, \sqrt{900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
4. Step-by-step derivation

   1. lift-sqrt.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-fma.f64 N/A

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

   5. pow2 N/A

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

   6. pow2 N/A

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

   7. distribute-rgt-in N/A

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

   8. metadata-eval N/A

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

   9. unpow-prod-down N/A

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

   10. metadata-eval N/A

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

   11. unpow-prod-down N/A

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

   12. lift-*.f64 N/A

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

   13. lift-pow.f64 N/A

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

   14. +-commutative N/A

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

   15. lift-pow.f64 N/A

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

   16. unpow2 N/A

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

   17. lift-*.f64 N/A

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

   18. *-commutative N/A

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

   19. lift-*.f64 N/A

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

   20. *-commutative N/A

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

   21. unpow2 N/A

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

   22. *-commutative N/A

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

   23. *-commutative N/A

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

5. Applied rewrites 99.9%

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

6. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-sin.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-sin.f64 N/A

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

   12. lift-*.f64 99.6

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

8. Applied rewrites 99.6%

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

9. Taylor expanded in y around 0

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

    1. *-commutative N/A

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

    2. lift-sin.f64 N/A

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

    3. lift-*.f64 99.3

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

11. Applied rewrites 99.3%

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

Alternative 4: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z, 30 \cdot \left(30 \cdot z\right), 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, \left|\mathsf{fma}\left(x, 30, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (fmax
       (-
        (sqrt
         (+
          (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
          (pow (* z 30.0) 2.0)))
        25.0)
       (-
        (fabs
         (+
          (+
           (* (sin (* 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))
      1e+151)
   (fmax
    (- (sqrt (fma z (* 30.0 (* 30.0 z)) (* 900.0 (fma x x (* y y))))) 25.0)
    (- (fabs (sin (* 30.0 z))) 0.2))
   (fmax (* y 30.0) (- (fabs (fma x 30.0 (* 30.0 z))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((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)) <= 1e+151) {
		tmp = fmax((sqrt(fma(z, (30.0 * (30.0 * z)), (900.0 * fma(x, x, (y * y))))) - 25.0), (fabs(sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((y * 30.0), (fabs(fma(x, 30.0, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(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)) <= 1e+151)
		tmp = fmax(Float64(sqrt(fma(z, Float64(30.0 * Float64(30.0 * z)), Float64(900.0 * fma(x, x, Float64(y * y))))) - 25.0), Float64(abs(sin(Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), Float64(abs(fma(x, 30.0, Float64(30.0 * z))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(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], 1e+151], N[Max[N[(N[Sqrt[N[(z * N[(30.0 * N[(30.0 * z), $MachinePrecision]), $MachinePrecision] + N[(900.0 * N[(x * x + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], N[(N[Abs[N[(x * 30.0 + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 1.00000000000000002e151

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lift-sin.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 98.2

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

   7. Applied rewrites 98.2%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. +-commutative N/A

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

      10. pow2 N/A

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

      11. associate-*l* N/A

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

      12. unpow-prod-down N/A

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

      13. metadata-eval N/A

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

      14. unpow-prod-down N/A

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

      15. metadata-eval N/A

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

      16. *-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

   9. Applied rewrites 98.1%

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

   if 1.00000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 9.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 20.4

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

   4. Applied rewrites 20.4%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 41.0%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 51.7

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

   10. Applied rewrites 51.7%

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

   11. Taylor expanded in z around 0

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

       1. lift-*.f64 82.9

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

   13. Applied rewrites 82.9%

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

Alternative 5: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(\mathsf{fma}\left(y, y, z \cdot z\right), 900, \left(x \cdot x\right) \cdot 900\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, \left|\mathsf{fma}\left(x, 30, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (fmax
       (-
        (sqrt
         (+
          (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
          (pow (* z 30.0) 2.0)))
        25.0)
       (-
        (fabs
         (+
          (+
           (* (sin (* 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))
      1e+151)
   (fmax
    (- (sqrt (fma (fma y y (* z z)) 900.0 (* (* x x) 900.0))) 25.0)
    (- (fabs (sin (* 30.0 z))) 0.2))
   (fmax (* y 30.0) (- (fabs (fma x 30.0 (* 30.0 z))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((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)) <= 1e+151) {
		tmp = fmax((sqrt(fma(fma(y, y, (z * z)), 900.0, ((x * x) * 900.0))) - 25.0), (fabs(sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((y * 30.0), (fabs(fma(x, 30.0, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(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)) <= 1e+151)
		tmp = fmax(Float64(sqrt(fma(fma(y, y, Float64(z * z)), 900.0, Float64(Float64(x * x) * 900.0))) - 25.0), Float64(abs(sin(Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), Float64(abs(fma(x, 30.0, Float64(30.0 * z))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(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], 1e+151], N[Max[N[(N[Sqrt[N[(N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision] * 900.0 + N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], N[(N[Abs[N[(x * 30.0 + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 1.00000000000000002e151

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lift-sin.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 98.2

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

   7. Applied rewrites 98.2%

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

   9. Applied rewrites 98.1%

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

   if 1.00000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 9.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 20.4

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

   4. Applied rewrites 20.4%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 41.0%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 51.7

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

   10. Applied rewrites 51.7%

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

   11. Taylor expanded in z around 0

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

       1. lift-*.f64 82.9

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

   13. Applied rewrites 82.9%

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

Alternative 6: 88.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot 30, x \cdot 30, \mathsf{fma}\left(y, y, z \cdot z\right) \cdot 900\right)} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, \left|\mathsf{fma}\left(x, 30, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (fmax
       (-
        (sqrt
         (+
          (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
          (pow (* z 30.0) 2.0)))
        25.0)
       (-
        (fabs
         (+
          (+
           (* (sin (* 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))
      1e+151)
   (fmax
    (- (sqrt (fma (* x 30.0) (* x 30.0) (* (fma y y (* z z)) 900.0))) 25.0)
    (- (fabs (* 30.0 z)) 0.2))
   (fmax (* y 30.0) (- (fabs (fma x 30.0 (* 30.0 z))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((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)) <= 1e+151) {
		tmp = fmax((sqrt(fma((x * 30.0), (x * 30.0), (fma(y, y, (z * z)) * 900.0))) - 25.0), (fabs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), (fabs(fma(x, 30.0, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(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)) <= 1e+151)
		tmp = fmax(Float64(sqrt(fma(Float64(x * 30.0), Float64(x * 30.0), Float64(fma(y, y, Float64(z * z)) * 900.0))) - 25.0), Float64(abs(Float64(30.0 * z)) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), Float64(abs(fma(x, 30.0, Float64(30.0 * z))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(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], 1e+151], N[Max[N[(N[Sqrt[N[(N[(x * 30.0), $MachinePrecision] * N[(x * 30.0), $MachinePrecision] + N[(N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision] * 900.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], N[(N[Abs[N[(x * 30.0 + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 1.00000000000000002e151

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lift-sin.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 98.2

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

   7. Applied rewrites 98.2%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. associate-+l+ N/A

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

      10. pow2 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. unpow-prod-down N/A

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

      14. metadata-eval N/A

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

      15. unpow-prod-down N/A

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

      16. metadata-eval N/A

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

      17. distribute-rgt-in N/A

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

      18. distribute-lft-in N/A

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

      19. lower-fma.f64 N/A

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

   9. Applied rewrites 98.1%

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

   10. Taylor expanded in z around 0

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

       1. lift-*.f64 97.3

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

   12. Applied rewrites 97.3%

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

   if 1.00000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 9.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 20.4

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

   4. Applied rewrites 20.4%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 41.0%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 51.7

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

   10. Applied rewrites 51.7%

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

   11. Taylor expanded in z around 0

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

       1. lift-*.f64 82.9

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

   13. Applied rewrites 82.9%

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

Alternative 7: 83.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq -0.1:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, \left|30 \cdot \left(x + z\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (fmax
       (-
        (sqrt
         (+
          (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
          (pow (* z 30.0) 2.0)))
        25.0)
       (-
        (fabs
         (+
          (+
           (* (sin (* 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))
      -0.1)
   (fmax (- (sqrt (* (* z z) 900.0)) 25.0) (- (fabs (* 30.0 z)) 0.2))
   (fmax (* y 30.0) (- (fabs (* 30.0 (+ x z))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((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)) <= -0.1) {
		tmp = fmax((sqrt(((z * z) * 900.0)) - 25.0), (fabs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), (fabs((30.0 * (x + z))) - 0.2));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (fmax((sqrt(((((x * 30.0d0) ** 2.0d0) + ((y * 30.0d0) ** 2.0d0)) + ((z * 30.0d0) ** 2.0d0))) - 25.0d0), (abs((((sin((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)) <= (-0.1d0)) then
        tmp = fmax((sqrt(((z * z) * 900.0d0)) - 25.0d0), (abs((30.0d0 * z)) - 0.2d0))
    else
        tmp = fmax((y * 30.0d0), (abs((30.0d0 * (x + z))) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (fmax((Math.sqrt(((Math.pow((x * 30.0), 2.0) + Math.pow((y * 30.0), 2.0)) + Math.pow((z * 30.0), 2.0))) - 25.0), (Math.abs((((Math.sin((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)) <= -0.1) {
		tmp = fmax((Math.sqrt(((z * z) * 900.0)) - 25.0), (Math.abs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), (Math.abs((30.0 * (x + z))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if fmax((math.sqrt(((math.pow((x * 30.0), 2.0) + math.pow((y * 30.0), 2.0)) + math.pow((z * 30.0), 2.0))) - 25.0), (math.fabs((((math.sin((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)) <= -0.1:
		tmp = fmax((math.sqrt(((z * z) * 900.0)) - 25.0), (math.fabs((30.0 * z)) - 0.2))
	else:
		tmp = fmax((y * 30.0), (math.fabs((30.0 * (x + z))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(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)) <= -0.1)
		tmp = fmax(Float64(sqrt(Float64(Float64(z * z) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * z)) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), Float64(abs(Float64(30.0 * Float64(x + z))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (max((sqrt(((((x * 30.0) ^ 2.0) + ((y * 30.0) ^ 2.0)) + ((z * 30.0) ^ 2.0))) - 25.0), (abs((((sin((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)) <= -0.1)
		tmp = max((sqrt(((z * z) * 900.0)) - 25.0), (abs((30.0 * z)) - 0.2));
	else
		tmp = max((y * 30.0), (abs((30.0 * (x + z))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(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], -0.1], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], N[(N[Abs[N[(30.0 * N[(x + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < -0.10000000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lift-sin.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 95.9

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

   7. Applied rewrites 95.9%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. pow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lift-*.f64 95.9

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

   10. Applied rewrites 95.9%

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

   11. Taylor expanded in z around 0

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

       1. lift-*.f64 95.4

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

   13. Applied rewrites 95.4%

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

   if -0.10000000000000001 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 38.5%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 20.7

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

   4. Applied rewrites 20.7%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 50.8

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

   10. Applied rewrites 50.8%

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

   11. Taylor expanded in z around 0

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

       1. distribute-lft-out N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 81.6

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

   13. Applied rewrites 81.6%

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

Alternative 8: 72.5% accurate, 18.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 45.7%

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

2. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. lift-*.f64 18.7

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

4. Applied rewrites 18.7%

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

5. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

7. Applied rewrites 37.6%

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

8. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lift-sin.f64 N/A

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

   5. lift-*.f64 45.3

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

10. Applied rewrites 45.3%

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

11. Taylor expanded in z around 0

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

    1. distribute-lft-out N/A

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

    2. lower-*.f64 N/A

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

    3. lower-+.f64 72.5

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

13. Applied rewrites 72.5%

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

Alternative 9: 44.7% accurate, 21.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 45.7%

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

2. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. lift-*.f64 18.7

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

4. Applied rewrites 18.7%

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

5. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

7. Applied rewrites 37.6%

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

8. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lift-sin.f64 N/A

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

   5. lift-*.f64 45.3

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

10. Applied rewrites 45.3%

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

11. Taylor expanded in x around inf

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

    1. *-commutative N/A

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

    2. lift-*.f64 44.7

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

13. Applied rewrites 44.7%

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

Reproduce

herbie shell --seed 2025110 
(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)))