Gyroid sphere

Percentage Accurate: 46.9% → 72.0%

Time: 4.3s

Alternatives: 10

Speedup: 6.0×

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: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot y\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(900 \cdot x, x, \mathsf{fma}\left(900 \cdot y, y, 900 \cdot \left(z \cdot z\right)\right)\right)} - 25, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot t\_0\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|t\_0 + z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 y))))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            (* (sin (* z 30.0)) (cos (* x 30.0)))))
          0.2))
        5e+151)
     (fmax
      (- (sqrt (fma (* 900.0 x) x (fma (* 900.0 y) y (* 900.0 (* z z))))) 25.0)
      (- (fabs (+ (sin (* 30.0 z)) (* (cos (* 30.0 z)) t_0))) 0.2))
     (fmax
      (* y (- 30.0 (* 25.0 (/ 1.0 y))))
      (- (fabs (+ t_0 (* z 30.0))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * y));
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2)) <= 5e+151) {
		tmp = fmax((sqrt(fma((900.0 * x), x, fma((900.0 * y), y, (900.0 * (z * z))))) - 25.0), (fabs((sin((30.0 * z)) + (cos((30.0 * z)) * t_0))) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs((t_0 + (z * 30.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * y))
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2)) <= 5e+151)
		tmp = fmax(Float64(sqrt(fma(Float64(900.0 * x), x, fma(Float64(900.0 * y), y, Float64(900.0 * Float64(z * z))))) - 25.0), Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(cos(Float64(30.0 * z)) * t_0))) - 0.2));
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(t_0 + Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 5e+151], N[Max[N[(N[Sqrt[N[(N[(900.0 * x), $MachinePrecision] * x + N[(N[(900.0 * y), $MachinePrecision] * y + N[(900.0 * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 5.0000000000000002e151

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   if 5.0000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.3%

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

Alternative 2: 70.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot y\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(y \cdot y, 900, 900 \cdot \mathsf{fma}\left(z, z, x \cdot x\right)\right)} - 25, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot t\_0\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|t\_0 + z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 y))))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            (* (sin (* z 30.0)) (cos (* x 30.0)))))
          0.2))
        5e+151)
     (fmax
      (- (sqrt (fma (* y y) 900.0 (* 900.0 (fma z z (* x x))))) 25.0)
      (- (fabs (+ (sin (* 30.0 z)) (* (cos (* 30.0 z)) t_0))) 0.2))
     (fmax
      (* y (- 30.0 (* 25.0 (/ 1.0 y))))
      (- (fabs (+ t_0 (* z 30.0))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * y));
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2)) <= 5e+151) {
		tmp = fmax((sqrt(fma((y * y), 900.0, (900.0 * fma(z, z, (x * x))))) - 25.0), (fabs((sin((30.0 * z)) + (cos((30.0 * z)) * t_0))) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs((t_0 + (z * 30.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * y))
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2)) <= 5e+151)
		tmp = fmax(Float64(sqrt(fma(Float64(y * y), 900.0, Float64(900.0 * fma(z, z, Float64(x * x))))) - 25.0), Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(cos(Float64(30.0 * z)) * t_0))) - 0.2));
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(t_0 + Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 5e+151], N[Max[N[(N[Sqrt[N[(N[(y * y), $MachinePrecision] * 900.0 + N[(900.0 * N[(z * z + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 5.0000000000000002e151

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. lift-*.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift-pow.f64 N/A

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

      12. unpow2 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. swap-sqr N/A

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

      16. lift-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. associate-+l+ N/A

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

      19. +-commutative N/A

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

      20. associate-+l+ N/A

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

   6. Applied rewrites 46.5%

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

   if 5.0000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.3%

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

Alternative 3: 70.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \sin \left(y \cdot 30\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + t\_1 \cdot \cos \left(z \cdot 30\right)\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot z\right), t\_1, t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))) (t_1 (sin (* y 30.0))))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (+ (* (sin (* x 30.0)) (cos (* y 30.0))) (* t_1 (cos (* z 30.0))))
            (* t_0 (cos (* x 30.0)))))
          0.2))
        5e+151)
     (fmax
      (- (sqrt (* 900.0 (fma z z (fma y y (* x x))))) 25.0)
      (- (fabs (fma (cos (* -30.0 z)) t_1 t_0)) 0.2))
     (fmax
      (* y (- 30.0 (* 25.0 (/ 1.0 y))))
      (- (fabs (+ (sin (* 30.0 y)) (* z 30.0))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = sin((y * 30.0));
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (t_1 * cos((z * 30.0)))) + (t_0 * cos((x * 30.0))))) - 0.2)) <= 5e+151) {
		tmp = fmax((sqrt((900.0 * fma(z, z, fma(y, y, (x * x))))) - 25.0), (fabs(fma(cos((-30.0 * z)), t_1, t_0)) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs((sin((30.0 * y)) + (z * 30.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = sin(Float64(y * 30.0))
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(t_1 * cos(Float64(z * 30.0)))) + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2)) <= 5e+151)
		tmp = fmax(Float64(sqrt(Float64(900.0 * fma(z, z, fma(y, y, Float64(x * x))))) - 25.0), Float64(abs(fma(cos(Float64(-30.0 * z)), t_1, t_0)) - 0.2));
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(sin(Float64(30.0 * y)) + Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 5e+151], N[Max[N[(N[Sqrt[N[(900.0 * N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * t$95$1 + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 5.0000000000000002e151

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   6. Applied rewrites 46.5%

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

   if 5.0000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.3%

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

Alternative 4: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(900 \cdot x, x, \mathsf{fma}\left(900 \cdot y, y, 900 \cdot \left(z \cdot z\right)\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (fmax
       (-
        (sqrt
         (+
          (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
          (pow (* z 30.0) 2.0)))
        25.0)
       (-
        (fabs
         (+
          (+
           (* (sin (* x 30.0)) (cos (* y 30.0)))
           (* (sin (* y 30.0)) (cos (* z 30.0))))
          (* (sin (* z 30.0)) (cos (* x 30.0)))))
        0.2))
      5e+151)
   (fmax
    (- (sqrt (fma (* 900.0 x) x (fma (* 900.0 y) y (* 900.0 (* z z))))) 25.0)
    (- (fabs (sin (* 30.0 z))) 0.2))
   (fmax
    (* y (- 30.0 (* 25.0 (/ 1.0 y))))
    (- (fabs (+ (sin (* 30.0 y)) (* z 30.0))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2)) <= 5e+151) {
		tmp = fmax((sqrt(fma((900.0 * x), x, fma((900.0 * y), y, (900.0 * (z * z))))) - 25.0), (fabs(sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs((sin((30.0 * y)) + (z * 30.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2)) <= 5e+151)
		tmp = fmax(Float64(sqrt(fma(Float64(900.0 * x), x, fma(Float64(900.0 * y), y, Float64(900.0 * Float64(z * z))))) - 25.0), Float64(abs(sin(Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(sin(Float64(30.0 * y)) + Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 5e+151], N[Max[N[(N[Sqrt[N[(N[(900.0 * x), $MachinePrecision] * x + N[(N[(900.0 * y), $MachinePrecision] * y + N[(900.0 * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 5.0000000000000002e151

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   if 5.0000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.3%

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

Alternative 5: 70.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot 900, x, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (fmax
       (-
        (sqrt
         (+
          (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
          (pow (* z 30.0) 2.0)))
        25.0)
       (-
        (fabs
         (+
          (+
           (* (sin (* x 30.0)) (cos (* y 30.0)))
           (* (sin (* y 30.0)) (cos (* z 30.0))))
          (* (sin (* z 30.0)) (cos (* x 30.0)))))
        0.2))
      5e+151)
   (fmax
    (- (sqrt (fma (* x 900.0) x (* 900.0 (fma y y (* z z))))) 25.0)
    (- (fabs (sin (* 30.0 z))) 0.2))
   (fmax
    (* y (- 30.0 (* 25.0 (/ 1.0 y))))
    (- (fabs (+ (sin (* 30.0 y)) (* z 30.0))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2)) <= 5e+151) {
		tmp = fmax((sqrt(fma((x * 900.0), x, (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs(sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs((sin((30.0 * y)) + (z * 30.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2)) <= 5e+151)
		tmp = fmax(Float64(sqrt(fma(Float64(x * 900.0), x, Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(sin(Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(sin(Float64(30.0 * y)) + Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 5e+151], N[Max[N[(N[Sqrt[N[(N[(x * 900.0), $MachinePrecision] * x + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 5.0000000000000002e151

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 46.2

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

       4. lift-fma.f64 N/A

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

       5. lift-*.f64 N/A

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

       6. lift-*.f64 N/A

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

       7. associate-*l* N/A

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

       8. unpow2 N/A

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

       9. lift-pow.f64 N/A

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

       10. distribute-lft-out N/A

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

       11. lower-*.f64 N/A

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

       12. lift-pow.f64 N/A

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

       13. unpow2 N/A

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

       14. lower-fma.f64 46.2

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

   11. Applied rewrites 46.2%

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

   if 5.0000000000000002e151 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.3%

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

Alternative 6: 70.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.44 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_0\right)\\ \mathbf{elif}\;x \leq 28500:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)))
   (if (<= x -1.44e+76)
     (fmax (* -30.0 x) t_0)
     (if (<= x 28500.0)
       (fmax
        (* y (- 30.0 (* 25.0 (/ 1.0 y))))
        (- (fabs (+ (sin (* 30.0 y)) (* z 30.0))) 0.2))
       (fmax (* x (- 30.0 (* 25.0 (/ 1.0 x)))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * z))) - 0.2;
	double tmp;
	if (x <= -1.44e+76) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (x <= 28500.0) {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs((sin((30.0 * y)) + (z * 30.0))) - 0.2));
	} else {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((30.0d0 * z))) - 0.2d0
    if (x <= (-1.44d+76)) then
        tmp = fmax(((-30.0d0) * x), t_0)
    else if (x <= 28500.0d0) then
        tmp = fmax((y * (30.0d0 - (25.0d0 * (1.0d0 / y)))), (abs((sin((30.0d0 * y)) + (z * 30.0d0))) - 0.2d0))
    else
        tmp = fmax((x * (30.0d0 - (25.0d0 * (1.0d0 / x)))), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * z))) - 0.2;
	double tmp;
	if (x <= -1.44e+76) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (x <= 28500.0) {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (Math.abs((Math.sin((30.0 * y)) + (z * 30.0))) - 0.2));
	} else {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * z))) - 0.2
	tmp = 0
	if x <= -1.44e+76:
		tmp = fmax((-30.0 * x), t_0)
	elif x <= 28500.0:
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (math.fabs((math.sin((30.0 * y)) + (z * 30.0))) - 0.2))
	else:
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * z))) - 0.2)
	tmp = 0.0
	if (x <= -1.44e+76)
		tmp = fmax(Float64(-30.0 * x), t_0);
	elseif (x <= 28500.0)
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(sin(Float64(30.0 * y)) + Float64(z * 30.0))) - 0.2));
	else
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * z))) - 0.2;
	tmp = 0.0;
	if (x <= -1.44e+76)
		tmp = max((-30.0 * x), t_0);
	elseif (x <= 28500.0)
		tmp = max((y * (30.0 - (25.0 * (1.0 / y)))), (abs((sin((30.0 * y)) + (z * 30.0))) - 0.2));
	else
		tmp = max((x * (30.0 - (25.0 * (1.0 / x)))), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.44e+76], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 28500.0], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44e76

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around -inf

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

       1. lower-*.f64 17.2

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

   12. Applied rewrites 17.2%

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

   if -1.44e76 < x < 28500

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 56.3%

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

   if 28500 < x

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower--.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-/.f64 29.7

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

   12. Applied rewrites 29.7%

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

Alternative 7: 62.1% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ \mathbf{if}\;x \leq -5.7 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_0\right)\\ \mathbf{elif}\;x \leq 33000000000:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)))
   (if (<= x -5.7e+75)
     (fmax (* -30.0 x) t_0)
     (if (<= x 33000000000.0)
       (fmax
        (* y (- 30.0 (* 25.0 (/ 1.0 y))))
        (-
         (fabs (+ (* 30.0 y) (* z (+ 30.0 (* -450.0 (* z (* 30.0 y)))))))
         0.2))
       (fmax (* x (- 30.0 (* 25.0 (/ 1.0 x)))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * z))) - 0.2;
	double tmp;
	if (x <= -5.7e+75) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (x <= 33000000000.0) {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	} else {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((30.0d0 * z))) - 0.2d0
    if (x <= (-5.7d+75)) then
        tmp = fmax(((-30.0d0) * x), t_0)
    else if (x <= 33000000000.0d0) then
        tmp = fmax((y * (30.0d0 - (25.0d0 * (1.0d0 / y)))), (abs(((30.0d0 * y) + (z * (30.0d0 + ((-450.0d0) * (z * (30.0d0 * y))))))) - 0.2d0))
    else
        tmp = fmax((x * (30.0d0 - (25.0d0 * (1.0d0 / x)))), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * z))) - 0.2;
	double tmp;
	if (x <= -5.7e+75) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (x <= 33000000000.0) {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (Math.abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	} else {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * z))) - 0.2
	tmp = 0
	if x <= -5.7e+75:
		tmp = fmax((-30.0 * x), t_0)
	elif x <= 33000000000.0:
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (math.fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2))
	else:
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * z))) - 0.2)
	tmp = 0.0
	if (x <= -5.7e+75)
		tmp = fmax(Float64(-30.0 * x), t_0);
	elseif (x <= 33000000000.0)
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(Float64(30.0 * y) + Float64(z * Float64(30.0 + Float64(-450.0 * Float64(z * Float64(30.0 * y))))))) - 0.2));
	else
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * z))) - 0.2;
	tmp = 0.0;
	if (x <= -5.7e+75)
		tmp = max((-30.0 * x), t_0);
	elseif (x <= 33000000000.0)
		tmp = max((y * (30.0 - (25.0 * (1.0 / y)))), (abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	else
		tmp = max((x * (30.0 - (25.0 * (1.0 / x)))), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -5.7e+75], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 33000000000.0], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * y), $MachinePrecision] + N[(z * N[(30.0 + N[(-450.0 * N[(z * N[(30.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7000000000000004e75

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around -inf

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

       1. lower-*.f64 17.2

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

   12. Applied rewrites 17.2%

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

   if -5.7000000000000004e75 < x < 3.3e10

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

       1. lower-*.f64 46.3

          \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   13. Applied rewrites 46.3%

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

   14. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]
   15. Step-by-step derivation

       1. lower-*.f64 41.5

          \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   16. Applied rewrites 41.5%

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   if 3.3e10 < x

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower--.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-/.f64 29.7

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

   12. Applied rewrites 29.7%

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

Alternative 8: 62.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ \mathbf{if}\;x \leq -5.7 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, t\_0\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)))
   (if (<= x -5.7e+75)
     (fmax (* -30.0 x) t_0)
     (if (<= x 4.4e+21)
       (fmax
        (* y (- 30.0 (* 25.0 (/ 1.0 y))))
        (-
         (fabs (+ (* 30.0 y) (* z (+ 30.0 (* -450.0 (* z (* 30.0 y)))))))
         0.2))
       (fmax (* 30.0 x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * z))) - 0.2;
	double tmp;
	if (x <= -5.7e+75) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (x <= 4.4e+21) {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	} else {
		tmp = fmax((30.0 * x), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((30.0d0 * z))) - 0.2d0
    if (x <= (-5.7d+75)) then
        tmp = fmax(((-30.0d0) * x), t_0)
    else if (x <= 4.4d+21) then
        tmp = fmax((y * (30.0d0 - (25.0d0 * (1.0d0 / y)))), (abs(((30.0d0 * y) + (z * (30.0d0 + ((-450.0d0) * (z * (30.0d0 * y))))))) - 0.2d0))
    else
        tmp = fmax((30.0d0 * x), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * z))) - 0.2;
	double tmp;
	if (x <= -5.7e+75) {
		tmp = fmax((-30.0 * x), t_0);
	} else if (x <= 4.4e+21) {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (Math.abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	} else {
		tmp = fmax((30.0 * x), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * z))) - 0.2
	tmp = 0
	if x <= -5.7e+75:
		tmp = fmax((-30.0 * x), t_0)
	elif x <= 4.4e+21:
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (math.fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2))
	else:
		tmp = fmax((30.0 * x), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * z))) - 0.2)
	tmp = 0.0
	if (x <= -5.7e+75)
		tmp = fmax(Float64(-30.0 * x), t_0);
	elseif (x <= 4.4e+21)
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(Float64(30.0 * y) + Float64(z * Float64(30.0 + Float64(-450.0 * Float64(z * Float64(30.0 * y))))))) - 0.2));
	else
		tmp = fmax(Float64(30.0 * x), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * z))) - 0.2;
	tmp = 0.0;
	if (x <= -5.7e+75)
		tmp = max((-30.0 * x), t_0);
	elseif (x <= 4.4e+21)
		tmp = max((y * (30.0 - (25.0 * (1.0 / y)))), (abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	else
		tmp = max((30.0 * x), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -5.7e+75], N[Max[N[(-30.0 * x), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 4.4e+21], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * y), $MachinePrecision] + N[(z * N[(30.0 + N[(-450.0 * N[(z * N[(30.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * x), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7000000000000004e75

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around -inf

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

       1. lower-*.f64 17.2

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

   12. Applied rewrites 17.2%

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

   if -5.7000000000000004e75 < x < 4.4e21

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

       1. lower-*.f64 46.3

          \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   13. Applied rewrites 46.3%

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

   14. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]
   15. Step-by-step derivation

       1. lower-*.f64 41.5

          \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   16. Applied rewrites 41.5%

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   if 4.4e21 < x

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around inf

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

       1. lower-*.f64 18.3

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

   12. Applied rewrites 18.3%

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

Alternative 9: 51.4% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.7e+75)
   (fmax (* -30.0 x) (- (fabs (sin (* 30.0 z))) 0.2))
   (fmax
    (* y (- 30.0 (* 25.0 (/ 1.0 y))))
    (- (fabs (+ (* 30.0 y) (* z (+ 30.0 (* -450.0 (* z (* 30.0 y))))))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.7e+75) {
		tmp = fmax((-30.0 * x), (fabs(sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.7d+75)) then
        tmp = fmax(((-30.0d0) * x), (abs(sin((30.0d0 * z))) - 0.2d0))
    else
        tmp = fmax((y * (30.0d0 - (25.0d0 * (1.0d0 / y)))), (abs(((30.0d0 * y) + (z * (30.0d0 + ((-450.0d0) * (z * (30.0d0 * y))))))) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.7e+75) {
		tmp = fmax((-30.0 * x), (Math.abs(Math.sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (Math.abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.7e+75:
		tmp = fmax((-30.0 * x), (math.fabs(math.sin((30.0 * z))) - 0.2))
	else:
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (math.fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.7e+75)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(sin(Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(Float64(30.0 * y) + Float64(z * Float64(30.0 + Float64(-450.0 * Float64(z * Float64(30.0 * y))))))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.7e+75)
		tmp = max((-30.0 * x), (abs(sin((30.0 * z))) - 0.2));
	else
		tmp = max((y * (30.0 - (25.0 * (1.0 / y)))), (abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.7e+75], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * y), $MachinePrecision] + N[(z * N[(30.0 + N[(-450.0 * N[(z * N[(30.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7000000000000004e75

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. swap-sqr N/A

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-pow.f64 N/A

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

      16. unpow2 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. swap-sqr N/A

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

      20. metadata-eval N/A

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

      21. associate-*l* N/A

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

      22. *-commutative N/A

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

      23. lift-pow.f64 N/A

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

      24. unpow2 N/A

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

      25. lift-*.f64 N/A

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

      26. lift-*.f64 N/A

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

      27. swap-sqr N/A

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.2

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

   9. Applied rewrites 46.2%

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

   10. Taylor expanded in x around -inf

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

       1. lower-*.f64 17.2

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

   12. Applied rewrites 17.2%

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

   if -5.7000000000000004e75 < x

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.7

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   7. Applied rewrites 29.7%

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      8. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

      9. lower-*.f64 35.6

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 35.6%

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

   11. Taylor expanded in y around 0

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

       1. lower-*.f64 46.3

          \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   13. Applied rewrites 46.3%

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

   14. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]
   15. Step-by-step derivation

       1. lower-*.f64 41.5

          \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

   16. Applied rewrites 41.5%

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 41.5% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (* y (- 30.0 (* 25.0 (/ 1.0 y))))
  (- (fabs (+ (* 30.0 y) (* z (+ 30.0 (* -450.0 (* z (* 30.0 y))))))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = fmax((y * (30.0d0 - (25.0d0 * (1.0d0 / y)))), (abs(((30.0d0 * y) + (z * (30.0d0 + ((-450.0d0) * (z * (30.0d0 * y))))))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax((y * (30.0 - (25.0 * (1.0 / y)))), (Math.abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
}

Python

def code(x, y, z):
	return fmax((y * (30.0 - (25.0 * (1.0 / y)))), (math.fabs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(Float64(Float64(30.0 * y) + Float64(z * Float64(30.0 + Float64(-450.0 * Float64(z * Float64(30.0 * y))))))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max((y * (30.0 - (25.0 * (1.0 / y)))), (abs(((30.0 * y) + (z * (30.0 + (-450.0 * (z * (30.0 * y))))))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * y), $MachinePrecision] + N[(z * N[(30.0 + N[(-450.0 * N[(z * N[(30.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 46.9%

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

2. Taylor expanded in x around 0

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

   1. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-cos.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-sin.f64 N/A

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

   8. lower-*.f64 46.6

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

4. Applied rewrites 46.6%

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

5. Taylor expanded in y around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 29.7

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

7. Applied rewrites 29.7%

   \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)\right| - 0.2\right) \]

8. Taylor expanded in z around 0

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

   1. lower-+.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \color{blue}{\left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)}\right| - \frac{1}{5}\right) \]

   2. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(\color{blue}{30} + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + \color{blue}{-450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

   5. lower-+.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \color{blue}{\left(z \cdot \sin \left(30 \cdot y\right)\right)}\right)\right| - \frac{1}{5}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \color{blue}{\sin \left(30 \cdot y\right)}\right)\right)\right| - \frac{1}{5}\right) \]

   7. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

   8. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]

   9. lower-*.f64 35.6

      \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\sin \left(30 \cdot y\right) + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

10. Applied rewrites 35.6%

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

11. Taylor expanded in y around 0

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

    1. lower-*.f64 46.3

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \sin \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

13. Applied rewrites 46.3%

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

14. Taylor expanded in y around 0

    \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - \frac{1}{5}\right) \]
15. Step-by-step derivation

    1. lower-*.f64 41.5

       \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]

16. Applied rewrites 41.5%

    \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|30 \cdot y + z \cdot \left(30 + -450 \cdot \left(z \cdot \left(30 \cdot y\right)\right)\right)\right| - 0.2\right) \]
17. Add Preprocessing

Reproduce

herbie shell --seed 2025154 
(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)))