Gyroid sphere

Percentage Accurate: 45.6% → 90.0%

Time: 5.3s

Alternatives: 7

Speedup: 1.4×

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: 45.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\cos \left(-30 \cdot y\right), \sin \left(30 \cdot x\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\\ t_1 := \mathsf{max}\left(\mathsf{fma}\left(30, \mathsf{hypot}\left(z, y\right), -25\right), t\_0\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 102000000:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, \mathsf{hypot}\left(x, y\right), -25\right), t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs
           (fma
            (cos (* -30.0 x))
            (sin (* 30.0 z))
            (fma
             (cos (* -30.0 y))
             (sin (* 30.0 x))
             (* (cos (* -30.0 z)) (sin (* 30.0 y))))))
          0.2))
        (t_1 (fmax (fma 30.0 (hypot z y) -25.0) t_0)))
   (if (<= z -5.2e+17)
     t_1
     (if (<= z 102000000.0) (fmax (fma 30.0 (hypot x y) -25.0) t_0) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), fma(cos((-30.0 * y)), sin((30.0 * x)), (cos((-30.0 * z)) * sin((30.0 * y)))))) - 0.2;
	double t_1 = fmax(fma(30.0, hypot(z, y), -25.0), t_0);
	double tmp;
	if (z <= -5.2e+17) {
		tmp = t_1;
	} else if (z <= 102000000.0) {
		tmp = fmax(fma(30.0, hypot(x, y), -25.0), t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), fma(cos(Float64(-30.0 * y)), sin(Float64(30.0 * x)), Float64(cos(Float64(-30.0 * z)) * sin(Float64(30.0 * y)))))) - 0.2)
	t_1 = fmax(fma(30.0, hypot(z, y), -25.0), t_0)
	tmp = 0.0
	if (z <= -5.2e+17)
		tmp = t_1;
	elseif (z <= 102000000.0)
		tmp = fmax(fma(30.0, hypot(x, y), -25.0), t_0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$1 = N[Max[N[(30.0 * N[Sqrt[z ^ 2 + y ^ 2], $MachinePrecision] + -25.0), $MachinePrecision], t$95$0], $MachinePrecision]}, If[LessEqual[z, -5.2e+17], t$95$1, If[LessEqual[z, 102000000.0], N[Max[N[(30.0 * N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision] + -25.0), $MachinePrecision], t$95$0], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e17 or 1.02e8 < z

   1. Initial program 31.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 31.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 31.6

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

   3. Applied rewrites 31.6%

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

   5. Applied rewrites 32.1%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 32.1%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. pow2 N/A

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

      3. pow2 N/A

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

      4. lower-hypot.f64 80.3

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

   10. Applied rewrites 80.3%

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

   if -5.2e17 < z < 1.02e8

   1. Initial program 58.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 58.7

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 58.6

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

   3. Applied rewrites 58.6%

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

   5. Applied rewrites 58.9%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in z around 0

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. lower-hypot.f64 98.9

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

   10. Applied rewrites 98.9%

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

Alternative 2: 84.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \cos \left(-30 \cdot y\right)\\ t_2 := \sin \left(30 \cdot x\right)\\ t_3 := \sin \left(30 \cdot y\right)\\ t_4 := \cos \left(-30 \cdot x\right)\\ t_5 := \cos \left(-30 \cdot z\right)\\ t_6 := \left|\mathsf{fma}\left(t\_4, t\_0, \mathsf{fma}\left(t\_1, t\_2, t\_5 \cdot t\_3\right)\right)\right| - 0.2\\ \mathbf{if}\;z \leq -2 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, -z, -25\right), t\_6\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, \mathsf{hypot}\left(x, y\right), -25\right), t\_6\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, \sqrt{\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)}, -25\right), \left|\mathsf{fma}\left(t\_1, t\_2, t\_3\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot z, \left|\mathsf{fma}\left(t\_4, t\_0, \mathsf{fma}\left(\sin \left(x \cdot 30\right), t\_1, t\_5 \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (cos (* -30.0 y)))
        (t_2 (sin (* 30.0 x)))
        (t_3 (sin (* 30.0 y)))
        (t_4 (cos (* -30.0 x)))
        (t_5 (cos (* -30.0 z)))
        (t_6 (- (fabs (fma t_4 t_0 (fma t_1 t_2 (* t_5 t_3)))) 0.2)))
   (if (<= z -2e+133)
     (fmax (fma 30.0 (- z) -25.0) t_6)
     (if (<= z 8.5e+29)
       (fmax (fma 30.0 (hypot x y) -25.0) t_6)
       (if (<= z 3.75e+143)
         (fmax
          (fma 30.0 (sqrt (fma z z (fma y y (* x x)))) -25.0)
          (- (fabs (fma t_1 t_2 t_3)) 0.2))
         (fmax
          (* 30.0 z)
          (-
           (fabs
            (fma t_4 t_0 (fma (sin (* x 30.0)) t_1 (* t_5 (sin (* y 30.0))))))
           0.2)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = cos((-30.0 * y));
	double t_2 = sin((30.0 * x));
	double t_3 = sin((30.0 * y));
	double t_4 = cos((-30.0 * x));
	double t_5 = cos((-30.0 * z));
	double t_6 = fabs(fma(t_4, t_0, fma(t_1, t_2, (t_5 * t_3)))) - 0.2;
	double tmp;
	if (z <= -2e+133) {
		tmp = fmax(fma(30.0, -z, -25.0), t_6);
	} else if (z <= 8.5e+29) {
		tmp = fmax(fma(30.0, hypot(x, y), -25.0), t_6);
	} else if (z <= 3.75e+143) {
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, (x * x)))), -25.0), (fabs(fma(t_1, t_2, t_3)) - 0.2));
	} else {
		tmp = fmax((30.0 * z), (fabs(fma(t_4, t_0, fma(sin((x * 30.0)), t_1, (t_5 * sin((y * 30.0)))))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = cos(Float64(-30.0 * y))
	t_2 = sin(Float64(30.0 * x))
	t_3 = sin(Float64(30.0 * y))
	t_4 = cos(Float64(-30.0 * x))
	t_5 = cos(Float64(-30.0 * z))
	t_6 = Float64(abs(fma(t_4, t_0, fma(t_1, t_2, Float64(t_5 * t_3)))) - 0.2)
	tmp = 0.0
	if (z <= -2e+133)
		tmp = fmax(fma(30.0, Float64(-z), -25.0), t_6);
	elseif (z <= 8.5e+29)
		tmp = fmax(fma(30.0, hypot(x, y), -25.0), t_6);
	elseif (z <= 3.75e+143)
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, Float64(x * x)))), -25.0), Float64(abs(fma(t_1, t_2, t_3)) - 0.2));
	else
		tmp = fmax(Float64(30.0 * z), Float64(abs(fma(t_4, t_0, fma(sin(Float64(x * 30.0)), t_1, Float64(t_5 * sin(Float64(y * 30.0)))))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$5 = N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$6 = N[(N[Abs[N[(t$95$4 * t$95$0 + N[(t$95$1 * t$95$2 + N[(t$95$5 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -2e+133], N[Max[N[(30.0 * (-z) + -25.0), $MachinePrecision], t$95$6], $MachinePrecision], If[LessEqual[z, 8.5e+29], N[Max[N[(30.0 * N[Sqrt[x ^ 2 + y ^ 2], $MachinePrecision] + -25.0), $MachinePrecision], t$95$6], $MachinePrecision], If[LessEqual[z, 3.75e+143], N[Max[N[(30.0 * N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -25.0), $MachinePrecision], N[(N[Abs[N[(t$95$1 * t$95$2 + t$95$3), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * z), $MachinePrecision], N[(N[Abs[N[(t$95$4 * t$95$0 + N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * t$95$1 + N[(t$95$5 * N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2e133

   1. Initial program 13.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 13.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 13.2

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

   3. Applied rewrites 13.2%

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

   5. Applied rewrites 13.8%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 13.8%

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

   8. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 75.5

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

   10. Applied rewrites 75.5%

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

   if -2e133 < z < 8.5000000000000006e29

   1. Initial program 58.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 58.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 58.8

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

   3. Applied rewrites 58.8%

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

   5. Applied rewrites 59.1%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 59.1%

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

   8. Taylor expanded in z around 0

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

      1. pow2 N/A

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

      2. pow2 N/A

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

      3. lower-hypot.f64 92.7

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

   10. Applied rewrites 92.7%

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

   if 8.5000000000000006e29 < z < 3.74999999999999987e143

   1. Initial program 54.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 54.4

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 54.4

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

   3. Applied rewrites 54.4%

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

   5. Applied rewrites 54.9%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 54.9%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-cos.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-sin.f64 N/A

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

      8. lift-*.f64 54.9

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

   10. Applied rewrites 54.9%

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

   if 3.74999999999999987e143 < z

   1. Initial program 12.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 12.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 12.2

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

   3. Applied rewrites 12.2%

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

   5. Applied rewrites 12.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqrt-prod N/A

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

      4. metadata-eval N/A

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

      5. unpow1/2 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 12.9

         \[\leadsto \mathsf{max}\left(\color{blue}{{\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5} \cdot 30} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), \cos \left(-30 \cdot y\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right) \]

      9. lift-pow.f64 N/A

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

      10. unpow1/2 N/A

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

      11. lower-sqrt.f64 12.9

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

   7. Applied rewrites 12.9%

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

   8. Taylor expanded in z around inf

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

      1. lift-*.f64 76.3

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

   10. Applied rewrites 76.3%

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

Alternative 3: 62.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(-30 \cdot y\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), t\_0, \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_1\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, \sqrt{\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)}, -25\right), \left|\mathsf{fma}\left(t\_0, \sin \left(30 \cdot x\right), \sin \left(30 \cdot y\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot y, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (cos (* -30.0 y)))
        (t_1
         (-
          (fabs
           (fma
            (cos (* -30.0 x))
            (sin (* 30.0 z))
            (fma (sin (* x 30.0)) t_0 (* (cos (* -30.0 z)) (sin (* y 30.0))))))
          0.2)))
   (if (<= y -4.6e+128)
     (fmax (* -30.0 y) t_1)
     (if (<= y 6.6e+142)
       (fmax
        (fma 30.0 (sqrt (fma z z (fma y y (* x x)))) -25.0)
        (- (fabs (fma t_0 (sin (* 30.0 x)) (sin (* 30.0 y)))) 0.2))
       (fmax (* 30.0 y) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = cos((-30.0 * y));
	double t_1 = fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), fma(sin((x * 30.0)), t_0, (cos((-30.0 * z)) * sin((y * 30.0)))))) - 0.2;
	double tmp;
	if (y <= -4.6e+128) {
		tmp = fmax((-30.0 * y), t_1);
	} else if (y <= 6.6e+142) {
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, (x * x)))), -25.0), (fabs(fma(t_0, sin((30.0 * x)), sin((30.0 * y)))) - 0.2));
	} else {
		tmp = fmax((30.0 * y), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = cos(Float64(-30.0 * y))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), fma(sin(Float64(x * 30.0)), t_0, Float64(cos(Float64(-30.0 * z)) * sin(Float64(y * 30.0)))))) - 0.2)
	tmp = 0.0
	if (y <= -4.6e+128)
		tmp = fmax(Float64(-30.0 * y), t_1);
	elseif (y <= 6.6e+142)
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, Float64(x * x)))), -25.0), Float64(abs(fma(t_0, sin(Float64(30.0 * x)), sin(Float64(30.0 * y)))) - 0.2));
	else
		tmp = fmax(Float64(30.0 * y), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -4.6e+128], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[y, 6.6e+142], N[Max[N[(30.0 * N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * y), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999996e128

   1. Initial program 16.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 16.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 16.9

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

   3. Applied rewrites 16.9%

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

   5. Applied rewrites 16.9%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqrt-prod N/A

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

      4. metadata-eval N/A

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

      5. unpow1/2 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 17.1

         \[\leadsto \mathsf{max}\left(\color{blue}{{\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5} \cdot 30} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), \cos \left(-30 \cdot y\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right) \]

      9. lift-pow.f64 N/A

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

      10. unpow1/2 N/A

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

      11. lower-sqrt.f64 17.1

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

   7. Applied rewrites 17.1%

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

   8. Taylor expanded in y around -inf

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

      1. lift-*.f64 76.1

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

   10. Applied rewrites 76.1%

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

   if -4.59999999999999996e128 < y < 6.6000000000000004e142

   1. Initial program 58.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 58.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 58.0

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

   3. Applied rewrites 58.0%

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

   5. Applied rewrites 58.4%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 58.4%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-cos.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-sin.f64 N/A

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

      8. lift-*.f64 57.8

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

   10. Applied rewrites 57.8%

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

   if 6.6000000000000004e142 < y

   1. Initial program 11.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 11.5

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 11.5

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

   3. Applied rewrites 11.5%

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

   5. Applied rewrites 11.5%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqrt-prod N/A

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

      4. metadata-eval N/A

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

      5. unpow1/2 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 12.1

         \[\leadsto \mathsf{max}\left(\color{blue}{{\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5} \cdot 30} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), \cos \left(-30 \cdot y\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right) \]

      9. lift-pow.f64 N/A

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

      10. unpow1/2 N/A

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

      11. lower-sqrt.f64 12.1

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

   7. Applied rewrites 12.1%

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

   8. Taylor expanded in y around inf

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

      1. lift-*.f64 75.5

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

   10. Applied rewrites 75.5%

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

Alternative 4: 63.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(-30 \cdot y\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), t\_0, \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_1\right)\\ \mathbf{elif}\;x \leq 10^{+118}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, \sqrt{\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)}, -25\right), \left|\mathsf{fma}\left(t\_0, \sin \left(30 \cdot x\right), \sin \left(30 \cdot y\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (cos (* -30.0 y)))
        (t_1
         (-
          (fabs
           (fma
            (cos (* -30.0 x))
            (sin (* 30.0 z))
            (fma (sin (* x 30.0)) t_0 (* (cos (* -30.0 z)) (sin (* y 30.0))))))
          0.2)))
   (if (<= x -1.55e+142)
     (fmax (* -30.0 x) t_1)
     (if (<= x 1e+118)
       (fmax
        (fma 30.0 (sqrt (fma z z (fma y y (* x x)))) -25.0)
        (- (fabs (fma t_0 (sin (* 30.0 x)) (sin (* 30.0 y)))) 0.2))
       (fmax (* 30.0 x) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = cos((-30.0 * y));
	double t_1 = fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), fma(sin((x * 30.0)), t_0, (cos((-30.0 * z)) * sin((y * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.55e+142) {
		tmp = fmax((-30.0 * x), t_1);
	} else if (x <= 1e+118) {
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, (x * x)))), -25.0), (fabs(fma(t_0, sin((30.0 * x)), sin((30.0 * y)))) - 0.2));
	} else {
		tmp = fmax((30.0 * x), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = cos(Float64(-30.0 * y))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), fma(sin(Float64(x * 30.0)), t_0, Float64(cos(Float64(-30.0 * z)) * sin(Float64(y * 30.0)))))) - 0.2)
	tmp = 0.0
	if (x <= -1.55e+142)
		tmp = fmax(Float64(-30.0 * x), t_1);
	elseif (x <= 1e+118)
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, Float64(x * x)))), -25.0), Float64(abs(fma(t_0, sin(Float64(30.0 * x)), sin(Float64(30.0 * y)))) - 0.2));
	else
		tmp = fmax(Float64(30.0 * x), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.55e+142], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[x, 1e+118], N[Max[N[(30.0 * N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * x), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e142

   1. Initial program 12.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 12.4

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 12.4

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

   3. Applied rewrites 12.4%

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

   5. Applied rewrites 12.4%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqrt-prod N/A

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

      4. metadata-eval N/A

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

      5. unpow1/2 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 12.7

         \[\leadsto \mathsf{max}\left(\color{blue}{{\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5} \cdot 30} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), \cos \left(-30 \cdot y\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right) \]

      9. lift-pow.f64 N/A

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

      10. unpow1/2 N/A

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

      11. lower-sqrt.f64 12.7

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

   7. Applied rewrites 12.7%

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

   8. Taylor expanded in x around -inf

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

      1. lift-*.f64 78.0

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

   10. Applied rewrites 78.0%

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

   if -1.55e142 < x < 9.99999999999999967e117

   1. Initial program 58.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 58.4

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 58.4

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

   3. Applied rewrites 58.4%

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

   5. Applied rewrites 58.8%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 58.8%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-cos.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-sin.f64 N/A

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

      8. lift-*.f64 58.2

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

   10. Applied rewrites 58.2%

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

   if 9.99999999999999967e117 < x

   1. Initial program 17.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 17.7

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 17.7

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

   3. Applied rewrites 17.7%

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

   5. Applied rewrites 17.7%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqrt-prod N/A

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

      4. metadata-eval N/A

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

      5. unpow1/2 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 18.2

         \[\leadsto \mathsf{max}\left(\color{blue}{{\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5} \cdot 30} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), \cos \left(-30 \cdot y\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right) \]

      9. lift-pow.f64 N/A

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

      10. unpow1/2 N/A

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

      11. lower-sqrt.f64 18.2

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

   7. Applied rewrites 18.2%

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

   8. Taylor expanded in x around inf

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

      1. lift-*.f64 74.5

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

   10. Applied rewrites 74.5%

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

Alternative 5: 54.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(-30 \cdot y\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), t\_0, \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, \sqrt{\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)}, -25\right), \left|\mathsf{fma}\left(t\_0, \sin \left(30 \cdot x\right), \sin \left(30 \cdot y\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (cos (* -30.0 y))))
   (if (<= y -4.6e+128)
     (fmax
      (* -30.0 y)
      (-
       (fabs
        (fma
         (cos (* -30.0 x))
         (sin (* 30.0 z))
         (fma (sin (* x 30.0)) t_0 (* (cos (* -30.0 z)) (sin (* y 30.0))))))
       0.2))
     (fmax
      (fma 30.0 (sqrt (fma z z (fma y y (* x x)))) -25.0)
      (- (fabs (fma t_0 (sin (* 30.0 x)) (sin (* 30.0 y)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = cos((-30.0 * y));
	double tmp;
	if (y <= -4.6e+128) {
		tmp = fmax((-30.0 * y), (fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), fma(sin((x * 30.0)), t_0, (cos((-30.0 * z)) * sin((y * 30.0)))))) - 0.2));
	} else {
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, (x * x)))), -25.0), (fabs(fma(t_0, sin((30.0 * x)), sin((30.0 * y)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = cos(Float64(-30.0 * y))
	tmp = 0.0
	if (y <= -4.6e+128)
		tmp = fmax(Float64(-30.0 * y), Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), fma(sin(Float64(x * 30.0)), t_0, Float64(cos(Float64(-30.0 * z)) * sin(Float64(y * 30.0)))))) - 0.2));
	else
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, Float64(x * x)))), -25.0), Float64(abs(fma(t_0, sin(Float64(30.0 * x)), sin(Float64(30.0 * y)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -4.6e+128], N[Max[N[(-30.0 * y), $MachinePrecision], N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999996e128

   1. Initial program 16.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 16.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 16.9

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

   3. Applied rewrites 16.9%

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

   5. Applied rewrites 16.9%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqrt-prod N/A

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

      4. metadata-eval N/A

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

      5. unpow1/2 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 17.1

         \[\leadsto \mathsf{max}\left(\color{blue}{{\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5} \cdot 30} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), \cos \left(-30 \cdot y\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right) \]

      9. lift-pow.f64 N/A

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

      10. unpow1/2 N/A

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

      11. lower-sqrt.f64 17.1

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

   7. Applied rewrites 17.1%

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

   8. Taylor expanded in y around -inf

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

      1. lift-*.f64 76.1

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

   10. Applied rewrites 76.1%

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

   if -4.59999999999999996e128 < y

   1. Initial program 50.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 50.7

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 50.6

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

   3. Applied rewrites 50.6%

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

   5. Applied rewrites 51.1%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 51.1%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-cos.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-sin.f64 N/A

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

      8. lift-*.f64 50.6

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

   10. Applied rewrites 50.6%

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

Alternative 6: 54.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(-30 \cdot y\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), t\_0, \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, \sqrt{\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)}, -25\right), \left|\mathsf{fma}\left(t\_0, \sin \left(30 \cdot x\right), \sin \left(30 \cdot y\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (cos (* -30.0 y))))
   (if (<= x -1.55e+142)
     (fmax
      (* -30.0 x)
      (-
       (fabs
        (fma
         (cos (* -30.0 x))
         (sin (* 30.0 z))
         (fma (sin (* x 30.0)) t_0 (* (cos (* -30.0 z)) (sin (* y 30.0))))))
       0.2))
     (fmax
      (fma 30.0 (sqrt (fma z z (fma y y (* x x)))) -25.0)
      (- (fabs (fma t_0 (sin (* 30.0 x)) (sin (* 30.0 y)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = cos((-30.0 * y));
	double tmp;
	if (x <= -1.55e+142) {
		tmp = fmax((-30.0 * x), (fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), fma(sin((x * 30.0)), t_0, (cos((-30.0 * z)) * sin((y * 30.0)))))) - 0.2));
	} else {
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, (x * x)))), -25.0), (fabs(fma(t_0, sin((30.0 * x)), sin((30.0 * y)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = cos(Float64(-30.0 * y))
	tmp = 0.0
	if (x <= -1.55e+142)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), fma(sin(Float64(x * 30.0)), t_0, Float64(cos(Float64(-30.0 * z)) * sin(Float64(y * 30.0)))))) - 0.2));
	else
		tmp = fmax(fma(30.0, sqrt(fma(z, z, fma(y, y, Float64(x * x)))), -25.0), Float64(abs(fma(t_0, sin(Float64(30.0 * x)), sin(Float64(30.0 * y)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -1.55e+142], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55e142

   1. Initial program 12.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 12.4

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 12.4

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

   3. Applied rewrites 12.4%

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

   5. Applied rewrites 12.4%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. sqrt-prod N/A

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

      4. metadata-eval N/A

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

      5. unpow1/2 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 12.7

         \[\leadsto \mathsf{max}\left(\color{blue}{{\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5} \cdot 30} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \mathsf{fma}\left(\sin \left(x \cdot 30\right), \cos \left(-30 \cdot y\right), \cos \left(-30 \cdot z\right) \cdot \sin \left(y \cdot 30\right)\right)\right)\right| - 0.2\right) \]

      9. lift-pow.f64 N/A

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

      10. unpow1/2 N/A

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

      11. lower-sqrt.f64 12.7

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

   7. Applied rewrites 12.7%

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

   8. Taylor expanded in x around -inf

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

      1. lift-*.f64 78.0

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

   10. Applied rewrites 78.0%

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

   if -1.55e142 < x

   1. Initial program 51.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 51.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. unpow-prod-down N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. distribute-rgt-out N/A

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

      15. lower-*.f64 N/A

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

      16. metadata-eval N/A

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

      17. unpow2 N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 51.0

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

   3. Applied rewrites 51.0%

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

   5. Applied rewrites 51.4%

      \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   7. Applied rewrites 51.4%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-cos.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-sin.f64 N/A

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

      8. lift-*.f64 50.9

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

   10. Applied rewrites 50.9%

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

Alternative 7: 45.6% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 45.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-pow.f64 N/A

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

   4. unpow2 N/A

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

   5. lower-fma.f64 45.6

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lift-pow.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. unpow-prod-down N/A

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

   11. lift-pow.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. unpow-prod-down N/A

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

   14. distribute-rgt-out N/A

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

   15. lower-*.f64 N/A

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

   16. metadata-eval N/A

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

   17. unpow2 N/A

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

   18. lower-fma.f64 N/A

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

   19. unpow2 N/A

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

   20. lower-*.f64 45.6

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

3. Applied rewrites 45.6%

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

5. Applied rewrites 46.0%

   \[\leadsto \mathsf{max}\left(\color{blue}{\mathsf{fma}\left({900}^{0.5}, {\left(\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{0.5}, -25\right)}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

7. Applied rewrites 46.0%

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

8. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lift-cos.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-sin.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift-sin.f64 N/A

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

   8. lift-*.f64 45.6

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

10. Applied rewrites 45.6%

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

Reproduce

herbie shell --seed 2025107 
(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)))