Gyroid sphere

Percentage Accurate: 46.9% → 99.9%

Time: 13.6s

Alternatives: 12

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 46.9% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 49.3%

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

   1. associate-+l+ N/A

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

   2. unpow-prod-down N/A

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

   3. metadata-eval N/A

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

   4. *-commutative N/A

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

   5. unpow-prod-down N/A

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

   6. metadata-eval N/A

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

   7. *-commutative N/A

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

   8. unpow-prod-down N/A

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

   9. metadata-eval N/A

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

   10. *-commutative N/A

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

   11. +-commutative N/A

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.6% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 49.3%

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

   1. associate-+l+ N/A

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

   2. unpow-prod-down N/A

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

   3. metadata-eval N/A

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

   4. *-commutative N/A

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

   5. unpow-prod-down N/A

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

   6. metadata-eval N/A

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

   7. *-commutative N/A

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

   8. unpow-prod-down N/A

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

   9. metadata-eval N/A

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

   10. *-commutative N/A

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

   11. +-commutative N/A

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-sin.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 99.8

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

7. Applied rewrites 99.8%

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

Alternative 3: 99.1% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 49.3%

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

   1. associate-+l+ N/A

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

   2. unpow-prod-down N/A

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

   3. metadata-eval N/A

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

   4. *-commutative N/A

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

   5. unpow-prod-down N/A

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

   6. metadata-eval N/A

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

   7. *-commutative N/A

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

   8. unpow-prod-down N/A

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

   9. metadata-eval N/A

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

   10. *-commutative N/A

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

   11. +-commutative N/A

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-sin.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 99.8

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

7. Applied rewrites 99.8%

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

8. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 99.3

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

10. Applied rewrites 99.3%

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

Alternative 4: 99.3% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(30.0 * N[Sqrt[y ^ 2 + z ^ 2], $MachinePrecision]), $MachinePrecision] ^ 2 + N[(30.0 * x), $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 49.3%

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

   1. associate-+l+ N/A

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

   2. unpow-prod-down N/A

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

   3. metadata-eval N/A

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

   4. *-commutative N/A

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

   5. unpow-prod-down N/A

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

   6. metadata-eval N/A

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

   7. *-commutative N/A

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

   8. unpow-prod-down N/A

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

   9. metadata-eval N/A

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

   10. *-commutative N/A

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

   11. +-commutative N/A

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-sin.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 99.8

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

7. Applied rewrites 99.8%

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

8. Taylor expanded in z around 0

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

   1. lower-sin.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 99.3

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

10. Applied rewrites 99.3%

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

Alternative 5: 89.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(x \cdot 30\right)\right| - 0.2\\ \mathbf{if}\;x \leq -3900000000000 \lor \neg \left(x \leq 7.6 \cdot 10^{+34}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(30 \cdot y, 30 \cdot x\right) - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(y, z\right) - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* x 30.0))) 0.2)))
   (if (or (<= x -3900000000000.0) (not (<= x 7.6e+34)))
     (fmax (- (hypot (* 30.0 y) (* 30.0 x)) 25.0) t_0)
     (fmax (- (* 30.0 (hypot y z)) 25.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((x * 30.0))) - 0.2;
	double tmp;
	if ((x <= -3900000000000.0) || !(x <= 7.6e+34)) {
		tmp = fmax((hypot((30.0 * y), (30.0 * x)) - 25.0), t_0);
	} else {
		tmp = fmax(((30.0 * hypot(y, z)) - 25.0), t_0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((x * 30.0))) - 0.2;
	double tmp;
	if ((x <= -3900000000000.0) || !(x <= 7.6e+34)) {
		tmp = fmax((Math.hypot((30.0 * y), (30.0 * x)) - 25.0), t_0);
	} else {
		tmp = fmax(((30.0 * Math.hypot(y, z)) - 25.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((x * 30.0))) - 0.2
	tmp = 0
	if (x <= -3900000000000.0) or not (x <= 7.6e+34):
		tmp = fmax((math.hypot((30.0 * y), (30.0 * x)) - 25.0), t_0)
	else:
		tmp = fmax(((30.0 * math.hypot(y, z)) - 25.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(x * 30.0))) - 0.2)
	tmp = 0.0
	if ((x <= -3900000000000.0) || !(x <= 7.6e+34))
		tmp = fmax(Float64(hypot(Float64(30.0 * y), Float64(30.0 * x)) - 25.0), t_0);
	else
		tmp = fmax(Float64(Float64(30.0 * hypot(y, z)) - 25.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((x * 30.0))) - 0.2;
	tmp = 0.0;
	if ((x <= -3900000000000.0) || ~((x <= 7.6e+34)))
		tmp = max((hypot((30.0 * y), (30.0 * x)) - 25.0), t_0);
	else
		tmp = max(((30.0 * hypot(y, z)) - 25.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[Or[LessEqual[x, -3900000000000.0], N[Not[LessEqual[x, 7.6e+34]], $MachinePrecision]], N[Max[N[(N[Sqrt[N[(30.0 * y), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(30.0 * N[Sqrt[y ^ 2 + z ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9e12 or 7.6000000000000003e34 < x

   1. Initial program 29.6%

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

      1. associate-+l+ N/A

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

      2. unpow-prod-down N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. unpow-prod-down N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. unpow-prod-down N/A

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

      9. metadata-eval N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 99.9

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in z around 0

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

      1. lower-sin.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.9

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

   10. Applied rewrites 99.9%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 88.9%

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

   if -3.9e12 < x < 7.6000000000000003e34

   1. Initial program 64.9%

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

      1. associate-+l+ N/A

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

      2. unpow-prod-down N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. unpow-prod-down N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. unpow-prod-down N/A

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

      9. metadata-eval N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 99.7

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

   7. Applied rewrites 99.7%

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

   8. Taylor expanded in z around 0

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

      1. lower-sin.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 98.8

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

   10. Applied rewrites 98.8%

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

   11. Taylor expanded in x around 0

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

       1. pow2 N/A

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

       2. pow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-hypot.f64 97.6

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

   13. Applied rewrites 97.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3900000000000 \lor \neg \left(x \leq 7.6 \cdot 10^{+34}\right):\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(30 \cdot y, 30 \cdot x\right) - 25, \left|\sin \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(y, z\right) - 25, \left|\sin \left(x \cdot 30\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(x \cdot 30\right)\\ \mathbf{if}\;x \leq -3900000000000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, t\_0\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot \mathsf{hypot}\left(y, z\right) - 25, \left|t\_0\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* x 30.0))))
   (if (<= x -3900000000000.0)
     (fmax (* -30.0 x) (- (fabs (fma y 30.0 t_0)) 0.2))
     (if (<= x 3.4e+40)
       (fmax (- (* 30.0 (hypot y z)) 25.0) (- (fabs t_0) 0.2))
       (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((x * 30.0));
	double tmp;
	if (x <= -3900000000000.0) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, t_0)) - 0.2));
	} else if (x <= 3.4e+40) {
		tmp = fmax(((30.0 * hypot(y, z)) - 25.0), (fabs(t_0) - 0.2));
	} else {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(x * 30.0))
	tmp = 0.0
	if (x <= -3900000000000.0)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, t_0)) - 0.2));
	elseif (x <= 3.4e+40)
		tmp = fmax(Float64(Float64(30.0 * hypot(y, z)) - 25.0), Float64(abs(t_0) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -3900000000000.0], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 3.4e+40], N[Max[N[(N[(30.0 * N[Sqrt[y ^ 2 + z ^ 2], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9e12

   1. Initial program 29.4%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 69.2

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

   5. Applied rewrites 69.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 69.2

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

   8. Applied rewrites 69.2%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-sin.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 87.4

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

   11. Applied rewrites 87.4%

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

   if -3.9e12 < x < 3.39999999999999989e40

   1. Initial program 64.9%

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

      1. associate-+l+ N/A

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

      2. unpow-prod-down N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. unpow-prod-down N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. unpow-prod-down N/A

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

      9. metadata-eval N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 99.7

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

   7. Applied rewrites 99.7%

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

   8. Taylor expanded in z around 0

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

      1. lower-sin.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 98.8

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

   10. Applied rewrites 98.8%

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

   11. Taylor expanded in x around 0

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

       1. pow2 N/A

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

       2. pow2 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-hypot.f64 97.6

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

   13. Applied rewrites 97.6%

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

   if 3.39999999999999989e40 < x

   1. Initial program 29.8%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 3.8

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

   5. Applied rewrites 3.8%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 3.6

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

   8. Applied rewrites 3.6%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 3.7

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

   11. Applied rewrites 3.7%

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

   12. Taylor expanded in x around 0

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

       1. lower-*.f64 75.7

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

   14. Applied rewrites 75.7%

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

Alternative 7: 72.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-10} \lor \neg \left(y \leq 25\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(x \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e-10) (not (<= y 25.0)))
   (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* x 30.0)))) 0.2))
   (fmax
    (- (sqrt (* (* x x) 900.0)) 25.0)
    (- (fabs (fma z 30.0 (sin (* y 30.0)))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e-10) || !(y <= 25.0)) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((x * 30.0)))) - 0.2));
	} else {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs(fma(z, 30.0, sin((y * 30.0)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e-10) || !(y <= 25.0))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(x * 30.0)))) - 0.2));
	else
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(fma(z, 30.0, sin(Float64(y * 30.0)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.8e-10], N[Not[LessEqual[y, 25.0]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0 + N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000003e-10 or 25 < y

   1. Initial program 36.1%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 16.1

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

   5. Applied rewrites 16.1%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 16.1

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

   8. Applied rewrites 16.1%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-sin.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 72.9

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

   11. Applied rewrites 72.9%

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

   if -6.8000000000000003e-10 < y < 25

   1. Initial program 63.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 52.7

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

   8. Applied rewrites 52.7%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-sin.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 74.5

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

   11. Applied rewrites 74.5%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, \color{blue}{30}, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-10} \lor \neg \left(y \leq 25\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(x \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-10} \lor \neg \left(y \leq 21.5\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(x \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e-10) (not (<= y 21.5)))
   (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* x 30.0)))) 0.2))
   (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* 30.0 z)) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e-10) || !(y <= 21.5)) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((x * 30.0)))) - 0.2));
	} else {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((30.0 * z)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e-10) || !(y <= 21.5))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(x * 30.0)))) - 0.2));
	else
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * z)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.8e-10], N[Not[LessEqual[y, 21.5]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000003e-10 or 21.5 < y

   1. Initial program 36.1%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 16.1

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

   5. Applied rewrites 16.1%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 16.1

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

   8. Applied rewrites 16.1%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-sin.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 72.9

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

   11. Applied rewrites 72.9%

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

   if -6.8000000000000003e-10 < y < 21.5

   1. Initial program 63.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 52.7

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

   8. Applied rewrites 52.7%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 52.4

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

   11. Applied rewrites 52.4%

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

   12. Taylor expanded in z around 0

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

       1. lower-*.f64 74.3

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

   14. Applied rewrites 74.3%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-10} \lor \neg \left(y \leq 21.5\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(x \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.6% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(x \cdot 30\right)\right| - 0.2\\ \mathbf{if}\;y \leq -5200000000000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, t\_0\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot y, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* x 30.0))) 0.2)))
   (if (<= y -5200000000000.0)
     (fmax (- (* -30.0 y) 25.0) t_0)
     (if (<= y 1.6e+71)
       (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* 30.0 z)) 0.2))
       (fmax (* 30.0 y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((x * 30.0))) - 0.2;
	double tmp;
	if (y <= -5200000000000.0) {
		tmp = fmax(((-30.0 * y) - 25.0), t_0);
	} else if (y <= 1.6e+71) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((30.0 * y), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((x * 30.0d0))) - 0.2d0
    if (y <= (-5200000000000.0d0)) then
        tmp = fmax((((-30.0d0) * y) - 25.0d0), t_0)
    else if (y <= 1.6d+71) then
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((30.0d0 * z)) - 0.2d0))
    else
        tmp = fmax((30.0d0 * y), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((x * 30.0))) - 0.2;
	double tmp;
	if (y <= -5200000000000.0) {
		tmp = fmax(((-30.0 * y) - 25.0), t_0);
	} else if (y <= 1.6e+71) {
		tmp = fmax((Math.sqrt(((x * x) * 900.0)) - 25.0), (Math.abs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((30.0 * y), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((x * 30.0))) - 0.2
	tmp = 0
	if y <= -5200000000000.0:
		tmp = fmax(((-30.0 * y) - 25.0), t_0)
	elif y <= 1.6e+71:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((30.0 * z)) - 0.2))
	else:
		tmp = fmax((30.0 * y), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(x * 30.0))) - 0.2)
	tmp = 0.0
	if (y <= -5200000000000.0)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), t_0);
	elseif (y <= 1.6e+71)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * z)) - 0.2));
	else
		tmp = fmax(Float64(30.0 * y), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((x * 30.0))) - 0.2;
	tmp = 0.0;
	if (y <= -5200000000000.0)
		tmp = max(((-30.0 * y) - 25.0), t_0);
	elseif (y <= 1.6e+71)
		tmp = max((sqrt(((x * x) * 900.0)) - 25.0), (abs((30.0 * z)) - 0.2));
	else
		tmp = max((30.0 * y), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -5200000000000.0], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 1.6e+71], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * y), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e12

   1. Initial program 28.4%

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

      1. associate-+l+ N/A

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

      2. unpow-prod-down N/A

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

      3. metadata-eval N/A

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

      4. *-commutative N/A

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

      5. unpow-prod-down N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. unpow-prod-down N/A

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

      9. metadata-eval N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 99.9

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in z around 0

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

      1. lower-sin.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.9

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

   10. Applied rewrites 99.9%

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

   11. Taylor expanded in y around -inf

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

       1. lower-*.f64 61.9

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

   13. Applied rewrites 61.9%

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

   if -5.2e12 < y < 1.60000000000000012e71

   1. Initial program 62.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 47.6

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 47.5

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

   8. Applied rewrites 47.5%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 47.2

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

   11. Applied rewrites 47.2%

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

   12. Taylor expanded in z around 0

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

       1. lower-*.f64 68.3

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

   14. Applied rewrites 68.3%

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

   if 1.60000000000000012e71 < y

   1. Initial program 35.9%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 10.2

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

   5. Applied rewrites 10.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 10.1

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

   8. Applied rewrites 10.1%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 9.0

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

   11. Applied rewrites 9.0%

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

   12. Taylor expanded in y around inf

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

       1. lower-*.f64 77.9

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

   14. Applied rewrites 77.9%

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

Alternative 10: 68.6% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(x \cdot 30\right)\right| - 0.2\\ \mathbf{if}\;y \leq -6200000000000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_0\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot y, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* x 30.0))) 0.2)))
   (if (<= y -6200000000000.0)
     (fmax (* -30.0 y) t_0)
     (if (<= y 1.6e+71)
       (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* 30.0 z)) 0.2))
       (fmax (* 30.0 y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((x * 30.0))) - 0.2;
	double tmp;
	if (y <= -6200000000000.0) {
		tmp = fmax((-30.0 * y), t_0);
	} else if (y <= 1.6e+71) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((30.0 * y), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((x * 30.0d0))) - 0.2d0
    if (y <= (-6200000000000.0d0)) then
        tmp = fmax(((-30.0d0) * y), t_0)
    else if (y <= 1.6d+71) then
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((30.0d0 * z)) - 0.2d0))
    else
        tmp = fmax((30.0d0 * y), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((x * 30.0))) - 0.2;
	double tmp;
	if (y <= -6200000000000.0) {
		tmp = fmax((-30.0 * y), t_0);
	} else if (y <= 1.6e+71) {
		tmp = fmax((Math.sqrt(((x * x) * 900.0)) - 25.0), (Math.abs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((30.0 * y), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((x * 30.0))) - 0.2
	tmp = 0
	if y <= -6200000000000.0:
		tmp = fmax((-30.0 * y), t_0)
	elif y <= 1.6e+71:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((30.0 * z)) - 0.2))
	else:
		tmp = fmax((30.0 * y), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(x * 30.0))) - 0.2)
	tmp = 0.0
	if (y <= -6200000000000.0)
		tmp = fmax(Float64(-30.0 * y), t_0);
	elseif (y <= 1.6e+71)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * z)) - 0.2));
	else
		tmp = fmax(Float64(30.0 * y), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((x * 30.0))) - 0.2;
	tmp = 0.0;
	if (y <= -6200000000000.0)
		tmp = max((-30.0 * y), t_0);
	elseif (y <= 1.6e+71)
		tmp = max((sqrt(((x * x) * 900.0)) - 25.0), (abs((30.0 * z)) - 0.2));
	else
		tmp = max((30.0 * y), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -6200000000000.0], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 1.6e+71], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * y), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2e12

   1. Initial program 28.4%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 13.8

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

   5. Applied rewrites 13.8%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 13.8

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

   8. Applied rewrites 13.8%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 12.7

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

   11. Applied rewrites 12.7%

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

   12. Taylor expanded in y around -inf

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

       1. lower-*.f64 61.7

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

   14. Applied rewrites 61.7%

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

   if -6.2e12 < y < 1.60000000000000012e71

   1. Initial program 62.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 47.6

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 47.5

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

   8. Applied rewrites 47.5%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 47.2

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

   11. Applied rewrites 47.2%

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

   12. Taylor expanded in z around 0

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

       1. lower-*.f64 68.3

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

   14. Applied rewrites 68.3%

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

   if 1.60000000000000012e71 < y

   1. Initial program 35.9%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 10.2

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

   5. Applied rewrites 10.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 10.1

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

   8. Applied rewrites 10.1%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 9.0

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

   11. Applied rewrites 9.0%

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

   12. Taylor expanded in y around inf

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

       1. lower-*.f64 77.9

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

   14. Applied rewrites 77.9%

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

Alternative 11: 67.4% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+152} \lor \neg \left(x \leq 2.15 \cdot 10^{+156}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e+152) (not (<= x 2.15e+156)))
   (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))
   (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* 30.0 z)) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+152) || !(x <= 2.15e+156)) {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((30.0 * 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 ((x <= (-4d+152)) .or. (.not. (x <= 2.15d+156))) then
        tmp = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    else
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((30.0d0 * z)) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+152) || !(x <= 2.15e+156)) {
		tmp = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((Math.sqrt(((x * x) * 900.0)) - 25.0), (Math.abs((30.0 * z)) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e+152) or not (x <= 2.15e+156):
		tmp = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	else:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((30.0 * z)) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e+152) || !(x <= 2.15e+156))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * z)) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e+152) || ~((x <= 2.15e+156)))
		tmp = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	else
		tmp = max((sqrt(((x * x) * 900.0)) - 25.0), (abs((30.0 * z)) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e+152], N[Not[LessEqual[x, 2.15e+156]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0000000000000002e152 or 2.14999999999999993e156 < x

   1. Initial program 9.1%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 46.4

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

   5. Applied rewrites 46.4%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 46.3

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

   8. Applied rewrites 46.3%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 46.4

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

   11. Applied rewrites 46.4%

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

   12. Taylor expanded in x around 0

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

       1. lower-*.f64 83.6

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

   14. Applied rewrites 83.6%

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

   if -4.0000000000000002e152 < x < 2.14999999999999993e156

   1. Initial program 63.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 37.4

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

   5. Applied rewrites 37.4%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 37.3

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

   8. Applied rewrites 37.3%

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

   9. Taylor expanded in y around 0

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

       1. lower-sin.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 36.4

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

   11. Applied rewrites 36.4%

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

   12. Taylor expanded in z around 0

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

       1. lower-*.f64 59.4

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

   14. Applied rewrites 59.4%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+152} \lor \neg \left(x \leq 2.15 \cdot 10^{+156}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.0% accurate, 9.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 49.3%

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

3. Taylor expanded in x around -inf

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

   1. lower-*.f64 20.7

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

5. Applied rewrites 20.7%

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

6. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-sin.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 20.4

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

8. Applied rewrites 20.4%

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

9. Taylor expanded in y around 0

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

    1. lower-sin.f64 N/A

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

    2. *-commutative N/A

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

    3. lower-*.f64 19.8

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

11. Applied rewrites 19.8%

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

12. Taylor expanded in x around 0

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

    1. lower-*.f64 33.8

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

14. Applied rewrites 33.8%

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

Reproduce

herbie shell --seed 2025043 
(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)))