Gyroid sphere

Percentage Accurate: 46.9% → 85.2%

Time: 10.7s

Alternatives: 15

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 46.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 85.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_0\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(\mathsf{hypot}\left(z, y\right), 30, -25\right), \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, x, -25\right), t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs (fma (cos (* -30.0 x)) (sin (* 30.0 z)) (sin (* 30.0 x))))
          0.2)))
   (if (<= x -3.5e+143)
     (fmax (* -30.0 x) t_0)
     (if (<= x 2.25e+127)
       (fmax
        (fma (hypot z y) 30.0 -25.0)
        (-
         (fabs
          (+
           (* (sin (* z 30.0)) (cos (* x 30.0)))
           (+
            (* (sin (* x 30.0)) (cos (* y 30.0)))
            (* (sin (* y 30.0)) (cos (* z 30.0))))))
         0.2))
       (fmax (fma 30.0 x -25.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), sin((30.0 * x)))) - 0.2;
	double tmp;
	if (x <= -3.5e+143) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (x <= 2.25e+127) {
		tmp = fmax(fma(hypot(z, y), 30.0, -25.0), (fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
	} else {
		tmp = fmax(fma(30.0, x, -25.0), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (x <= -3.5e+143)
		tmp = fmax(Float64(-30.0 * x), t_0);
	elseif (x <= 2.25e+127)
		tmp = fmax(fma(hypot(z, y), 30.0, -25.0), Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2));
	else
		tmp = fmax(fma(30.0, x, -25.0), t_0);
	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[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -3.5e+143], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 2.25e+127], N[Max[N[(N[Sqrt[z ^ 2 + y ^ 2], $MachinePrecision] * 30.0 + -25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * x + -25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.50000000000000008e143

   1. Initial program 16.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 16.0

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

   5. Applied rewrites 16.0%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 78.6

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

   8. Applied rewrites 78.6%

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

   if -3.50000000000000008e143 < x < 2.25000000000000017e127

   1. Initial program 61.0%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. unpow-prod-down N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. lift-pow.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. unpow-prod-down N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. unpow2 N/A

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

      21. lower-fma.f64 N/A

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

      22. unpow2 N/A

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

      23. lower-*.f64 60.9

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

   4. Applied rewrites 60.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. lower-hypot.f64 90.0

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

   7. Applied rewrites 90.0%

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

   8. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. unpow2 N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 90.0

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

   10. Applied rewrites 90.0%

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

   if 2.25000000000000017e127 < x

   1. Initial program 16.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 16.7

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

   5. Applied rewrites 16.7%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 79.8

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 79.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(\mathsf{hypot}\left(z, y\right), 30, -25\right), \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, x, -25\right), \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_1\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(\mathsf{hypot}\left(z, y\right), 30, -25\right), \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, x, -25\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= x -3.5e+143)
     (fmax (* -30.0 x) t_1)
     (if (<= x 2.25e+127)
       (fmax
        (fma (hypot z y) 30.0 -25.0)
        (- (fabs (fma (sin (* 30.0 y)) (cos (* -30.0 z)) t_0)) 0.2))
       (fmax (fma 30.0 x -25.0) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (x <= -3.5e+143) {
		tmp = fmax((-30.0 * x), t_1);
	} else if (x <= 2.25e+127) {
		tmp = fmax(fma(hypot(z, y), 30.0, -25.0), (fabs(fma(sin((30.0 * y)), cos((-30.0 * z)), t_0)) - 0.2));
	} else {
		tmp = fmax(fma(30.0, x, -25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (x <= -3.5e+143)
		tmp = fmax(Float64(-30.0 * x), t_1);
	elseif (x <= 2.25e+127)
		tmp = fmax(fma(hypot(z, y), 30.0, -25.0), Float64(abs(fma(sin(Float64(30.0 * y)), cos(Float64(-30.0 * z)), t_0)) - 0.2));
	else
		tmp = fmax(fma(30.0, x, -25.0), t_1);
	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[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -3.5e+143], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[x, 2.25e+127], N[Max[N[(N[Sqrt[z ^ 2 + y ^ 2], $MachinePrecision] * 30.0 + -25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * x + -25.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.50000000000000008e143

   1. Initial program 16.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 16.0

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

   5. Applied rewrites 16.0%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 78.6

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

   8. Applied rewrites 78.6%

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

   if -3.50000000000000008e143 < x < 2.25000000000000017e127

   1. Initial program 61.0%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. unpow-prod-down N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. lift-pow.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. unpow-prod-down N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. unpow2 N/A

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

      21. lower-fma.f64 N/A

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

      22. unpow2 N/A

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

      23. lower-*.f64 60.9

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

   4. Applied rewrites 60.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. lower-hypot.f64 90.0

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

   7. Applied rewrites 90.0%

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

   8. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. unpow2 N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 90.0

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

   10. Applied rewrites 90.0%

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

   11. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-sin.f64 N/A

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

       5. lower-*.f64 N/A

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

       6. cos-neg-rev N/A

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

       7. lower-cos.f64 N/A

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

       8. distribute-lft-neg-in N/A

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

       9. metadata-eval N/A

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

       10. lower-*.f64 N/A

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

       11. lower-sin.f64 N/A

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

       12. lower-*.f64 89.1

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

   13. Applied rewrites 89.1%

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

   if 2.25000000000000017e127 < x

   1. Initial program 16.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 16.7

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

   5. Applied rewrites 16.7%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 79.8

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 79.9%

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

Alternative 3: 63.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_1\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\left(30 - \frac{25}{y}\right) \cdot y, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= y -2.4e+152)
     (fmax (* -30.0 y) t_1)
     (if (<= y 1.26e+129)
       (fmax
        (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
        (- (fabs (fma (sin (* 30.0 y)) (cos (* -30.0 z)) t_0)) 0.2))
       (fmax (* (- 30.0 (/ 25.0 y)) y) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (y <= -2.4e+152) {
		tmp = fmax((-30.0 * y), t_1);
	} else if (y <= 1.26e+129) {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), cos((-30.0 * z)), t_0)) - 0.2));
	} else {
		tmp = fmax(((30.0 - (25.0 / y)) * y), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (y <= -2.4e+152)
		tmp = fmax(Float64(-30.0 * y), t_1);
	elseif (y <= 1.26e+129)
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), cos(Float64(-30.0 * z)), t_0)) - 0.2));
	else
		tmp = fmax(Float64(Float64(30.0 - Float64(25.0 / y)) * y), t_1);
	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[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -2.4e+152], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[y, 1.26e+129], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 - N[(25.0 / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3999999999999999e152

   1. Initial program 12.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 12.7

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

   5. Applied rewrites 12.7%

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

   6. Taylor expanded in y around -inf

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

      1. lower-*.f64 77.9

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

   8. Applied rewrites 77.9%

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

   if -2.3999999999999999e152 < y < 1.26e129

   1. Initial program 61.1%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. unpow-prod-down N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. lift-pow.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. unpow-prod-down N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. unpow2 N/A

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

      21. lower-fma.f64 N/A

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

      22. unpow2 N/A

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

      23. lower-*.f64 61.0

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

   4. Applied rewrites 61.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. cos-neg-rev N/A

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

      7. lower-cos.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. lower-*.f64 60.5

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

   7. Applied rewrites 60.5%

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

   if 1.26e129 < y

   1. Initial program 12.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 12.6

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

   5. Applied rewrites 12.6%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 86.0

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

   8. Applied rewrites 86.0%

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

Alternative 4: 63.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_1\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \mathsf{fma}\left(x, x, \mathsf{fma}\left(z, z, y \cdot y\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\left(30 - \frac{25}{y}\right) \cdot y, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= y -2.4e+152)
     (fmax (* -30.0 y) t_1)
     (if (<= y 1.26e+129)
       (fmax
        (- (sqrt (* 900.0 (fma x x (fma z z (* y y))))) 25.0)
        (- (fabs (fma (sin (* 30.0 y)) (cos (* -30.0 z)) t_0)) 0.2))
       (fmax (* (- 30.0 (/ 25.0 y)) y) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (y <= -2.4e+152) {
		tmp = fmax((-30.0 * y), t_1);
	} else if (y <= 1.26e+129) {
		tmp = fmax((sqrt((900.0 * fma(x, x, fma(z, z, (y * y))))) - 25.0), (fabs(fma(sin((30.0 * y)), cos((-30.0 * z)), t_0)) - 0.2));
	} else {
		tmp = fmax(((30.0 - (25.0 / y)) * y), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (y <= -2.4e+152)
		tmp = fmax(Float64(-30.0 * y), t_1);
	elseif (y <= 1.26e+129)
		tmp = fmax(Float64(sqrt(Float64(900.0 * fma(x, x, fma(z, z, Float64(y * y))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), cos(Float64(-30.0 * z)), t_0)) - 0.2));
	else
		tmp = fmax(Float64(Float64(30.0 - Float64(25.0 / y)) * y), t_1);
	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[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -2.4e+152], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[y, 1.26e+129], N[Max[N[(N[Sqrt[N[(900.0 * N[(x * x + N[(z * z + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 - N[(25.0 / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3999999999999999e152

   1. Initial program 12.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 12.7

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

   5. Applied rewrites 12.7%

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

   6. Taylor expanded in y around -inf

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

      1. lower-*.f64 77.9

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

   8. Applied rewrites 77.9%

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

   if -2.3999999999999999e152 < y < 1.26e129

   1. Initial program 61.1%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. unpow-prod-down N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. lift-pow.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. unpow-prod-down N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. unpow2 N/A

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

      21. lower-fma.f64 N/A

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

      22. unpow2 N/A

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

      23. lower-*.f64 61.0

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

   4. Applied rewrites 61.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. cos-neg-rev N/A

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

      7. lower-cos.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. lower-*.f64 60.5

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

   7. Applied rewrites 60.5%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-out N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 60.5

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

      8. lift-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 60.5

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

   9. Applied rewrites 60.5%

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

   if 1.26e129 < y

   1. Initial program 12.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 12.6

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

   5. Applied rewrites 12.6%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 86.0

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

   8. Applied rewrites 86.0%

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

Alternative 5: 63.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_0\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \mathsf{fma}\left(x, x, \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\left(30 - \frac{25}{y}\right) \cdot y, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs (fma (cos (* -30.0 x)) (sin (* 30.0 z)) (sin (* 30.0 x))))
          0.2)))
   (if (<= y -2.4e+152)
     (fmax (* -30.0 y) t_0)
     (if (<= y 1.26e+129)
       (fmax (- (sqrt (* 900.0 (fma x x (fma y y (* z z))))) 25.0) t_0)
       (fmax (* (- 30.0 (/ 25.0 y)) y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), sin((30.0 * x)))) - 0.2;
	double tmp;
	if (y <= -2.4e+152) {
		tmp = fmax((-30.0 * y), t_0);
	} else if (y <= 1.26e+129) {
		tmp = fmax((sqrt((900.0 * fma(x, x, fma(y, y, (z * z))))) - 25.0), t_0);
	} else {
		tmp = fmax(((30.0 - (25.0 / y)) * y), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (y <= -2.4e+152)
		tmp = fmax(Float64(-30.0 * y), t_0);
	elseif (y <= 1.26e+129)
		tmp = fmax(Float64(sqrt(Float64(900.0 * fma(x, x, fma(y, y, Float64(z * z))))) - 25.0), t_0);
	else
		tmp = fmax(Float64(Float64(30.0 - Float64(25.0 / y)) * y), t_0);
	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[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -2.4e+152], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 1.26e+129], N[Max[N[(N[Sqrt[N[(900.0 * N[(x * x + N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(30.0 - N[(25.0 / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3999999999999999e152

   1. Initial program 12.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 12.7

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

   5. Applied rewrites 12.7%

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

   6. Taylor expanded in y around -inf

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

      1. lower-*.f64 77.9

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

   8. Applied rewrites 77.9%

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

   if -2.3999999999999999e152 < y < 1.26e129

   1. Initial program 61.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 60.6

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

   5. Applied rewrites 60.6%

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

   7. Applied rewrites 60.5%

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

   if 1.26e129 < y

   1. Initial program 12.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 12.6

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

   5. Applied rewrites 12.6%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 86.0

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

   8. Applied rewrites 86.0%

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

Alternative 6: 60.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot x\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), t\_0\right)\right| - 0.2\\ \mathbf{if}\;x \leq -11000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(-30 \cdot y\right), \sin \left(30 \cdot y\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z, z, y \cdot y\right) \cdot 900} - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, x, -25\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 x)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) (sin (* 30.0 z)) t_0)) 0.2)))
   (if (<= x -11000.0)
     (fmax
      (- (* -30.0 x) 25.0)
      (- (fabs (fma t_0 (cos (* -30.0 y)) (sin (* 30.0 y)))) 0.2))
     (if (<= x 1.6e+28)
       (fmax (- (sqrt (* (fma z z (* y y)) 900.0)) 25.0) t_1)
       (fmax (fma 30.0 x -25.0) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * x));
	double t_1 = fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), t_0)) - 0.2;
	double tmp;
	if (x <= -11000.0) {
		tmp = fmax(((-30.0 * x) - 25.0), (fabs(fma(t_0, cos((-30.0 * y)), sin((30.0 * y)))) - 0.2));
	} else if (x <= 1.6e+28) {
		tmp = fmax((sqrt((fma(z, z, (y * y)) * 900.0)) - 25.0), t_1);
	} else {
		tmp = fmax(fma(30.0, x, -25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * x))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), t_0)) - 0.2)
	tmp = 0.0
	if (x <= -11000.0)
		tmp = fmax(Float64(Float64(-30.0 * x) - 25.0), Float64(abs(fma(t_0, cos(Float64(-30.0 * y)), sin(Float64(30.0 * y)))) - 0.2));
	elseif (x <= 1.6e+28)
		tmp = fmax(Float64(sqrt(Float64(fma(z, z, Float64(y * y)) * 900.0)) - 25.0), t_1);
	else
		tmp = fmax(fma(30.0, x, -25.0), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * x), $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] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -11000.0], N[Max[N[(N[(-30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.6e+28], N[Max[N[(N[Sqrt[N[(N[(z * z + N[(y * y), $MachinePrecision]), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[N[(30.0 * x + -25.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -11000

   1. Initial program 31.2%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. cos-neg-rev N/A

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

      7. lower-cos.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. lower-*.f64 57.6

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

   8. Applied rewrites 57.6%

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

   if -11000 < x < 1.6e28

   1. Initial program 66.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 65.4

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 64.6

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

   8. Applied rewrites 64.6%

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

   if 1.6e28 < x

   1. Initial program 29.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 29.1

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

   5. Applied rewrites 29.1%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 63.3

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

   8. Applied rewrites 63.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 63.3%

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

Alternative 7: 58.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_0\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z, z, x \cdot x\right) \cdot 900} - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\left(30 - \frac{25}{y}\right) \cdot y, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs (fma (cos (* -30.0 x)) (sin (* 30.0 z)) (sin (* 30.0 x))))
          0.2)))
   (if (<= y -1.05e+85)
     (fmax (* -30.0 y) t_0)
     (if (<= y 5.5e+38)
       (fmax (- (sqrt (* (fma z z (* x x)) 900.0)) 25.0) t_0)
       (fmax (* (- 30.0 (/ 25.0 y)) y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(cos((-30.0 * x)), sin((30.0 * z)), sin((30.0 * x)))) - 0.2;
	double tmp;
	if (y <= -1.05e+85) {
		tmp = fmax((-30.0 * y), t_0);
	} else if (y <= 5.5e+38) {
		tmp = fmax((sqrt((fma(z, z, (x * x)) * 900.0)) - 25.0), t_0);
	} else {
		tmp = fmax(((30.0 - (25.0 / y)) * y), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(cos(Float64(-30.0 * x)), sin(Float64(30.0 * z)), sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (y <= -1.05e+85)
		tmp = fmax(Float64(-30.0 * y), t_0);
	elseif (y <= 5.5e+38)
		tmp = fmax(Float64(sqrt(Float64(fma(z, z, Float64(x * x)) * 900.0)) - 25.0), t_0);
	else
		tmp = fmax(Float64(Float64(30.0 - Float64(25.0 / y)) * y), t_0);
	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[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -1.05e+85], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 5.5e+38], N[Max[N[(N[Sqrt[N[(N[(z * z + N[(x * x), $MachinePrecision]), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(30.0 - N[(25.0 / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000005e85

   1. Initial program 29.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 29.2

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

   5. Applied rewrites 29.2%

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

   6. Taylor expanded in y around -inf

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

      1. lower-*.f64 74.3

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

   8. Applied rewrites 74.3%

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

   if -1.05000000000000005e85 < y < 5.5000000000000003e38

   1. Initial program 59.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 58.8

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-sqrt.f64 N/A

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

      3. distribute-lft-out N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 54.2

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

   8. Applied rewrites 54.2%

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

   if 5.5000000000000003e38 < y

   1. Initial program 33.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 33.7

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

   5. Applied rewrites 33.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 74.5

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

   8. Applied rewrites 74.5%

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

Alternative 8: 58.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\left(30 - \frac{25}{y}\right) \cdot y, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= y -1.02e+85)
     (fmax (* -30.0 y) t_1)
     (if (<= y 2.5e+109)
       (fmax
        (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
        (- (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) t_0)) 0.2))
       (fmax (* (- 30.0 (/ 25.0 y)) y) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (y <= -1.02e+85) {
		tmp = fmax((-30.0 * y), t_1);
	} else if (y <= 2.5e+109) {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), t_0)) - 0.2));
	} else {
		tmp = fmax(((30.0 - (25.0 / y)) * y), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (y <= -1.02e+85)
		tmp = fmax(Float64(-30.0 * y), t_1);
	elseif (y <= 2.5e+109)
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), t_0)) - 0.2));
	else
		tmp = fmax(Float64(Float64(30.0 - Float64(25.0 / y)) * y), t_1);
	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[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -1.02e+85], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[y, 2.5e+109], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 - N[(25.0 / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e85

   1. Initial program 30.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 30.7

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

   5. Applied rewrites 30.7%

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

   6. Taylor expanded in y around -inf

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

      1. lower-*.f64 72.9

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

   8. Applied rewrites 72.9%

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

   if -1.02e85 < y < 2.5000000000000001e109

   1. Initial program 59.8%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. unpow-prod-down N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. lift-pow.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. unpow-prod-down N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. unpow2 N/A

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

      21. lower-fma.f64 N/A

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

      22. unpow2 N/A

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

      23. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. cos-neg-rev N/A

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

      7. lower-cos.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. lower-*.f64 59.2

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

   7. Applied rewrites 59.2%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 53.7%

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   if 2.5000000000000001e109 < y

   1. Initial program 21.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 21.2

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

   5. Applied rewrites 21.2%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 83.3

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

   8. Applied rewrites 83.3%

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

Alternative 9: 58.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, y, -25\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= y -1.02e+85)
     (fmax (* -30.0 y) t_1)
     (if (<= y 2.5e+109)
       (fmax
        (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
        (- (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) t_0)) 0.2))
       (fmax (fma 30.0 y -25.0) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (y <= -1.02e+85) {
		tmp = fmax((-30.0 * y), t_1);
	} else if (y <= 2.5e+109) {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), t_0)) - 0.2));
	} else {
		tmp = fmax(fma(30.0, y, -25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (y <= -1.02e+85)
		tmp = fmax(Float64(-30.0 * y), t_1);
	elseif (y <= 2.5e+109)
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), t_0)) - 0.2));
	else
		tmp = fmax(fma(30.0, y, -25.0), t_1);
	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[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -1.02e+85], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[y, 2.5e+109], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * y + -25.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e85

   1. Initial program 30.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 30.7

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

   5. Applied rewrites 30.7%

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

   6. Taylor expanded in y around -inf

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

      1. lower-*.f64 72.9

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

   8. Applied rewrites 72.9%

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

   if -1.02e85 < y < 2.5000000000000001e109

   1. Initial program 59.8%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. unpow-prod-down N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. lift-pow.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. unpow-prod-down N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. unpow2 N/A

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

      21. lower-fma.f64 N/A

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

      22. unpow2 N/A

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

      23. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. cos-neg-rev N/A

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

      7. lower-cos.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. lower-*.f64 59.2

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

   7. Applied rewrites 59.2%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 53.7%

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   if 2.5000000000000001e109 < y

   1. Initial program 21.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 21.2

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

   5. Applied rewrites 21.2%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 83.3

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

   8. Applied rewrites 83.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 83.2%

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

Alternative 10: 58.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_1\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(30, x, -25\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= x -4.6e+147)
     (fmax (* -30.0 x) t_1)
     (if (<= x 5.2e+119)
       (fmax
        (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
        (- (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) t_0)) 0.2))
       (fmax (fma 30.0 x -25.0) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (x <= -4.6e+147) {
		tmp = fmax((-30.0 * x), t_1);
	} else if (x <= 5.2e+119) {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), t_0)) - 0.2));
	} else {
		tmp = fmax(fma(30.0, x, -25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (x <= -4.6e+147)
		tmp = fmax(Float64(-30.0 * x), t_1);
	elseif (x <= 5.2e+119)
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), t_0)) - 0.2));
	else
		tmp = fmax(fma(30.0, x, -25.0), t_1);
	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[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -4.6e+147], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[x, 5.2e+119], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * x + -25.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999998e147

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 13.2

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

   5. Applied rewrites 13.2%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 77.8

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

   8. Applied rewrites 77.8%

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

   if -4.5999999999999998e147 < x < 5.2e119

   1. Initial program 61.6%

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

      1. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. unpow-prod-down N/A

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

      7. lower-fma.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. unpow-prod-down N/A

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

      14. lift-pow.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. unpow-prod-down N/A

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

      17. distribute-rgt-out N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. unpow2 N/A

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

      21. lower-fma.f64 N/A

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

      22. unpow2 N/A

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

      23. lower-*.f64 61.5

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

   4. Applied rewrites 61.5%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. cos-neg-rev N/A

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

      7. lower-cos.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sin.f64 N/A

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

      12. lower-*.f64 60.9

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 54.3%

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   if 5.2e119 < x

   1. Initial program 18.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 18.0

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

   5. Applied rewrites 18.0%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 77.0

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

   8. Applied rewrites 77.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 77.0%

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

Alternative 11: 58.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_1\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+119}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= x -4.6e+147)
     (fmax (* -30.0 x) t_1)
     (if (<= x 5.2e+119)
       (fmax
        (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
        (- (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) t_0)) 0.2))
       (fmax (* 30.0 x) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (x <= -4.6e+147) {
		tmp = fmax((-30.0 * x), t_1);
	} else if (x <= 5.2e+119) {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), t_0)) - 0.2));
	} else {
		tmp = fmax((30.0 * x), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (x <= -4.6e+147)
		tmp = fmax(Float64(-30.0 * x), t_1);
	elseif (x <= 5.2e+119)
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), t_0)) - 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[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -4.6e+147], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[x, 5.2e+119], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + t$95$0), $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 < -4.5999999999999998e147

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. cos-neg-rev N/A

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

      4. lower-cos.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-sin.f64 N/A

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

      11. lower-*.f64 13.2

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

   5. Applied rewrites 13.2%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 77.8

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

   8. Applied rewrites 77.8%

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

   if -4.5999999999999998e147 < x < 5.2e119

   1. Initial program 61.6%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. 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. lift-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right)} + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. lift-pow.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{\color{blue}{\left(x \cdot 30\right)}}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow-prod-down N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{x}^{2} \cdot {30}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left({x}^{2}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, \color{blue}{900}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      11. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{\left(y \cdot 30\right)}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {\color{blue}{\left(y \cdot 30\right)}}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      13. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{y}^{2} \cdot {30}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      14. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{\left(z \cdot 30\right)}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + {\color{blue}{\left(z \cdot 30\right)}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      16. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{z}^{2} \cdot {30}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      17. distribute-rgt-out N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{900} \cdot \left({y}^{2} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      20. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \left(\color{blue}{y \cdot y} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      21. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \color{blue}{\mathsf{fma}\left(y, y, {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      22. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      23. lower-*.f64 61.5

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   4. Applied rewrites 61.5%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right) + \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot y\right) \cdot \cos \left(30 \cdot z\right)} + \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - \frac{1}{5}\right) \]

      4. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\color{blue}{\sin \left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \color{blue}{\left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      6. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(\color{blue}{-30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(-30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      11. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \color{blue}{\sin \left(30 \cdot z\right)}\right)\right| - \frac{1}{5}\right) \]

      12. lower-*.f64 60.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \color{blue}{\left(30 \cdot z\right)}\right)\right| - 0.2\right) \]

   7. Applied rewrites 60.9%

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 54.3%

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   if 5.2e119 < x

   1. Initial program 18.0%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right) + \sin \left(30 \cdot x\right)}\right| - \frac{1}{5}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - \frac{1}{5}\right) \]

      3. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(\color{blue}{-30} \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(-30 \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \color{blue}{\sin \left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \color{blue}{\left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \color{blue}{\sin \left(30 \cdot x\right)}\right)\right| - \frac{1}{5}\right) \]

      11. lower-*.f64 18.0

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \color{blue}{\left(30 \cdot x\right)}\right)\right| - 0.2\right) \]

   5. Applied rewrites 18.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\color{blue}{\left(30 - 25 \cdot \frac{1}{x}\right) \cdot x}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\color{blue}{\left(30 - 25 \cdot \frac{1}{x}\right) \cdot x}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{max}\left(\color{blue}{\left(30 - 25 \cdot \frac{1}{x}\right)} \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{max}\left(\left(30 - \color{blue}{\frac{25 \cdot 1}{x}}\right) \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\left(30 - \frac{\color{blue}{25}}{x}\right) \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      6. lower-/.f64 77.0

         \[\leadsto \mathsf{max}\left(\left(30 - \color{blue}{\frac{25}{x}}\right) \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   8. Applied rewrites 77.0%

      \[\leadsto \mathsf{max}\left(\color{blue}{\left(30 - \frac{25}{x}\right) \cdot x}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 77.0%

       \[\leadsto \mathsf{max}\left(30 \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 61.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, t\_1\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2)))
   (if (<= z -1.7e+75)
     (fmax (* -30.0 z) t_1)
     (if (<= z 1.16e+33)
       (fmax
        (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
        (- (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) t_0)) 0.2))
       (fmax (* 30.0 z) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2;
	double tmp;
	if (z <= -1.7e+75) {
		tmp = fmax((-30.0 * z), t_1);
	} else if (z <= 1.16e+33) {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), t_0)) - 0.2));
	} else {
		tmp = fmax((30.0 * z), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2)
	tmp = 0.0
	if (z <= -1.7e+75)
		tmp = fmax(Float64(-30.0 * z), t_1);
	elseif (z <= 1.16e+33)
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), t_0)) - 0.2));
	else
		tmp = fmax(Float64(30.0 * z), t_1);
	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[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -1.7e+75], N[Max[N[(-30.0 * z), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, 1.16e+33], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * z), $MachinePrecision], t$95$1], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000006e75

   1. Initial program 17.2%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right) + \sin \left(30 \cdot x\right)}\right| - \frac{1}{5}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - \frac{1}{5}\right) \]

      3. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(\color{blue}{-30} \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(-30 \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \color{blue}{\sin \left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \color{blue}{\left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \color{blue}{\sin \left(30 \cdot x\right)}\right)\right| - \frac{1}{5}\right) \]

      11. lower-*.f64 17.2

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \color{blue}{\left(30 \cdot x\right)}\right)\right| - 0.2\right) \]

   5. Applied rewrites 17.2%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in z around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot z}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 76.7

         \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot z}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   8. Applied rewrites 76.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot z}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   if -1.70000000000000006e75 < z < 1.16000000000000001e33

   1. Initial program 59.5%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right)} + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. lift-pow.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{\color{blue}{\left(x \cdot 30\right)}}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow-prod-down N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{x}^{2} \cdot {30}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left({x}^{2}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, \color{blue}{900}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      11. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{\left(y \cdot 30\right)}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {\color{blue}{\left(y \cdot 30\right)}}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      13. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{y}^{2} \cdot {30}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      14. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{\left(z \cdot 30\right)}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + {\color{blue}{\left(z \cdot 30\right)}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      16. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{z}^{2} \cdot {30}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      17. distribute-rgt-out N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{900} \cdot \left({y}^{2} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      20. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \left(\color{blue}{y \cdot y} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      21. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \color{blue}{\mathsf{fma}\left(y, y, {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      22. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      23. lower-*.f64 59.4

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   4. Applied rewrites 59.4%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right) + \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot y\right) \cdot \cos \left(30 \cdot z\right)} + \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - \frac{1}{5}\right) \]

      4. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\color{blue}{\sin \left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \color{blue}{\left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      6. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(\color{blue}{-30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(-30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      11. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \color{blue}{\sin \left(30 \cdot z\right)}\right)\right| - \frac{1}{5}\right) \]

      12. lower-*.f64 58.8

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \color{blue}{\left(30 \cdot z\right)}\right)\right| - 0.2\right) \]

   7. Applied rewrites 58.8%

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.7%

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]

   if 1.16000000000000001e33 < z

   1. Initial program 28.5%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right) + \sin \left(30 \cdot x\right)}\right| - \frac{1}{5}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - \frac{1}{5}\right) \]

      3. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(\color{blue}{-30} \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(-30 \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \color{blue}{\sin \left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \color{blue}{\left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \color{blue}{\sin \left(30 \cdot x\right)}\right)\right| - \frac{1}{5}\right) \]

      11. lower-*.f64 28.5

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \color{blue}{\left(30 \cdot x\right)}\right)\right| - 0.2\right) \]

   5. Applied rewrites 28.5%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{30 \cdot z}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 62.6

         \[\leadsto \mathsf{max}\left(\color{blue}{30 \cdot z}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   8. Applied rewrites 62.6%

      \[\leadsto \mathsf{max}\left(\color{blue}{30 \cdot z}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 50.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), t\_0\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z))))
   (if (<= y -1.02e+85)
     (fmax
      (* -30.0 y)
      (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2))
     (fmax
      (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
      (- (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) t_0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double tmp;
	if (y <= -1.02e+85) {
		tmp = fmax((-30.0 * y), (fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	tmp = 0.0
	if (y <= -1.02e+85)
		tmp = fmax(Float64(-30.0 * y), Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), t_0)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -1.02e+85], N[Max[N[(-30.0 * y), $MachinePrecision], N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e85

   1. Initial program 30.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right) + \sin \left(30 \cdot x\right)}\right| - \frac{1}{5}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - \frac{1}{5}\right) \]

      3. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(\color{blue}{-30} \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(-30 \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \color{blue}{\sin \left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \color{blue}{\left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \color{blue}{\sin \left(30 \cdot x\right)}\right)\right| - \frac{1}{5}\right) \]

      11. lower-*.f64 30.7

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \color{blue}{\left(30 \cdot x\right)}\right)\right| - 0.2\right) \]

   5. Applied rewrites 30.7%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in y around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot y}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 72.9

         \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot y}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   8. Applied rewrites 72.9%

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot y}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   if -1.02e85 < y

   1. Initial program 52.4%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. 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. lift-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right)} + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. lift-pow.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{\color{blue}{\left(x \cdot 30\right)}}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow-prod-down N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{x}^{2} \cdot {30}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left({x}^{2}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, \color{blue}{900}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      11. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{\left(y \cdot 30\right)}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {\color{blue}{\left(y \cdot 30\right)}}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      13. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{y}^{2} \cdot {30}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      14. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{\left(z \cdot 30\right)}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + {\color{blue}{\left(z \cdot 30\right)}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      16. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{z}^{2} \cdot {30}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      17. distribute-rgt-out N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{900} \cdot \left({y}^{2} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      20. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \left(\color{blue}{y \cdot y} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      21. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \color{blue}{\mathsf{fma}\left(y, y, {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      22. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      23. lower-*.f64 52.4

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   4. Applied rewrites 52.4%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right) + \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot y\right) \cdot \cos \left(30 \cdot z\right)} + \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - \frac{1}{5}\right) \]

      4. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\color{blue}{\sin \left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \color{blue}{\left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      6. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(\color{blue}{-30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(-30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      11. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \color{blue}{\sin \left(30 \cdot z\right)}\right)\right| - \frac{1}{5}\right) \]

      12. lower-*.f64 51.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \color{blue}{\left(30 \cdot z\right)}\right)\right| - 0.2\right) \]

   7. Applied rewrites 51.9%

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 47.0%

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 49.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), t\_0\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z))))
   (if (<= x -4.6e+147)
     (fmax
      (* -30.0 x)
      (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2))
     (fmax
      (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
      (- (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) t_0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double tmp;
	if (x <= -4.6e+147) {
		tmp = fmax((-30.0 * x), (fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	tmp = 0.0
	if (x <= -4.6e+147)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), t_0)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -4.6e+147], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999998e147

   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. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right) + \sin \left(30 \cdot x\right)}\right| - \frac{1}{5}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - \frac{1}{5}\right) \]

      3. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot x\right)\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(\color{blue}{-30} \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \color{blue}{\left(-30 \cdot x\right)}, \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \color{blue}{\sin \left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \color{blue}{\left(30 \cdot z\right)}, \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \color{blue}{\sin \left(30 \cdot x\right)}\right)\right| - \frac{1}{5}\right) \]

      11. lower-*.f64 13.2

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \color{blue}{\left(30 \cdot x\right)}\right)\right| - 0.2\right) \]

   5. Applied rewrites 13.2%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)}\right| - 0.2\right) \]

   6. Taylor expanded in x around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - \frac{1}{5}\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 77.8

         \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   8. Applied rewrites 77.8%

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(30 \cdot z\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]

   if -4.5999999999999998e147 < x

   1. Initial program 53.1%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   2. Add Preprocessing
   3. 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. lift-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right)} + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      4. lift-pow.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{\color{blue}{\left(x \cdot 30\right)}}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      6. unpow-prod-down N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{x}^{2} \cdot {30}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left({x}^{2}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, \color{blue}{900}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      11. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{\left(y \cdot 30\right)}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {\color{blue}{\left(y \cdot 30\right)}}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      13. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{y}^{2} \cdot {30}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      14. lift-pow.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{\left(z \cdot 30\right)}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      15. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + {\color{blue}{\left(z \cdot 30\right)}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      16. unpow-prod-down N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{z}^{2} \cdot {30}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      17. distribute-rgt-out N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{900} \cdot \left({y}^{2} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      20. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \left(\color{blue}{y \cdot y} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      21. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \color{blue}{\mathsf{fma}\left(y, y, {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      22. unpow2 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

      23. lower-*.f64 53.0

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   4. Applied rewrites 53.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right) + \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot y\right) \cdot \cos \left(30 \cdot z\right)} + \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - \frac{1}{5}\right) \]

      4. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\color{blue}{\sin \left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \color{blue}{\left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      6. cos-neg-rev N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(\color{blue}{-30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(-30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      11. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \color{blue}{\sin \left(30 \cdot z\right)}\right)\right| - \frac{1}{5}\right) \]

      12. lower-*.f64 52.6

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \color{blue}{\left(30 \cdot z\right)}\right)\right| - 0.2\right) \]

   7. Applied rewrites 52.6%

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 47.2%

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 41.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, -450, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (sqrt (fma (* x x) 900.0 (* 900.0 (fma y y (* z z))))) 25.0)
  (-
   (fabs (fma (sin (* 30.0 y)) (fma (* z z) -450.0 1.0) (sin (* 30.0 z))))
   0.2)))

C

double code(double x, double y, double z) {
	return fmax((sqrt(fma((x * x), 900.0, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(fma(sin((30.0 * y)), fma((z * z), -450.0, 1.0), sin((30.0 * z)))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(Float64(sqrt(fma(Float64(x * x), 900.0, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(fma(sin(Float64(30.0 * y)), fma(Float64(z * z), -450.0, 1.0), sin(Float64(30.0 * z)))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * N[(N[(z * z), $MachinePrecision] * -450.0 + 1.0), $MachinePrecision] + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 48.4%

   \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. 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. lift-+.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right)} + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   3. associate-+l+ N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   4. lift-pow.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{\left(x \cdot 30\right)}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{{\color{blue}{\left(x \cdot 30\right)}}^{2} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   6. unpow-prod-down N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{{x}^{2} \cdot {30}^{2}} + \left({\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   7. lower-fma.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left({x}^{2}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   8. unpow2 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(\color{blue}{x \cdot x}, {30}^{2}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, \color{blue}{900}, {\left(y \cdot 30\right)}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   11. lift-pow.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{\left(y \cdot 30\right)}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   12. lift-*.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {\color{blue}{\left(y \cdot 30\right)}}^{2} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   13. unpow-prod-down N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{y}^{2} \cdot {30}^{2}} + {\left(z \cdot 30\right)}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   14. lift-pow.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{\left(z \cdot 30\right)}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   15. lift-*.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + {\color{blue}{\left(z \cdot 30\right)}}^{2}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   16. unpow-prod-down N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, {y}^{2} \cdot {30}^{2} + \color{blue}{{z}^{2} \cdot {30}^{2}}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   17. distribute-rgt-out N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   18. lower-*.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{{30}^{2} \cdot \left({y}^{2} + {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   19. metadata-eval N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \color{blue}{900} \cdot \left({y}^{2} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   20. unpow2 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \left(\color{blue}{y \cdot y} + {z}^{2}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   21. lower-fma.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \color{blue}{\mathsf{fma}\left(y, y, {z}^{2}\right)}\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   22. unpow2 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]

   23. lower-*.f64 48.4

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, \color{blue}{z \cdot z}\right)\right)} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

4. Applied rewrites 48.4%

   \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]
6. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right) + \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\sin \left(30 \cdot y\right) \cdot \cos \left(30 \cdot z\right)} + \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   3. lower-fma.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - \frac{1}{5}\right) \]

   4. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\color{blue}{\sin \left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \color{blue}{\left(30 \cdot y\right)}, \cos \left(30 \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

   6. cos-neg-rev N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

   7. lower-cos.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(\mathsf{neg}\left(30 \cdot z\right)\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

   8. distribute-lft-neg-in N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(\left(\mathsf{neg}\left(30\right)\right) \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(\color{blue}{-30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

   10. lower-*.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \color{blue}{\left(-30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

   11. lower-sin.f64 N/A

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \color{blue}{\sin \left(30 \cdot z\right)}\right)\right| - \frac{1}{5}\right) \]

   12. lower-*.f64 48.0

       \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \color{blue}{\left(30 \cdot z\right)}\right)\right| - 0.2\right) \]

7. Applied rewrites 48.0%

   \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot y\right), \cos \left(-30 \cdot z\right), \sin \left(30 \cdot z\right)\right)}\right| - 0.2\right) \]

8. Taylor expanded in z around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1 + \color{blue}{-450 \cdot {z}^{2}}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]
9. Step-by-step derivation

10. Applied rewrites 43.2%

    \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \mathsf{fma}\left(z \cdot z, \color{blue}{-450}, 1\right), \sin \left(30 \cdot z\right)\right)\right| - 0.2\right) \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025015 
(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)))