Gyroid sphere

Percentage Accurate: 46.7% → 88.7%

Time: 6.2s

Alternatives: 18

Speedup: 4.8×

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: 46.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := t\_0 \cdot \cos \left(x \cdot 30\right)\\ t_2 := \sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25\\ t_3 := \sin \left(y \cdot 30\right)\\ t_4 := \mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \mathsf{fma}\left(\cos \left(-30 \cdot z\right), t\_3, \cos \left(-30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right)\\ t_5 := \left|t\_4\right|\\ \mathbf{if}\;\mathsf{max}\left(t\_2, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + t\_3 \cdot \cos \left(z \cdot 30\right)\right) + t\_1\right| - 0.2\right) \leq 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(t\_2, \frac{{t\_5}^{3} + {-0.2}^{3}}{{t\_4}^{2} + \left(-0.2 \cdot -0.2 - t\_5 \cdot -0.2\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, \left|\mathsf{fma}\left(30, x, 30 \cdot y\right) + t\_1\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1 (* t_0 (cos (* x 30.0))))
        (t_2
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0))
        (t_3 (sin (* y 30.0)))
        (t_4
         (fma
          (cos (* -30.0 x))
          t_0
          (fma (cos (* -30.0 z)) t_3 (* (cos (* -30.0 y)) (sin (* 30.0 x))))))
        (t_5 (fabs t_4)))
   (if (<=
        (fmax
         t_2
         (-
          (fabs
           (+
            (+ (* (sin (* x 30.0)) (cos (* y 30.0))) (* t_3 (cos (* z 30.0))))
            t_1))
          0.2))
        1e+151)
     (fmax
      t_2
      (/
       (+ (pow t_5 3.0) (pow -0.2 3.0))
       (+ (pow t_4 2.0) (- (* -0.2 -0.2) (* t_5 -0.2)))))
     (fmax (* -30.0 z) (- (fabs (+ (fma 30.0 x (* 30.0 y)) t_1)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = t_0 * cos((x * 30.0));
	double t_2 = sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0;
	double t_3 = sin((y * 30.0));
	double t_4 = fma(cos((-30.0 * x)), t_0, fma(cos((-30.0 * z)), t_3, (cos((-30.0 * y)) * sin((30.0 * x)))));
	double t_5 = fabs(t_4);
	double tmp;
	if (fmax(t_2, (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (t_3 * cos((z * 30.0)))) + t_1)) - 0.2)) <= 1e+151) {
		tmp = fmax(t_2, ((pow(t_5, 3.0) + pow(-0.2, 3.0)) / (pow(t_4, 2.0) + ((-0.2 * -0.2) - (t_5 * -0.2)))));
	} else {
		tmp = fmax((-30.0 * z), (fabs((fma(30.0, x, (30.0 * y)) + t_1)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = Float64(t_0 * cos(Float64(x * 30.0)))
	t_2 = Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0)
	t_3 = sin(Float64(y * 30.0))
	t_4 = fma(cos(Float64(-30.0 * x)), t_0, fma(cos(Float64(-30.0 * z)), t_3, Float64(cos(Float64(-30.0 * y)) * sin(Float64(30.0 * x)))))
	t_5 = abs(t_4)
	tmp = 0.0
	if (fmax(t_2, Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(t_3 * cos(Float64(z * 30.0)))) + t_1)) - 0.2)) <= 1e+151)
		tmp = fmax(t_2, Float64(Float64((t_5 ^ 3.0) + (-0.2 ^ 3.0)) / Float64((t_4 ^ 2.0) + Float64(Float64(-0.2 * -0.2) - Float64(t_5 * -0.2)))));
	else
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + t_1)) - 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[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * t$95$3 + N[(N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Abs[t$95$4], $MachinePrecision]}, If[LessEqual[N[Max[t$95$2, 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$3 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 1e+151], N[Max[t$95$2, N[(N[(N[Power[t$95$5, 3.0], $MachinePrecision] + N[Power[-0.2, 3.0], $MachinePrecision]), $MachinePrecision] / N[(N[Power[t$95$4, 2.0], $MachinePrecision] + N[(N[(-0.2 * -0.2), $MachinePrecision] - N[(t$95$5 * -0.2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * z), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

   3. Applied rewrites 46.7%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \color{blue}{\frac{{\left(\left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \mathsf{fma}\left(\cos \left(-30 \cdot z\right), \sin \left(y \cdot 30\right), \cos \left(-30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right)\right|\right)}^{3} + {-0.2}^{3}}{{\left(\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \mathsf{fma}\left(\cos \left(-30 \cdot z\right), \sin \left(y \cdot 30\right), \cos \left(-30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right)\right)}^{2} + \left(-0.2 \cdot -0.2 - \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \mathsf{fma}\left(\cos \left(-30 \cdot z\right), \sin \left(y \cdot 30\right), \cos \left(-30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right)\right| \cdot -0.2\right)}}\right) \]

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

   1. Initial program 46.7%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 18.6

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

   4. Applied rewrites 18.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 37.1

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 63.4

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

   10. Applied rewrites 63.4%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 71.2

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

   13. Applied rewrites 71.2%

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

Alternative 2: 88.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := t\_0 \cdot \cos \left(x \cdot 30\right)\\ t_2 := \sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25\\ t_3 := \sin \left(y \cdot 30\right)\\ t_4 := \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \mathsf{fma}\left(\cos \left(-30 \cdot z\right), t\_3, \cos \left(-30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right)\right|\\ \mathbf{if}\;\mathsf{max}\left(t\_2, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + t\_3 \cdot \cos \left(z \cdot 30\right)\right) + t\_1\right| - 0.2\right) \leq 10^{+151}:\\ \;\;\;\;\mathsf{max}\left(t\_2, \left(1 - \frac{0.2}{t\_4}\right) \cdot t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, \left|\mathsf{fma}\left(30, x, 30 \cdot y\right) + t\_1\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1 (* t_0 (cos (* x 30.0))))
        (t_2
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0))
        (t_3 (sin (* y 30.0)))
        (t_4
         (fabs
          (fma
           (cos (* -30.0 x))
           t_0
           (fma
            (cos (* -30.0 z))
            t_3
            (* (cos (* -30.0 y)) (sin (* 30.0 x))))))))
   (if (<=
        (fmax
         t_2
         (-
          (fabs
           (+
            (+ (* (sin (* x 30.0)) (cos (* y 30.0))) (* t_3 (cos (* z 30.0))))
            t_1))
          0.2))
        1e+151)
     (fmax t_2 (* (- 1.0 (/ 0.2 t_4)) t_4))
     (fmax (* -30.0 z) (- (fabs (+ (fma 30.0 x (* 30.0 y)) t_1)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = t_0 * cos((x * 30.0));
	double t_2 = sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0;
	double t_3 = sin((y * 30.0));
	double t_4 = fabs(fma(cos((-30.0 * x)), t_0, fma(cos((-30.0 * z)), t_3, (cos((-30.0 * y)) * sin((30.0 * x))))));
	double tmp;
	if (fmax(t_2, (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (t_3 * cos((z * 30.0)))) + t_1)) - 0.2)) <= 1e+151) {
		tmp = fmax(t_2, ((1.0 - (0.2 / t_4)) * t_4));
	} else {
		tmp = fmax((-30.0 * z), (fabs((fma(30.0, x, (30.0 * y)) + t_1)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = Float64(t_0 * cos(Float64(x * 30.0)))
	t_2 = Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0)
	t_3 = sin(Float64(y * 30.0))
	t_4 = abs(fma(cos(Float64(-30.0 * x)), t_0, fma(cos(Float64(-30.0 * z)), t_3, Float64(cos(Float64(-30.0 * y)) * sin(Float64(30.0 * x))))))
	tmp = 0.0
	if (fmax(t_2, Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(t_3 * cos(Float64(z * 30.0)))) + t_1)) - 0.2)) <= 1e+151)
		tmp = fmax(t_2, Float64(Float64(1.0 - Float64(0.2 / t_4)) * t_4));
	else
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + t_1)) - 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[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[(N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] * t$95$3 + N[(N[Cos[N[(-30.0 * y), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[t$95$2, 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$3 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 1e+151], N[Max[t$95$2, N[(N[(1.0 - N[(0.2 / t$95$4), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * z), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

      1. lift--.f64 N/A

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

      2. sub-to-mult N/A

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

      3. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 46.7%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \color{blue}{\left(1 - \frac{0.2}{\left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \mathsf{fma}\left(\cos \left(-30 \cdot z\right), \sin \left(y \cdot 30\right), \cos \left(-30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right)\right|}\right) \cdot \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \mathsf{fma}\left(\cos \left(-30 \cdot z\right), \sin \left(y \cdot 30\right), \cos \left(-30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right)\right|}\right) \]

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

   1. Initial program 46.7%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 18.6

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

   4. Applied rewrites 18.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 37.1

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 63.4

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

   10. Applied rewrites 63.4%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 71.2

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

   13. Applied rewrites 71.2%

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

Alternative 3: 88.3% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin (* z 30.0)) (cos (* x 30.0))))
        (t_1
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)))
   (if (<=
        (fmax
         t_1
         (-
          (fabs
           (+
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            t_0))
          0.2))
        1e+151)
     (fmax
      t_1
      (-
       (fabs (+ (sin (* 30.0 x)) (* (cos (* 30.0 x)) (sin (* 30.0 z)))))
       0.2))
     (fmax (* -30.0 z) (- (fabs (+ (fma 30.0 x (* 30.0 y)) t_0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0)) * cos((x * 30.0));
	double t_1 = sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0;
	double tmp;
	if (fmax(t_1, (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + t_0)) - 0.2)) <= 1e+151) {
		tmp = fmax(t_1, (fabs((sin((30.0 * x)) + (cos((30.0 * x)) * sin((30.0 * z))))) - 0.2));
	} else {
		tmp = fmax((-30.0 * z), (fabs((fma(30.0, x, (30.0 * y)) + t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0)))
	t_1 = Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0)
	tmp = 0.0
	if (fmax(t_1, 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)))) + t_0)) - 0.2)) <= 1e+151)
		tmp = fmax(t_1, Float64(abs(Float64(sin(Float64(30.0 * x)) + Float64(cos(Float64(30.0 * x)) * sin(Float64(30.0 * z))))) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + t_0)) - 0.2));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

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

   1. Initial program 46.7%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 18.6

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

   4. Applied rewrites 18.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 37.1

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 63.4

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

   10. Applied rewrites 63.4%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 71.2

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

   13. Applied rewrites 71.2%

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

Alternative 4: 88.3% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))) (t_1 (* t_0 (cos (* x 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)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            t_1))
          0.2))
        1e+151)
     (fmax
      (- (sqrt (fma (* z z) 900.0 (fma (* x x) 900.0 (* (* y y) 900.0)))) 25.0)
      (- (fabs (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x)))) 0.2))
     (fmax (* -30.0 z) (- (fabs (+ (fma 30.0 x (* 30.0 y)) t_1)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = t_0 * cos((x * 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))) + (sin((y * 30.0)) * cos((z * 30.0)))) + t_1)) - 0.2)) <= 1e+151) {
		tmp = fmax((sqrt(fma((z * z), 900.0, fma((x * x), 900.0, ((y * y) * 900.0)))) - 25.0), (fabs(fma(cos((-30.0 * x)), t_0, sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax((-30.0 * z), (fabs((fma(30.0, x, (30.0 * y)) + t_1)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = Float64(t_0 * cos(Float64(x * 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(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + t_1)) - 0.2)) <= 1e+151)
		tmp = fmax(Float64(sqrt(fma(Float64(z * z), 900.0, fma(Float64(x * x), 900.0, Float64(Float64(y * y) * 900.0)))) - 25.0), Float64(abs(fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + t_1)) - 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[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $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] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 1e+151], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0 + N[(N[(x * x), $MachinePrecision] * 900.0 + N[(N[(y * y), $MachinePrecision] * 900.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(-30.0 * z), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   6. Applied rewrites 46.2%

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

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

   1. Initial program 46.7%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 18.6

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

   4. Applied rewrites 18.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 37.1

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 63.4

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

   10. Applied rewrites 63.4%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 71.2

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

   13. Applied rewrites 71.2%

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

Alternative 5: 88.0% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin (* z 30.0)) (cos (* x 30.0))))
        (t_1
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)))
   (if (<=
        (fmax
         t_1
         (-
          (fabs
           (+
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            t_0))
          0.2))
        1e+151)
     (fmax t_1 (- (fabs (sin (* 30.0 z))) 0.2))
     (fmax (* -30.0 z) (- (fabs (+ (fma 30.0 x (* 30.0 y)) t_0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0)) * cos((x * 30.0));
	double t_1 = sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0;
	double tmp;
	if (fmax(t_1, (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + t_0)) - 0.2)) <= 1e+151) {
		tmp = fmax(t_1, (fabs(sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((-30.0 * z), (fabs((fma(30.0, x, (30.0 * y)) + t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0)))
	t_1 = Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0)
	tmp = 0.0
	if (fmax(t_1, 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)))) + t_0)) - 0.2)) <= 1e+151)
		tmp = fmax(t_1, Float64(abs(sin(Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + t_0)) - 0.2));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

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

   1. Initial program 46.7%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 18.6

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

   4. Applied rewrites 18.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 37.1

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 63.4

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

   10. Applied rewrites 63.4%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 71.2

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

   13. Applied rewrites 71.2%

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

Alternative 6: 88.0% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin (* z 30.0)) (cos (* x 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)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            t_0))
          0.2))
        1e+151)
     (fmax
      (-
       (sqrt (fma (* (* y 30.0) 30.0) y (fma (* 900.0 z) z (* (* 900.0 x) x))))
       25.0)
      (- (fabs (sin (* 30.0 z))) 0.2))
     (fmax (* -30.0 z) (- (fabs (+ (fma 30.0 x (* 30.0 y)) t_0)) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0)) * cos((x * 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))) + (sin((y * 30.0)) * cos((z * 30.0)))) + t_0)) - 0.2)) <= 1e+151) {
		tmp = fmax((sqrt(fma(((y * 30.0) * 30.0), y, fma((900.0 * z), z, ((900.0 * x) * x)))) - 25.0), (fabs(sin((30.0 * z))) - 0.2));
	} else {
		tmp = fmax((-30.0 * z), (fabs((fma(30.0, x, (30.0 * y)) + t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 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(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + t_0)) - 0.2)) <= 1e+151)
		tmp = fmax(Float64(sqrt(fma(Float64(Float64(y * 30.0) * 30.0), y, fma(Float64(900.0 * z), z, Float64(Float64(900.0 * x) * x)))) - 25.0), Float64(abs(sin(Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + t_0)) - 0.2));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. swap-sqr N/A

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

      8. lower-*.f32 N/A

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

      9. lower-unsound-*.f32 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-unsound-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. lift-pow.f64 N/A

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

      15. unpow2 N/A

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

      16. swap-sqr N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 45.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \mathsf{fma}\left(y \cdot y, \color{blue}{900}, {\left(z \cdot 30\right)}^{2}\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

      20. lift-*.f64 N/A

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

      21. lift-pow.f64 N/A

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

      22. unpow2 N/A

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

      23. *-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 45.9%

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

       1. lift-fma.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-fma.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lift-*.f64 N/A

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

       7. metadata-eval N/A

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

       8. swap-sqr N/A

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

       9. unpow2 N/A

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

       10. lift-*.f64 N/A

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

       11. metadata-eval N/A

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

       12. swap-sqr N/A

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

       13. unpow2 N/A

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

       14. associate-+l+ N/A

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

       15. lift-*.f64 N/A

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

       16. metadata-eval N/A

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

       17. swap-sqr N/A

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

       18. *-commutative N/A

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

       19. associate-*r* N/A

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

       20. lower-fma.f64 N/A

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

       21. lower-*.f64 N/A

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

       22. lower-*.f64 N/A

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

   11. Applied rewrites 45.9%

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

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

   1. Initial program 46.7%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 18.6

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

   4. Applied rewrites 18.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 37.1

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 63.4

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

   10. Applied rewrites 63.4%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 71.2

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

   13. Applied rewrites 71.2%

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

Alternative 7: 65.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|t\_0\right| - 0.2\\ t_2 := 25 \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + t\_2\right)\right), t\_1\right)\\ \mathbf{elif}\;z \leq -800000:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot z, 900, 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, t\_1\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-122}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|t\_0 + 30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(\left(y \cdot 30\right) \cdot 30, y, \mathsf{fma}\left(900 \cdot z, z, \left(900 \cdot x\right) \cdot x\right)\right)} - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - t\_2\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs t_0) 0.2))
        (t_2 (* 25.0 (/ 1.0 z))))
   (if (<= z -4.5e+152)
     (fmax (* -1.0 (* z (+ 30.0 t_2))) t_1)
     (if (<= z -800000.0)
       (fmax
        (- (sqrt (fma (* z z) 900.0 (* 900.0 (fma x x (* y y))))) 25.0)
        t_1)
       (if (<= z 4.6e-122)
         (fmax
          (* x (- 30.0 (* 25.0 (/ 1.0 x))))
          (- (fabs (+ t_0 (* 30.0 x))) 0.2))
         (if (<= z 1.05e+142)
           (fmax
            (-
             (sqrt
              (fma
               (* (* y 30.0) 30.0)
               y
               (fma (* 900.0 z) z (* (* 900.0 x) x))))
             25.0)
            t_1)
           (fmax (* z (- 30.0 t_2)) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(t_0) - 0.2;
	double t_2 = 25.0 * (1.0 / z);
	double tmp;
	if (z <= -4.5e+152) {
		tmp = fmax((-1.0 * (z * (30.0 + t_2))), t_1);
	} else if (z <= -800000.0) {
		tmp = fmax((sqrt(fma((z * z), 900.0, (900.0 * fma(x, x, (y * y))))) - 25.0), t_1);
	} else if (z <= 4.6e-122) {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (fabs((t_0 + (30.0 * x))) - 0.2));
	} else if (z <= 1.05e+142) {
		tmp = fmax((sqrt(fma(((y * 30.0) * 30.0), y, fma((900.0 * z), z, ((900.0 * x) * x)))) - 25.0), t_1);
	} else {
		tmp = fmax((z * (30.0 - t_2)), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(t_0) - 0.2)
	t_2 = Float64(25.0 * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -4.5e+152)
		tmp = fmax(Float64(-1.0 * Float64(z * Float64(30.0 + t_2))), t_1);
	elseif (z <= -800000.0)
		tmp = fmax(Float64(sqrt(fma(Float64(z * z), 900.0, Float64(900.0 * fma(x, x, Float64(y * y))))) - 25.0), t_1);
	elseif (z <= 4.6e-122)
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), Float64(abs(Float64(t_0 + Float64(30.0 * x))) - 0.2));
	elseif (z <= 1.05e+142)
		tmp = fmax(Float64(sqrt(fma(Float64(Float64(y * 30.0) * 30.0), y, fma(Float64(900.0 * z), z, Float64(Float64(900.0 * x) * x)))) - 25.0), t_1);
	else
		tmp = fmax(Float64(z * Float64(30.0 - t_2)), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$2 = N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+152], N[Max[N[(-1.0 * N[(z * N[(30.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, -800000.0], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0 + N[(900.0 * N[(x * x + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, 4.6e-122], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1.05e+142], N[Max[N[(N[Sqrt[N[(N[(N[(y * 30.0), $MachinePrecision] * 30.0), $MachinePrecision] * y + N[(N[(900.0 * z), $MachinePrecision] * z + N[(N[(900.0 * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[N[(z * N[(30.0 - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.5000000000000001e152

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 28.7

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

   10. Applied rewrites 28.7%

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

   if -4.5000000000000001e152 < z < -8e5

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. swap-sqr N/A

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

      8. lower-*.f32 N/A

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

      9. lower-unsound-*.f32 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-unsound-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. lift-pow.f64 N/A

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

      15. unpow2 N/A

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

      16. swap-sqr N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 45.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \mathsf{fma}\left(y \cdot y, \color{blue}{900}, {\left(z \cdot 30\right)}^{2}\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

      20. lift-*.f64 N/A

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

      21. lift-pow.f64 N/A

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

      22. unpow2 N/A

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

      23. *-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 45.9%

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

       1. lift-fma.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. metadata-eval N/A

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

       5. swap-sqr N/A

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

       6. unpow2 N/A

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

       7. add-flip N/A

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

       8. associate-+r- N/A

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lift-*.f64 N/A

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

       12. metadata-eval N/A

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

       13. swap-sqr N/A

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

       14. unpow2 N/A

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

       15. +-commutative N/A

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

   11. Applied rewrites 45.9%

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

   if -8e5 < z < 4.60000000000000014e-122

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

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

   10. Applied rewrites 28.5%

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

   11. Taylor expanded in x around 0

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

       1. lower-+.f64 N/A

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

       2. lower-sin.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-*.f64 42.6

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

   13. Applied rewrites 42.6%

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

   if 4.60000000000000014e-122 < z < 1.05e142

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. swap-sqr N/A

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

      8. lower-*.f32 N/A

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

      9. lower-unsound-*.f32 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-unsound-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. lift-pow.f64 N/A

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

      15. unpow2 N/A

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

      16. swap-sqr N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 45.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \mathsf{fma}\left(y \cdot y, \color{blue}{900}, {\left(z \cdot 30\right)}^{2}\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

      20. lift-*.f64 N/A

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

      21. lift-pow.f64 N/A

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

      22. unpow2 N/A

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

      23. *-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 45.9%

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

       1. lift-fma.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-fma.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lift-*.f64 N/A

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

       7. metadata-eval N/A

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

       8. swap-sqr N/A

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

       9. unpow2 N/A

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

       10. lift-*.f64 N/A

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

       11. metadata-eval N/A

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

       12. swap-sqr N/A

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

       13. unpow2 N/A

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

       14. associate-+l+ N/A

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

       15. lift-*.f64 N/A

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

       16. metadata-eval N/A

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

       17. swap-sqr N/A

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

       18. *-commutative N/A

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

       19. associate-*r* N/A

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

       20. lower-fma.f64 N/A

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

       21. lower-*.f64 N/A

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

       22. lower-*.f64 N/A

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

   11. Applied rewrites 45.9%

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

   if 1.05e142 < z

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.0

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

   10. Applied rewrites 29.0%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 65.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|t\_0\right| - 0.2\\ t_2 := 25 \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + t\_2\right)\right), t\_1\right)\\ \mathbf{elif}\;z \leq -800000:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot z, 900, 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, t\_1\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-122}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|t\_0 + 30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \mathsf{fma}\left(900 \cdot y, y, \left(900 \cdot z\right) \cdot z\right)\right)} - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - t\_2\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs t_0) 0.2))
        (t_2 (* 25.0 (/ 1.0 z))))
   (if (<= z -4.5e+152)
     (fmax (* -1.0 (* z (+ 30.0 t_2))) t_1)
     (if (<= z -800000.0)
       (fmax
        (- (sqrt (fma (* z z) 900.0 (* 900.0 (fma x x (* y y))))) 25.0)
        t_1)
       (if (<= z 4.6e-122)
         (fmax
          (* x (- 30.0 (* 25.0 (/ 1.0 x))))
          (- (fabs (+ t_0 (* 30.0 x))) 0.2))
         (if (<= z 1.05e+142)
           (fmax
            (-
             (sqrt (fma (* x x) 900.0 (fma (* 900.0 y) y (* (* 900.0 z) z))))
             25.0)
            t_1)
           (fmax (* z (- 30.0 t_2)) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(t_0) - 0.2;
	double t_2 = 25.0 * (1.0 / z);
	double tmp;
	if (z <= -4.5e+152) {
		tmp = fmax((-1.0 * (z * (30.0 + t_2))), t_1);
	} else if (z <= -800000.0) {
		tmp = fmax((sqrt(fma((z * z), 900.0, (900.0 * fma(x, x, (y * y))))) - 25.0), t_1);
	} else if (z <= 4.6e-122) {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (fabs((t_0 + (30.0 * x))) - 0.2));
	} else if (z <= 1.05e+142) {
		tmp = fmax((sqrt(fma((x * x), 900.0, fma((900.0 * y), y, ((900.0 * z) * z)))) - 25.0), t_1);
	} else {
		tmp = fmax((z * (30.0 - t_2)), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(t_0) - 0.2)
	t_2 = Float64(25.0 * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -4.5e+152)
		tmp = fmax(Float64(-1.0 * Float64(z * Float64(30.0 + t_2))), t_1);
	elseif (z <= -800000.0)
		tmp = fmax(Float64(sqrt(fma(Float64(z * z), 900.0, Float64(900.0 * fma(x, x, Float64(y * y))))) - 25.0), t_1);
	elseif (z <= 4.6e-122)
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), Float64(abs(Float64(t_0 + Float64(30.0 * x))) - 0.2));
	elseif (z <= 1.05e+142)
		tmp = fmax(Float64(sqrt(fma(Float64(x * x), 900.0, fma(Float64(900.0 * y), y, Float64(Float64(900.0 * z) * z)))) - 25.0), t_1);
	else
		tmp = fmax(Float64(z * Float64(30.0 - t_2)), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$2 = N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+152], N[Max[N[(-1.0 * N[(z * N[(30.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, -800000.0], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0 + N[(900.0 * N[(x * x + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, 4.6e-122], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1.05e+142], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0 + N[(N[(900.0 * y), $MachinePrecision] * y + N[(N[(900.0 * z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[N[(z * N[(30.0 - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.5000000000000001e152

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 28.7

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

   10. Applied rewrites 28.7%

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

   if -4.5000000000000001e152 < z < -8e5

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. swap-sqr N/A

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

      8. lower-*.f32 N/A

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

      9. lower-unsound-*.f32 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-unsound-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. lift-pow.f64 N/A

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

      15. unpow2 N/A

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

      16. swap-sqr N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 45.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \mathsf{fma}\left(y \cdot y, \color{blue}{900}, {\left(z \cdot 30\right)}^{2}\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

      20. lift-*.f64 N/A

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

      21. lift-pow.f64 N/A

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

      22. unpow2 N/A

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

      23. *-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 45.9%

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

       1. lift-fma.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. metadata-eval N/A

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

       5. swap-sqr N/A

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

       6. unpow2 N/A

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

       7. add-flip N/A

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

       8. associate-+r- N/A

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lift-*.f64 N/A

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

       12. metadata-eval N/A

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

       13. swap-sqr N/A

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

       14. unpow2 N/A

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

       15. +-commutative N/A

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

   11. Applied rewrites 45.9%

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

   if -8e5 < z < 4.60000000000000014e-122

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

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

   10. Applied rewrites 28.5%

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

   11. Taylor expanded in x around 0

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

       1. lower-+.f64 N/A

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

       2. lower-sin.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-*.f64 42.6

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

   13. Applied rewrites 42.6%

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

   if 4.60000000000000014e-122 < z < 1.05e142

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. swap-sqr N/A

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

      8. lower-*.f32 N/A

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

      9. lower-unsound-*.f32 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-unsound-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. lift-pow.f64 N/A

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

      15. unpow2 N/A

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

      16. swap-sqr N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 45.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \mathsf{fma}\left(y \cdot y, \color{blue}{900}, {\left(z \cdot 30\right)}^{2}\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

      20. lift-*.f64 N/A

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

      21. lift-pow.f64 N/A

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

      22. unpow2 N/A

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

      23. *-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 45.9%

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

       1. lift-fma.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lift-*.f64 N/A

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

       8. metadata-eval N/A

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

       9. swap-sqr N/A

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

       10. unpow2 N/A

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

       11. lower-fma.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 N/A

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

       14. unpow2 N/A

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

       15. *-commutative N/A

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

       16. *-commutative N/A

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

       17. swap-sqr N/A

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

       18. metadata-eval N/A

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

       19. associate-*r* N/A

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

       20. lower-*.f64 N/A

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

       21. lower-*.f64 45.9

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

   11. Applied rewrites 45.9%

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

   if 1.05e142 < z

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.0

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

   10. Applied rewrites 29.0%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 65.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|t\_0\right| - 0.2\\ t_2 := \mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot z, 900, 900 \cdot \mathsf{fma}\left(x, x, y \cdot y\right)\right)} - 25, t\_1\right)\\ t_3 := 25 \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + t\_3\right)\right), t\_1\right)\\ \mathbf{elif}\;z \leq -800000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-122}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|t\_0 + 30 \cdot x\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - t\_3\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs t_0) 0.2))
        (t_2
         (fmax
          (- (sqrt (fma (* z z) 900.0 (* 900.0 (fma x x (* y y))))) 25.0)
          t_1))
        (t_3 (* 25.0 (/ 1.0 z))))
   (if (<= z -4.5e+152)
     (fmax (* -1.0 (* z (+ 30.0 t_3))) t_1)
     (if (<= z -800000.0)
       t_2
       (if (<= z 4.6e-122)
         (fmax
          (* x (- 30.0 (* 25.0 (/ 1.0 x))))
          (- (fabs (+ t_0 (* 30.0 x))) 0.2))
         (if (<= z 1.05e+142) t_2 (fmax (* z (- 30.0 t_3)) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(t_0) - 0.2;
	double t_2 = fmax((sqrt(fma((z * z), 900.0, (900.0 * fma(x, x, (y * y))))) - 25.0), t_1);
	double t_3 = 25.0 * (1.0 / z);
	double tmp;
	if (z <= -4.5e+152) {
		tmp = fmax((-1.0 * (z * (30.0 + t_3))), t_1);
	} else if (z <= -800000.0) {
		tmp = t_2;
	} else if (z <= 4.6e-122) {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (fabs((t_0 + (30.0 * x))) - 0.2));
	} else if (z <= 1.05e+142) {
		tmp = t_2;
	} else {
		tmp = fmax((z * (30.0 - t_3)), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(t_0) - 0.2)
	t_2 = fmax(Float64(sqrt(fma(Float64(z * z), 900.0, Float64(900.0 * fma(x, x, Float64(y * y))))) - 25.0), t_1)
	t_3 = Float64(25.0 * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -4.5e+152)
		tmp = fmax(Float64(-1.0 * Float64(z * Float64(30.0 + t_3))), t_1);
	elseif (z <= -800000.0)
		tmp = t_2;
	elseif (z <= 4.6e-122)
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), Float64(abs(Float64(t_0 + Float64(30.0 * x))) - 0.2));
	elseif (z <= 1.05e+142)
		tmp = t_2;
	else
		tmp = fmax(Float64(z * Float64(30.0 - t_3)), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$2 = N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0 + N[(900.0 * N[(x * x + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+152], N[Max[N[(-1.0 * N[(z * N[(30.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, -800000.0], t$95$2, If[LessEqual[z, 4.6e-122], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1.05e+142], t$95$2, N[Max[N[(z * N[(30.0 - t$95$3), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5000000000000001e152

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 28.7

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

   10. Applied rewrites 28.7%

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

   if -4.5000000000000001e152 < z < -8e5 or 4.60000000000000014e-122 < z < 1.05e142

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. swap-sqr N/A

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

      8. lower-*.f32 N/A

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

      9. lower-unsound-*.f32 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-unsound-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lift-*.f64 N/A

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

      14. lift-pow.f64 N/A

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

      15. unpow2 N/A

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

      16. swap-sqr N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 45.9

          \[\leadsto \mathsf{max}\left(\sqrt{\mathsf{fma}\left(x \cdot x, 900, \mathsf{fma}\left(y \cdot y, \color{blue}{900}, {\left(z \cdot 30\right)}^{2}\right)\right)} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

      20. lift-*.f64 N/A

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

      21. lift-pow.f64 N/A

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

      22. unpow2 N/A

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

      23. *-commutative N/A

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

      24. *-commutative N/A

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

   9. Applied rewrites 45.9%

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

       1. lift-fma.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. metadata-eval N/A

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

       5. swap-sqr N/A

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

       6. unpow2 N/A

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

       7. add-flip N/A

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

       8. associate-+r- N/A

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

       9. lift-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lift-*.f64 N/A

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

       12. metadata-eval N/A

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

       13. swap-sqr N/A

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

       14. unpow2 N/A

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

       15. +-commutative N/A

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

   11. Applied rewrites 45.9%

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

   if -8e5 < z < 4.60000000000000014e-122

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

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

   10. Applied rewrites 28.5%

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

   11. Taylor expanded in x around 0

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

       1. lower-+.f64 N/A

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

       2. lower-sin.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-*.f64 42.6

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

   13. Applied rewrites 42.6%

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

   if 1.05e142 < z

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 29.0

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

   10. Applied rewrites 29.0%

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

Alternative 10: 61.3% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot z\right)\\ t_1 := \left|t\_0\right| - 0.2\\ t_2 := 25 \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -1020000:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + t\_2\right)\right), t\_1\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|t\_0 + 30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - t\_2\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 z)))
        (t_1 (- (fabs t_0) 0.2))
        (t_2 (* 25.0 (/ 1.0 z))))
   (if (<= z -1020000.0)
     (fmax (* -1.0 (* z (+ 30.0 t_2))) t_1)
     (if (<= z 3.7e+39)
       (fmax
        (* x (- 30.0 (* 25.0 (/ 1.0 x))))
        (- (fabs (+ t_0 (* 30.0 x))) 0.2))
       (fmax (* z (- 30.0 t_2)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * z));
	double t_1 = fabs(t_0) - 0.2;
	double t_2 = 25.0 * (1.0 / z);
	double tmp;
	if (z <= -1020000.0) {
		tmp = fmax((-1.0 * (z * (30.0 + t_2))), t_1);
	} else if (z <= 3.7e+39) {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (fabs((t_0 + (30.0 * x))) - 0.2));
	} else {
		tmp = fmax((z * (30.0 - t_2)), t_1);
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = sin((30.0d0 * z))
    t_1 = abs(t_0) - 0.2d0
    t_2 = 25.0d0 * (1.0d0 / z)
    if (z <= (-1020000.0d0)) then
        tmp = fmax(((-1.0d0) * (z * (30.0d0 + t_2))), t_1)
    else if (z <= 3.7d+39) then
        tmp = fmax((x * (30.0d0 - (25.0d0 * (1.0d0 / x)))), (abs((t_0 + (30.0d0 * x))) - 0.2d0))
    else
        tmp = fmax((z * (30.0d0 - t_2)), t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin((30.0 * z));
	double t_1 = Math.abs(t_0) - 0.2;
	double t_2 = 25.0 * (1.0 / z);
	double tmp;
	if (z <= -1020000.0) {
		tmp = fmax((-1.0 * (z * (30.0 + t_2))), t_1);
	} else if (z <= 3.7e+39) {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (Math.abs((t_0 + (30.0 * x))) - 0.2));
	} else {
		tmp = fmax((z * (30.0 - t_2)), t_1);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin((30.0 * z))
	t_1 = math.fabs(t_0) - 0.2
	t_2 = 25.0 * (1.0 / z)
	tmp = 0
	if z <= -1020000.0:
		tmp = fmax((-1.0 * (z * (30.0 + t_2))), t_1)
	elif z <= 3.7e+39:
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (math.fabs((t_0 + (30.0 * x))) - 0.2))
	else:
		tmp = fmax((z * (30.0 - t_2)), t_1)
	return tmp

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * z))
	t_1 = Float64(abs(t_0) - 0.2)
	t_2 = Float64(25.0 * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -1020000.0)
		tmp = fmax(Float64(-1.0 * Float64(z * Float64(30.0 + t_2))), t_1);
	elseif (z <= 3.7e+39)
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), Float64(abs(Float64(t_0 + Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(z * Float64(30.0 - t_2)), t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin((30.0 * z));
	t_1 = abs(t_0) - 0.2;
	t_2 = 25.0 * (1.0 / z);
	tmp = 0.0;
	if (z <= -1020000.0)
		tmp = max((-1.0 * (z * (30.0 + t_2))), t_1);
	elseif (z <= 3.7e+39)
		tmp = max((x * (30.0 - (25.0 * (1.0 / x)))), (abs((t_0 + (30.0 * x))) - 0.2));
	else
		tmp = max((z * (30.0 - t_2)), t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[t$95$0], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$2 = N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1020000.0], N[Max[N[(-1.0 * N[(z * N[(30.0 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, 3.7e+39], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * N[(30.0 - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1], $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02e6

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.3

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in x around 0

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

      1. lower-sin.f64 N/A

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

      2. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 28.7

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

   10. Applied rewrites 28.7%

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

   if -1.02e6 < z < 3.70000000000000012e39

   1. Initial program 46.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\sin \left(30 \cdot z\right) + \color{blue}{30 \cdot x}\right| - \frac{1}{5}\right) \]
   12. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\sin \left(30 \cdot z\right) + 30 \cdot \color{blue}{x}\right| - \frac{1}{5}\right) \]

       2. lower-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - \frac{1}{5}\right) \]

       3. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - \frac{1}{5}\right) \]

       4. lower-*.f64 42.6

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]

   13. Applied rewrites 42.6%

       \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\sin \left(30 \cdot z\right) + \color{blue}{30 \cdot x}\right| - 0.2\right) \]

   if 3.70000000000000012e39 < z

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \color{blue}{\left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - \color{blue}{25 \cdot \frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \color{blue}{\frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-/.f64 29.0

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 29.0%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 51.9% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ t_1 := 25 \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + t\_1\right)\right), t\_0\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - t\_1\right), t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)) (t_1 (* 25.0 (/ 1.0 z))))
   (if (<= z -1.1e-23)
     (fmax (* -1.0 (* z (+ 30.0 t_1))) t_0)
     (if (<= z 1.55e+33)
       (fmax (fma x 30.0 (* (/ -25.0 x) x)) t_0)
       (fmax (* z (- 30.0 t_1)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * z))) - 0.2;
	double t_1 = 25.0 * (1.0 / z);
	double tmp;
	if (z <= -1.1e-23) {
		tmp = fmax((-1.0 * (z * (30.0 + t_1))), t_0);
	} else if (z <= 1.55e+33) {
		tmp = fmax(fma(x, 30.0, ((-25.0 / x) * x)), t_0);
	} else {
		tmp = fmax((z * (30.0 - t_1)), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * z))) - 0.2)
	t_1 = Float64(25.0 * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -1.1e-23)
		tmp = fmax(Float64(-1.0 * Float64(z * Float64(30.0 + t_1))), t_0);
	elseif (z <= 1.55e+33)
		tmp = fmax(fma(x, 30.0, Float64(Float64(-25.0 / x) * x)), t_0);
	else
		tmp = fmax(Float64(z * Float64(30.0 - t_1)), t_0);
	end
	return 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]}, Block[{t$95$1 = N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-23], N[Max[N[(-1.0 * N[(z * N[(30.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 1.55e+33], N[Max[N[(x * 30.0 + N[(N[(-25.0 / x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(z * N[(30.0 - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e-23

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-1 \cdot \left(z \cdot \left(30 + 25 \cdot \frac{1}{z}\right)\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \color{blue}{\left(z \cdot \left(30 + 25 \cdot \frac{1}{z}\right)\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(z \cdot \color{blue}{\left(30 + 25 \cdot \frac{1}{z}\right)}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + \color{blue}{25 \cdot \frac{1}{z}}\right)\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + 25 \cdot \color{blue}{\frac{1}{z}}\right)\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      5. lower-/.f64 28.7

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + 25 \cdot \frac{1}{\color{blue}{z}}\right)\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.7%

       \[\leadsto \mathsf{max}\left(\color{blue}{-1 \cdot \left(z \cdot \left(30 + 25 \cdot \frac{1}{z}\right)\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if -1.1e-23 < z < 1.55e33

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
   11. Step-by-step derivation

       1. lift-*.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. lift--.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. sub-flip N/A

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       4. distribute-rgt-in N/A

          \[\leadsto \mathsf{max}\left(30 \cdot x + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{max}\left(x \cdot 30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)} \cdot x, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       6. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       7. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       10. mult-flip-rev N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(\frac{25}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       11. distribute-neg-frac N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{\mathsf{neg}\left(25\right)}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       12. metadata-eval N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       13. lower-/.f64 28.5

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   12. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if 1.55e33 < z

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \color{blue}{\left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - \color{blue}{25 \cdot \frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \color{blue}{\frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-/.f64 29.0

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 29.0%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 51.9% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ \mathbf{if}\;x \leq -410000000:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(x \cdot \left(30 + 25 \cdot \frac{1}{x}\right)\right), t\_0\right)\\ \mathbf{elif}\;x \leq 1.05:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - 25 \cdot \frac{1}{z}\right), t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)))
   (if (<= x -410000000.0)
     (fmax (* -1.0 (* x (+ 30.0 (* 25.0 (/ 1.0 x))))) t_0)
     (if (<= x 1.05)
       (fmax (* z (- 30.0 (* 25.0 (/ 1.0 z)))) t_0)
       (fmax (fma x 30.0 (* (/ -25.0 x) 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 <= -410000000.0) {
		tmp = fmax((-1.0 * (x * (30.0 + (25.0 * (1.0 / x))))), t_0);
	} else if (x <= 1.05) {
		tmp = fmax((z * (30.0 - (25.0 * (1.0 / z)))), t_0);
	} else {
		tmp = fmax(fma(x, 30.0, ((-25.0 / x) * 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 <= -410000000.0)
		tmp = fmax(Float64(-1.0 * Float64(x * Float64(30.0 + Float64(25.0 * Float64(1.0 / x))))), t_0);
	elseif (x <= 1.05)
		tmp = fmax(Float64(z * Float64(30.0 - Float64(25.0 * Float64(1.0 / z)))), t_0);
	else
		tmp = fmax(fma(x, 30.0, Float64(Float64(-25.0 / x) * x)), t_0);
	end
	return 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, -410000000.0], N[Max[N[(-1.0 * N[(x * N[(30.0 + N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 1.05], N[Max[N[(z * N[(30.0 - N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(x * 30.0 + N[(N[(-25.0 / x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1e8

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-1 \cdot \left(x \cdot \left(30 + 25 \cdot \frac{1}{x}\right)\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \color{blue}{\left(x \cdot \left(30 + 25 \cdot \frac{1}{x}\right)\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(x \cdot \color{blue}{\left(30 + 25 \cdot \frac{1}{x}\right)}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(x \cdot \left(30 + \color{blue}{25 \cdot \frac{1}{x}}\right)\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(x \cdot \left(30 + 25 \cdot \color{blue}{\frac{1}{x}}\right)\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      5. lower-/.f64 28.5

         \[\leadsto \mathsf{max}\left(-1 \cdot \left(x \cdot \left(30 + 25 \cdot \frac{1}{\color{blue}{x}}\right)\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{-1 \cdot \left(x \cdot \left(30 + 25 \cdot \frac{1}{x}\right)\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if -4.1e8 < x < 1.05000000000000004

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \color{blue}{\left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - \color{blue}{25 \cdot \frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \color{blue}{\frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-/.f64 29.0

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 29.0%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if 1.05000000000000004 < x

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
   11. Step-by-step derivation

       1. lift-*.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. lift--.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. sub-flip N/A

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       4. distribute-rgt-in N/A

          \[\leadsto \mathsf{max}\left(30 \cdot x + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{max}\left(x \cdot 30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)} \cdot x, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       6. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       7. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       10. mult-flip-rev N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(\frac{25}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       11. distribute-neg-frac N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{\mathsf{neg}\left(25\right)}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       12. metadata-eval N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       13. lower-/.f64 28.5

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   12. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 39.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ \mathbf{if}\;y \leq -3 \cdot 10^{-129}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), t\_0\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-175}:\\ \;\;\;\;\mathsf{max}\left(z \cdot \left(30 - 25 \cdot \frac{1}{z}\right), t\_0\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)))
   (if (<= y -3e-129)
     (fmax (fma x 30.0 (* (/ -25.0 x) x)) t_0)
     (if (<= y 4.8e-175)
       (fmax (* z (- 30.0 (* 25.0 (/ 1.0 z)))) t_0)
       (if (<= y 9.6e+61)
         (fmax (- (* 30.0 x) 25.0) t_0)
         (fmax (* y (- 30.0 (* 25.0 (/ 1.0 y)))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * z))) - 0.2;
	double tmp;
	if (y <= -3e-129) {
		tmp = fmax(fma(x, 30.0, ((-25.0 / x) * x)), t_0);
	} else if (y <= 4.8e-175) {
		tmp = fmax((z * (30.0 - (25.0 * (1.0 / z)))), t_0);
	} else if (y <= 9.6e+61) {
		tmp = fmax(((30.0 * x) - 25.0), t_0);
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), 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 (y <= -3e-129)
		tmp = fmax(fma(x, 30.0, Float64(Float64(-25.0 / x) * x)), t_0);
	elseif (y <= 4.8e-175)
		tmp = fmax(Float64(z * Float64(30.0 - Float64(25.0 * Float64(1.0 / z)))), t_0);
	elseif (y <= 9.6e+61)
		tmp = fmax(Float64(Float64(30.0 * x) - 25.0), t_0);
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), t_0);
	end
	return 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[y, -3e-129], N[Max[N[(x * 30.0 + N[(N[(-25.0 / x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 4.8e-175], N[Max[N[(z * N[(30.0 - N[(25.0 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 9.6e+61], N[Max[N[(N[(30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.9999999999999998e-129

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
   11. Step-by-step derivation

       1. lift-*.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. lift--.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. sub-flip N/A

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       4. distribute-rgt-in N/A

          \[\leadsto \mathsf{max}\left(30 \cdot x + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{max}\left(x \cdot 30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)} \cdot x, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       6. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       7. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       10. mult-flip-rev N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(\frac{25}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       11. distribute-neg-frac N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{\mathsf{neg}\left(25\right)}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       12. metadata-eval N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       13. lower-/.f64 28.5

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   12. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if -2.9999999999999998e-129 < y < 4.8e-175

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \color{blue}{\left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - \color{blue}{25 \cdot \frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \color{blue}{\frac{1}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-/.f64 29.0

         \[\leadsto \mathsf{max}\left(z \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{z}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 29.0%

       \[\leadsto \mathsf{max}\left(\color{blue}{z \cdot \left(30 - 25 \cdot \frac{1}{z}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if 4.8e-175 < y < 9.5999999999999995e61

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(30 \cdot x - \color{blue}{25}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   12. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto \mathsf{max}\left(30 \cdot x - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       2. lower-*.f64 28.5

          \[\leadsto \mathsf{max}\left(30 \cdot x - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   13. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(30 \cdot x - \color{blue}{25}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if 9.5999999999999995e61 < y

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \color{blue}{\left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - \color{blue}{25 \cdot \frac{1}{y}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \color{blue}{\frac{1}{y}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-/.f64 28.5

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 39.2% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ \mathbf{if}\;y \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)))
   (if (<= y 9.6e+61)
     (fmax (fma x 30.0 (* (/ -25.0 x) x)) t_0)
     (fmax (* y (- 30.0 (* 25.0 (/ 1.0 y)))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * z))) - 0.2;
	double tmp;
	if (y <= 9.6e+61) {
		tmp = fmax(fma(x, 30.0, ((-25.0 / x) * x)), t_0);
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), 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 (y <= 9.6e+61)
		tmp = fmax(fma(x, 30.0, Float64(Float64(-25.0 / x) * x)), t_0);
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), t_0);
	end
	return 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[y, 9.6e+61], N[Max[N[(x * 30.0 + N[(N[(-25.0 / x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 9.5999999999999995e61

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
   11. Step-by-step derivation

       1. lift-*.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. lift--.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. sub-flip N/A

          \[\leadsto \mathsf{max}\left(x \cdot \left(30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       4. distribute-rgt-in N/A

          \[\leadsto \mathsf{max}\left(30 \cdot x + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{max}\left(x \cdot 30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)} \cdot x, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       6. lower-fma.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       7. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       8. lift-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       9. lift-/.f64 N/A

          \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       10. mult-flip-rev N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(\frac{25}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       11. distribute-neg-frac N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{\mathsf{neg}\left(25\right)}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       12. metadata-eval N/A

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

       13. lower-/.f64 28.5

           \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   12. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if 9.5999999999999995e61 < y

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \color{blue}{\left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - \color{blue}{25 \cdot \frac{1}{y}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \color{blue}{\frac{1}{y}}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-/.f64 28.5

         \[\leadsto \mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{y}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{y \cdot \left(30 - 25 \cdot \frac{1}{y}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 28.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax (fma x 30.0 (* (/ -25.0 x) x)) (- (fabs (sin (* 30.0 z))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax(fma(x, 30.0, ((-25.0 / x) * x)), (fabs(sin((30.0 * z))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(fma(x, 30.0, Float64(Float64(-25.0 / x) * x)), Float64(abs(sin(Float64(30.0 * z))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(x * 30.0 + N[(N[(-25.0 / x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 46.7%

   \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

2. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   2. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   5. lower-cos.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

   7. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   8. lower-*.f64 46.3

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

4. Applied rewrites 46.3%

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
6. Step-by-step derivation

   1. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   2. lower-*.f64 46.0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

7. Applied rewrites 46.0%

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

8. Taylor expanded in x around inf

   \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
9. 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 28.5

      \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

10. Applied rewrites 28.5%

    \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
11. Step-by-step derivation

    1. lift-*.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. lift--.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. sub-flip N/A

       \[\leadsto \mathsf{max}\left(x \cdot \left(30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)}\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    4. distribute-rgt-in N/A

       \[\leadsto \mathsf{max}\left(30 \cdot x + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    5. *-commutative N/A

       \[\leadsto \mathsf{max}\left(x \cdot 30 + \color{blue}{\left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right)} \cdot x, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    6. lower-fma.f64 N/A

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    7. lower-*.f64 N/A

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    8. lift-*.f64 N/A

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    9. lift-/.f64 N/A

       \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(25 \cdot \frac{1}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    10. mult-flip-rev N/A

        \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \left(\mathsf{neg}\left(\frac{25}{x}\right)\right) \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    11. distribute-neg-frac N/A

        \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{\mathsf{neg}\left(25\right)}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    12. metadata-eval N/A

        \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    13. lower-/.f64 28.5

        \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, 30, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

12. Applied rewrites 28.5%

    \[\leadsto \mathsf{max}\left(\mathsf{fma}\left(x, \color{blue}{30}, \frac{-25}{x} \cdot x\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
13. Add Preprocessing

Alternative 16: 28.5% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(30 \cdot x - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax (- (* 30.0 x) 25.0) (- (fabs (sin (* 30.0 z))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax(((30.0 * x) - 25.0), (fabs(sin((30.0 * z))) - 0.2));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = fmax(((30.0d0 * x) - 25.0d0), (abs(sin((30.0d0 * z))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax(((30.0 * x) - 25.0), (Math.abs(Math.sin((30.0 * z))) - 0.2));
}

Python

def code(x, y, z):
	return fmax(((30.0 * x) - 25.0), (math.fabs(math.sin((30.0 * z))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(Float64(30.0 * x) - 25.0), Float64(abs(sin(Float64(30.0 * z))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max(((30.0 * x) - 25.0), (abs(sin((30.0 * z))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[(30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 46.7%

   \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

2. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   2. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   5. lower-cos.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

   7. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   8. lower-*.f64 46.3

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

4. Applied rewrites 46.3%

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
6. Step-by-step derivation

   1. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   2. lower-*.f64 46.0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

7. Applied rewrites 46.0%

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

8. Taylor expanded in x around inf

   \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
9. 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 28.5

      \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

10. Applied rewrites 28.5%

    \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

11. Taylor expanded in x around 0

    \[\leadsto \mathsf{max}\left(30 \cdot x - \color{blue}{25}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
12. Step-by-step derivation

    1. lower--.f64 N/A

       \[\leadsto \mathsf{max}\left(30 \cdot x - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

    2. lower-*.f64 28.5

       \[\leadsto \mathsf{max}\left(30 \cdot x - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

13. Applied rewrites 28.5%

    \[\leadsto \mathsf{max}\left(30 \cdot x - \color{blue}{25}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
14. Add Preprocessing

Alternative 17: 28.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right)\right| - 0.2\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 0.1:\\ \;\;\;\;\mathsf{max}\left(-25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x \cdot 30, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 z))) 0.2)))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            (* (sin (* z 30.0)) (cos (* x 30.0)))))
          0.2))
        0.1)
     (fmax -25.0 t_0)
     (fmax (* x 30.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * z))) - 0.2;
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2)) <= 0.1) {
		tmp = fmax(-25.0, t_0);
	} else {
		tmp = fmax((x * 30.0), 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 (fmax((sqrt(((((x * 30.0d0) ** 2.0d0) + ((y * 30.0d0) ** 2.0d0)) + ((z * 30.0d0) ** 2.0d0))) - 25.0d0), (abs((((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))) + (sin((z * 30.0d0)) * cos((x * 30.0d0))))) - 0.2d0)) <= 0.1d0) then
        tmp = fmax((-25.0d0), t_0)
    else
        tmp = fmax((x * 30.0d0), 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 (fmax((Math.sqrt(((Math.pow((x * 30.0), 2.0) + Math.pow((y * 30.0), 2.0)) + Math.pow((z * 30.0), 2.0))) - 25.0), (Math.abs((((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))) + (Math.sin((z * 30.0)) * Math.cos((x * 30.0))))) - 0.2)) <= 0.1) {
		tmp = fmax(-25.0, t_0);
	} else {
		tmp = fmax((x * 30.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * z))) - 0.2
	tmp = 0
	if fmax((math.sqrt(((math.pow((x * 30.0), 2.0) + math.pow((y * 30.0), 2.0)) + math.pow((z * 30.0), 2.0))) - 25.0), (math.fabs((((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))) + (math.sin((z * 30.0)) * math.cos((x * 30.0))))) - 0.2)) <= 0.1:
		tmp = fmax(-25.0, t_0)
	else:
		tmp = fmax((x * 30.0), 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 (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2)) <= 0.1)
		tmp = fmax(-25.0, t_0);
	else
		tmp = fmax(Float64(x * 30.0), 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 (max((sqrt(((((x * 30.0) ^ 2.0) + ((y * 30.0) ^ 2.0)) + ((z * 30.0) ^ 2.0))) - 25.0), (abs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2)) <= 0.1)
		tmp = max(-25.0, t_0);
	else
		tmp = max((x * 30.0), 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[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 0.1], N[Max[-25.0, t$95$0], $MachinePrecision], N[Max[N[(x * 30.0), $MachinePrecision], t$95$0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 0.10000000000000001

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(-25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 14.4%

       \[\leadsto \mathsf{max}\left(-25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   if 0.10000000000000001 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 46.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      5. lower-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

      7. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      8. lower-*.f64 46.3

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   4. Applied rewrites 46.3%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 46.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   7. Applied rewrites 46.0%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   9. 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 28.5

         \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   10. Applied rewrites 28.5%

       \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

   11. Taylor expanded in x around inf

       \[\leadsto \mathsf{max}\left(x \cdot 30, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 17.2%

       \[\leadsto \mathsf{max}\left(x \cdot 30, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 14.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(-25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax -25.0 (- (fabs (sin (* 30.0 z))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax(-25.0, (fabs(sin((30.0 * z))) - 0.2));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = fmax((-25.0d0), (abs(sin((30.0d0 * z))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax(-25.0, (Math.abs(Math.sin((30.0 * z))) - 0.2));
}

Python

def code(x, y, z):
	return fmax(-25.0, (math.fabs(math.sin((30.0 * z))) - 0.2))

Julia

function code(x, y, z)
	return fmax(-25.0, Float64(abs(sin(Float64(30.0 * z))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max(-25.0, (abs(sin((30.0 * z))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[-25.0, N[(N[Abs[N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 46.7%

   \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

2. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   2. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \color{blue}{\cos \left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   3. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \color{blue}{\left(30 \cdot x\right)} \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   5. lower-cos.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(\color{blue}{30} \cdot z\right)\right| - \frac{1}{5}\right) \]

   7. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   8. lower-*.f64 46.3

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right) \]

4. Applied rewrites 46.3%

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
6. Step-by-step derivation

   1. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]

   2. lower-*.f64 46.0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

7. Applied rewrites 46.0%

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

8. Taylor expanded in x around inf

   \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
9. 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 28.5

      \[\leadsto \mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{\color{blue}{x}}\right), \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

10. Applied rewrites 28.5%

    \[\leadsto \mathsf{max}\left(\color{blue}{x \cdot \left(30 - 25 \cdot \frac{1}{x}\right)}, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]

11. Taylor expanded in x around 0

    \[\leadsto \mathsf{max}\left(-25, \left|\sin \left(30 \cdot z\right)\right| - \frac{1}{5}\right) \]
12. Step-by-step derivation

13. Applied rewrites 14.4%

    \[\leadsto \mathsf{max}\left(-25, \left|\sin \left(30 \cdot z\right)\right| - 0.2\right) \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025162 
(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)))