Gyroid sphere

Percentage Accurate: 45.9% → 88.0%

Time: 6.1s

Alternatives: 14

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 45.9% accurate, 1.0× speedup

Math

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

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: 88.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25\\ t_2 := \mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\\ t_3 := \left|t\_2\right|\\ \mathbf{if}\;\mathsf{max}\left(t\_1, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 4 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(t\_1, \frac{{t\_3}^{3} + -0.008}{{t\_2}^{2} + \left(0.04 - t\_3 \cdot -0.2\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot \left(y \cdot \cos \left(30 \cdot z\right)\right)\right) + 30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 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))
        (t_2 (fma (cos (* -30.0 x)) t_0 (sin (* 30.0 x))))
        (t_3 (fabs t_2)))
   (if (<=
        (fmax
         t_1
         (-
          (fabs
           (+
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            (* t_0 (cos (* x 30.0)))))
          0.2))
        4e+147)
     (fmax
      t_1
      (/ (+ (pow t_3 3.0) -0.008) (+ (pow t_2 2.0) (- 0.04 (* t_3 -0.2)))))
     (fmax
      (- (* -30.0 y) 25.0)
      (-
       (fabs
        (+
         (fma 30.0 x (* 30.0 (* y (cos (* 30.0 z)))))
         (* 30.0 (* z (cos (* 30.0 x))))))
       0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 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 t_2 = fma(cos((-30.0 * x)), t_0, sin((30.0 * x)));
	double t_3 = fabs(t_2);
	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 * cos((x * 30.0))))) - 0.2)) <= 4e+147) {
		tmp = fmax(t_1, ((pow(t_3, 3.0) + -0.008) / (pow(t_2, 2.0) + (0.04 - (t_3 * -0.2)))));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * (y * cos((30.0 * z))))) + (30.0 * (z * cos((30.0 * x)))))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 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)
	t_2 = fma(cos(Float64(-30.0 * x)), t_0, sin(Float64(30.0 * x)))
	t_3 = abs(t_2)
	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)))) + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2)) <= 4e+147)
		tmp = fmax(t_1, Float64(Float64((t_3 ^ 3.0) + -0.008) / Float64((t_2 ^ 2.0) + Float64(0.04 - Float64(t_3 * -0.2)))));
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * Float64(y * cos(Float64(30.0 * z))))) + Float64(30.0 * Float64(z * cos(Float64(30.0 * x)))))) - 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[(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$2 = N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Abs[t$95$2], $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] + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 4e+147], N[Max[t$95$1, N[(N[(N[Power[t$95$3, 3.0], $MachinePrecision] + -0.008), $MachinePrecision] / N[(N[Power[t$95$2, 2.0], $MachinePrecision] + N[(0.04 - N[(t$95$3 * -0.2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * N[(y * N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(30.0 * N[(z * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 3.9999999999999999e147

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   6. Applied rewrites 45.6%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \color{blue}{\frac{{\left(\left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \sin \left(30 \cdot x\right)\right)\right|\right)}^{3} + -0.008}{{\left(\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \sin \left(30 \cdot x\right)\right)\right)}^{2} + \left(0.04 - \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), \sin \left(z \cdot 30\right), \sin \left(30 \cdot x\right)\right)\right| \cdot -0.2\right)}}\right) \]

   if 3.9999999999999999e147 < (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 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-cos.f64 N/A

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

       4. lower-*.f64 83.8%

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

   13. Applied rewrites 83.8%

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

Alternative 2: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25\\ t_1 := \cos \left(30 \cdot x\right)\\ \mathbf{if}\;\mathsf{max}\left(t\_0, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 4 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\sin \left(30 \cdot x\right) + t\_1 \cdot \sin \left(30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot \left(y \cdot \cos \left(30 \cdot z\right)\right)\right) + 30 \cdot \left(z \cdot t\_1\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0))
        (t_1 (cos (* 30.0 x))))
   (if (<=
        (fmax
         t_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))
        4e+147)
     (fmax t_0 (- (fabs (+ (sin (* 30.0 x)) (* t_1 (sin (* 30.0 z))))) 0.2))
     (fmax
      (- (* -30.0 y) 25.0)
      (-
       (fabs
        (+ (fma 30.0 x (* 30.0 (* y (cos (* 30.0 z))))) (* 30.0 (* z t_1))))
       0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0;
	double t_1 = cos((30.0 * x));
	double tmp;
	if (fmax(t_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)) <= 4e+147) {
		tmp = fmax(t_0, (fabs((sin((30.0 * x)) + (t_1 * sin((30.0 * z))))) - 0.2));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * (y * cos((30.0 * z))))) + (30.0 * (z * t_1)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = 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_1 = cos(Float64(30.0 * x))
	tmp = 0.0
	if (fmax(t_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)) <= 4e+147)
		tmp = fmax(t_0, Float64(abs(Float64(sin(Float64(30.0 * x)) + Float64(t_1 * sin(Float64(30.0 * z))))) - 0.2));
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * Float64(y * cos(Float64(30.0 * z))))) + Float64(30.0 * Float64(z * t_1)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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$1 = N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[t$95$0, 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], 4e+147], N[Max[t$95$0, N[(N[Abs[N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(t$95$1 * N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * N[(y * N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(30.0 * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 3.9999999999999999e147

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   if 3.9999999999999999e147 < (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 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-cos.f64 N/A

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

       4. lower-*.f64 83.8%

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

   13. Applied rewrites 83.8%

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

Alternative 3: 88.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 4 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z \cdot z, 900, \mathsf{fma}\left(x \cdot x, 900, \left(y \cdot y\right) \cdot 900\right)\right)} - 25, \left|\mathsf{fma}\left(\cos \left(-30 \cdot x\right), t\_0, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot \left(y \cdot \cos \left(30 \cdot z\right)\right)\right) + 30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 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 (cos (* x 30.0)))))
          0.2))
        4e+147)
     (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 y) 25.0)
      (-
       (fabs
        (+
         (fma 30.0 x (* 30.0 (* y (cos (* 30.0 z)))))
         (* 30.0 (* z (cos (* 30.0 x))))))
       0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 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 * cos((x * 30.0))))) - 0.2)) <= 4e+147) {
		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 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * (y * cos((30.0 * z))))) + (30.0 * (z * cos((30.0 * x)))))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 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)))) + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2)) <= 4e+147)
		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(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * Float64(y * cos(Float64(30.0 * z))))) + Float64(30.0 * Float64(z * cos(Float64(30.0 * x)))))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 4e+147], 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[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * N[(y * N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(30.0 * N[(z * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 3.9999999999999999e147

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   6. Applied rewrites 45.6%

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

   if 3.9999999999999999e147 < (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 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-cos.f64 N/A

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

       4. lower-*.f64 83.8%

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

   13. Applied rewrites 83.8%

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

Alternative 4: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25\\ \mathbf{if}\;\mathsf{max}\left(t\_0, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 4 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot \left(y \cdot \cos \left(30 \cdot z\right)\right)\right) + 30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)))
   (if (<=
        (fmax
         t_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))
        4e+147)
     (fmax t_0 (- (fabs (+ (sin (* 30.0 z)) (* 30.0 x))) 0.2))
     (fmax
      (- (* -30.0 y) 25.0)
      (-
       (fabs
        (+
         (fma 30.0 x (* 30.0 (* y (cos (* 30.0 z)))))
         (* 30.0 (* z (cos (* 30.0 x))))))
       0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = 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_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)) <= 4e+147) {
		tmp = fmax(t_0, (fabs((sin((30.0 * z)) + (30.0 * x))) - 0.2));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * (y * cos((30.0 * z))))) + (30.0 * (z * cos((30.0 * x)))))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = 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_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)) <= 4e+147)
		tmp = fmax(t_0, Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * Float64(y * cos(Float64(30.0 * z))))) + Float64(30.0 * Float64(z * cos(Float64(30.0 * x)))))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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$0, 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], 4e+147], N[Max[t$95$0, N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * N[(y * N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(30.0 * N[(z * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 3.9999999999999999e147

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   if 3.9999999999999999e147 < (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 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-cos.f64 N/A

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

       4. lower-*.f64 83.8%

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

   13. Applied rewrites 83.8%

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

Alternative 5: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 4 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)} \cdot \sqrt{900} - 25, \left|\mathsf{fma}\left(30, x, t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot \left(y \cdot \cos \left(30 \cdot z\right)\right)\right) + 30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 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 (cos (* x 30.0)))))
          0.2))
        4e+147)
     (fmax
      (- (* (sqrt (fma z z (fma y y (* x x)))) (sqrt 900.0)) 25.0)
      (- (fabs (fma 30.0 x t_0)) 0.2))
     (fmax
      (- (* -30.0 y) 25.0)
      (-
       (fabs
        (+
         (fma 30.0 x (* 30.0 (* y (cos (* 30.0 z)))))
         (* 30.0 (* z (cos (* 30.0 x))))))
       0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 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 * cos((x * 30.0))))) - 0.2)) <= 4e+147) {
		tmp = fmax(((sqrt(fma(z, z, fma(y, y, (x * x)))) * sqrt(900.0)) - 25.0), (fabs(fma(30.0, x, t_0)) - 0.2));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * (y * cos((30.0 * z))))) + (30.0 * (z * cos((30.0 * x)))))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 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)))) + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2)) <= 4e+147)
		tmp = fmax(Float64(Float64(sqrt(fma(z, z, fma(y, y, Float64(x * x)))) * sqrt(900.0)) - 25.0), Float64(abs(fma(30.0, x, t_0)) - 0.2));
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * Float64(y * cos(Float64(30.0 * z))))) + Float64(30.0 * Float64(z * cos(Float64(30.0 * x)))))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 4e+147], N[Max[N[(N[(N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[900.0], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * N[(y * N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(30.0 * N[(z * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 3.9999999999999999e147

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

       1. lift-sqrt.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. sqrt-prod N/A

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

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

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

       6. lower-unsound-sqrt.f64 N/A

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

       7. lower-unsound-sqrt.f64 45.6%

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

   11. Applied rewrites 45.6%

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

   if 3.9999999999999999e147 < (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 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-cos.f64 N/A

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

       4. lower-*.f64 83.8%

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

   13. Applied rewrites 83.8%

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

Alternative 6: 86.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{max}\left({\left(e^{0.25 \cdot \left(\log 900 + -2 \cdot \log \left(\frac{-1}{z}\right)\right)}\right)}^{2} - 25, t\_0\right)\\ \mathbf{elif}\;z \leq -80:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(900, {y}^{2}, 900 \cdot {z}^{2}\right)} - 25, t\_0\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot y\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left({\left(e^{0.25 \cdot \left(\log 900 + -2 \cdot \log \left(\frac{1}{z}\right)\right)}\right)}^{2} - 25, t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (+ (sin (* 30.0 z)) (* 30.0 x))) 0.2)))
   (if (<= z -1.08e+143)
     (fmax
      (-
       (pow (exp (* 0.25 (+ (log 900.0) (* -2.0 (log (/ -1.0 z)))))) 2.0)
       25.0)
      t_0)
     (if (<= z -80.0)
       (fmax (- (sqrt (fma 900.0 (pow y 2.0) (* 900.0 (pow z 2.0)))) 25.0) t_0)
       (if (<= z 2.3e+93)
         (fmax
          (- (* -30.0 y) 25.0)
          (-
           (fabs
            (+ (fma 30.0 x (* 30.0 y)) (* (sin (* z 30.0)) (cos (* x 30.0)))))
           0.2))
         (fmax
          (-
           (pow (exp (* 0.25 (+ (log 900.0) (* -2.0 (log (/ 1.0 z)))))) 2.0)
           25.0)
          t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((sin((30.0 * z)) + (30.0 * x))) - 0.2;
	double tmp;
	if (z <= -1.08e+143) {
		tmp = fmax((pow(exp((0.25 * (log(900.0) + (-2.0 * log((-1.0 / z)))))), 2.0) - 25.0), t_0);
	} else if (z <= -80.0) {
		tmp = fmax((sqrt(fma(900.0, pow(y, 2.0), (900.0 * pow(z, 2.0)))) - 25.0), t_0);
	} else if (z <= 2.3e+93) {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * y)) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2));
	} else {
		tmp = fmax((pow(exp((0.25 * (log(900.0) + (-2.0 * log((1.0 / z)))))), 2.0) - 25.0), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (z <= -1.08e+143)
		tmp = fmax(Float64((exp(Float64(0.25 * Float64(log(900.0) + Float64(-2.0 * log(Float64(-1.0 / z)))))) ^ 2.0) - 25.0), t_0);
	elseif (z <= -80.0)
		tmp = fmax(Float64(sqrt(fma(900.0, (y ^ 2.0), Float64(900.0 * (z ^ 2.0)))) - 25.0), t_0);
	elseif (z <= 2.3e+93)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2));
	else
		tmp = fmax(Float64((exp(Float64(0.25 * Float64(log(900.0) + Float64(-2.0 * log(Float64(1.0 / z)))))) ^ 2.0) - 25.0), t_0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -1.08e+143], N[Max[N[(N[Power[N[Exp[N[(0.25 * N[(N[Log[900.0], $MachinePrecision] + N[(-2.0 * N[Log[N[(-1.0 / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, -80.0], N[Max[N[(N[Sqrt[N[(900.0 * N[Power[y, 2.0], $MachinePrecision] + N[(900.0 * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 2.3e+93], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * y), $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], N[Max[N[(N[Power[N[Exp[N[(0.25 * N[(N[Log[900.0], $MachinePrecision] + N[(-2.0 * N[Log[N[(1.0 / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0799999999999999e143

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 44.9%

      \[\leadsto \mathsf{max}\left(\color{blue}{{\left(900 \cdot \mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{\left(\frac{0.5}{2}\right)} \cdot {\left(900 \cdot \mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{\left(\frac{0.5}{2}\right)}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]

   10. Taylor expanded in z around -inf

       \[\leadsto \mathsf{max}\left(\color{blue}{{\left(e^{\frac{1}{4} \cdot \left(\log 900 + -2 \cdot \log \left(\frac{-1}{z}\right)\right)}\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
   11. Step-by-step derivation

       1. metadata-eval N/A

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

       2. lower-pow.f64 N/A

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

   12. Applied rewrites 54.7%

       \[\leadsto \mathsf{max}\left(\color{blue}{{\left(e^{0.25 \cdot \left(\log 900 + -2 \cdot \log \left(\frac{-1}{z}\right)\right)}\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]

   if -1.0799999999999999e143 < z < -80

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {y}^{2} + 900 \cdot {z}^{2}}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 57.7%

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

   10. Applied rewrites 57.7%

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

   if -80 < z < 2.3000000000000002e93

   1. Initial program 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 69.8%

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

   13. Applied rewrites 69.8%

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

   if 2.3000000000000002e93 < z

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 44.9%

      \[\leadsto \mathsf{max}\left(\color{blue}{{\left(900 \cdot \mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{\left(\frac{0.5}{2}\right)} \cdot {\left(900 \cdot \mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{\left(\frac{0.5}{2}\right)}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]

   10. Taylor expanded in z around inf

       \[\leadsto \mathsf{max}\left(\color{blue}{{\left(e^{\frac{1}{4} \cdot \left(\log 900 + -2 \cdot \log \left(\frac{1}{z}\right)\right)}\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
   11. Step-by-step derivation

       1. metadata-eval N/A

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

       2. lower-pow.f64 N/A

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

   12. Applied rewrites 54.4%

       \[\leadsto \mathsf{max}\left(\color{blue}{{\left(e^{0.25 \cdot \left(\log 900 + -2 \cdot \log \left(\frac{1}{z}\right)\right)}\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 84.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} t_0 := \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\\ t_1 := \sin \left(z \cdot 30\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{max}\left({\left(e^{0.25 \cdot \left(\log 900 + -2 \cdot \log \left(\frac{-1}{z}\right)\right)}\right)}^{2} - 25, t\_0\right)\\ \mathbf{elif}\;z \leq -80:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(900, {y}^{2}, 900 \cdot {z}^{2}\right)} - 25, t\_0\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot y\right) + t\_1 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\left(\left|z\right| \cdot 30\right) \cdot \sqrt{1 - \left(-\frac{\mathsf{fma}\left(y, y, x \cdot x\right)}{z \cdot z}\right)} - 25, \left|\mathsf{fma}\left(30, x, t\_1\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (+ (sin (* 30.0 z)) (* 30.0 x))) 0.2))
        (t_1 (sin (* z 30.0))))
   (if (<= z -1.08e+143)
     (fmax
      (-
       (pow (exp (* 0.25 (+ (log 900.0) (* -2.0 (log (/ -1.0 z)))))) 2.0)
       25.0)
      t_0)
     (if (<= z -80.0)
       (fmax (- (sqrt (fma 900.0 (pow y 2.0) (* 900.0 (pow z 2.0)))) 25.0) t_0)
       (if (<= z 2.3e+93)
         (fmax
          (- (* -30.0 y) 25.0)
          (- (fabs (+ (fma 30.0 x (* 30.0 y)) (* t_1 (cos (* x 30.0))))) 0.2))
         (fmax
          (-
           (*
            (* (fabs z) 30.0)
            (sqrt (- 1.0 (- (/ (fma y y (* x x)) (* z z))))))
           25.0)
          (- (fabs (fma 30.0 x t_1)) 0.2)))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((sin((30.0 * z)) + (30.0 * x))) - 0.2;
	double t_1 = sin((z * 30.0));
	double tmp;
	if (z <= -1.08e+143) {
		tmp = fmax((pow(exp((0.25 * (log(900.0) + (-2.0 * log((-1.0 / z)))))), 2.0) - 25.0), t_0);
	} else if (z <= -80.0) {
		tmp = fmax((sqrt(fma(900.0, pow(y, 2.0), (900.0 * pow(z, 2.0)))) - 25.0), t_0);
	} else if (z <= 2.3e+93) {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * y)) + (t_1 * cos((x * 30.0))))) - 0.2));
	} else {
		tmp = fmax((((fabs(z) * 30.0) * sqrt((1.0 - -(fma(y, y, (x * x)) / (z * z))))) - 25.0), (fabs(fma(30.0, x, t_1)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * x))) - 0.2)
	t_1 = sin(Float64(z * 30.0))
	tmp = 0.0
	if (z <= -1.08e+143)
		tmp = fmax(Float64((exp(Float64(0.25 * Float64(log(900.0) + Float64(-2.0 * log(Float64(-1.0 / z)))))) ^ 2.0) - 25.0), t_0);
	elseif (z <= -80.0)
		tmp = fmax(Float64(sqrt(fma(900.0, (y ^ 2.0), Float64(900.0 * (z ^ 2.0)))) - 25.0), t_0);
	elseif (z <= 2.3e+93)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + Float64(t_1 * cos(Float64(x * 30.0))))) - 0.2));
	else
		tmp = fmax(Float64(Float64(Float64(abs(z) * 30.0) * sqrt(Float64(1.0 - Float64(-Float64(fma(y, y, Float64(x * x)) / Float64(z * z)))))) - 25.0), Float64(abs(fma(30.0, x, t_1)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1.08e+143], N[Max[N[(N[Power[N[Exp[N[(0.25 * N[(N[Log[900.0], $MachinePrecision] + N[(-2.0 * N[Log[N[(-1.0 / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, -80.0], N[Max[N[(N[Sqrt[N[(900.0 * N[Power[y, 2.0], $MachinePrecision] + N[(900.0 * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 2.3e+93], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * y), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(N[(N[Abs[z], $MachinePrecision] * 30.0), $MachinePrecision] * N[Sqrt[N[(1.0 - (-N[(N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + t$95$1), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0799999999999999e143

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 44.9%

      \[\leadsto \mathsf{max}\left(\color{blue}{{\left(900 \cdot \mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{\left(\frac{0.5}{2}\right)} \cdot {\left(900 \cdot \mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)\right)}^{\left(\frac{0.5}{2}\right)}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]

   10. Taylor expanded in z around -inf

       \[\leadsto \mathsf{max}\left(\color{blue}{{\left(e^{\frac{1}{4} \cdot \left(\log 900 + -2 \cdot \log \left(\frac{-1}{z}\right)\right)}\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
   11. Step-by-step derivation

       1. metadata-eval N/A

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

       2. lower-pow.f64 N/A

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

   12. Applied rewrites 54.7%

       \[\leadsto \mathsf{max}\left(\color{blue}{{\left(e^{0.25 \cdot \left(\log 900 + -2 \cdot \log \left(\frac{-1}{z}\right)\right)}\right)}^{2}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]

   if -1.0799999999999999e143 < z < -80

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {y}^{2} + 900 \cdot {z}^{2}}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 57.7%

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

   10. Applied rewrites 57.7%

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

   if -80 < z < 2.3000000000000002e93

   1. Initial program 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 69.8%

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

   13. Applied rewrites 69.8%

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

   if 2.3000000000000002e93 < z

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

       1. lift-sqrt.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. distribute-lft-in N/A

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

       6. lift-*.f64 N/A

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

       7. metadata-eval N/A

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

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

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

       9. lift-*.f64 N/A

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

       10. sub-to-mult-rev N/A

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

       11. lift-/.f64 N/A

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

       12. lift--.f64 N/A

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

       13. *-commutative N/A

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

       14. sqrt-prod N/A

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

   11. Applied rewrites 45.2%

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

Alternative 8: 81.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \mathsf{max}\left(\left(\left|z\right| \cdot 30\right) \cdot \sqrt{1 - \left(-\frac{\mathsf{fma}\left(y, y, x \cdot x\right)}{z \cdot z}\right)} - 25, \left|\mathsf{fma}\left(30, x, t\_0\right)\right| - 0.2\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot y\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1
         (fmax
          (-
           (*
            (* (fabs z) 30.0)
            (sqrt (- 1.0 (- (/ (fma y y (* x x)) (* z z))))))
           25.0)
          (- (fabs (fma 30.0 x t_0)) 0.2))))
   (if (<= z -3.9e+52)
     t_1
     (if (<= z 2.3e+93)
       (fmax
        (- (* -30.0 y) 25.0)
        (- (fabs (+ (fma 30.0 x (* 30.0 y)) (* t_0 (cos (* x 30.0))))) 0.2))
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fmax((((fabs(z) * 30.0) * sqrt((1.0 - -(fma(y, y, (x * x)) / (z * z))))) - 25.0), (fabs(fma(30.0, x, t_0)) - 0.2));
	double tmp;
	if (z <= -3.9e+52) {
		tmp = t_1;
	} else if (z <= 2.3e+93) {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((fma(30.0, x, (30.0 * y)) + (t_0 * cos((x * 30.0))))) - 0.2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = fmax(Float64(Float64(Float64(abs(z) * 30.0) * sqrt(Float64(1.0 - Float64(-Float64(fma(y, y, Float64(x * x)) / Float64(z * z)))))) - 25.0), Float64(abs(fma(30.0, x, t_0)) - 0.2))
	tmp = 0.0
	if (z <= -3.9e+52)
		tmp = t_1;
	elseif (z <= 2.3e+93)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(fma(30.0, x, Float64(30.0 * y)) + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2));
	else
		tmp = t_1;
	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[Max[N[(N[(N[(N[Abs[z], $MachinePrecision] * 30.0), $MachinePrecision] * N[Sqrt[N[(1.0 - (-N[(N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -3.9e+52], t$95$1, If[LessEqual[z, 2.3e+93], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(30.0 * x + N[(30.0 * y), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e52 or 2.3000000000000002e93 < z

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

       1. lift-sqrt.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. distribute-lft-in N/A

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

       6. lift-*.f64 N/A

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

       7. metadata-eval N/A

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

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

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

       9. lift-*.f64 N/A

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

       10. sub-to-mult-rev N/A

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

       11. lift-/.f64 N/A

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

       12. lift--.f64 N/A

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

       13. *-commutative N/A

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

       14. sqrt-prod N/A

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

   11. Applied rewrites 45.2%

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

   if -3.9e52 < z < 2.3000000000000002e93

   1. Initial program 45.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-*.f64 29.7%

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

   4. Applied rewrites 29.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-*.f64 48.4%

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-cos.f64 N/A

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

      5. lower-*.f64 65.7%

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 69.8%

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

   13. Applied rewrites 69.8%

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

Alternative 9: 73.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\left(\left|z\right| \cdot 30\right) \cdot \sqrt{1 - \left(-\frac{\mathsf{fma}\left(y, y, x \cdot x\right)}{z \cdot z}\right)} - 25, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+146}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(900, {y}^{2}, 900 \cdot {z}^{2}\right)} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fmax
          (-
           (*
            (* (fabs z) 30.0)
            (sqrt (- 1.0 (- (/ (fma y y (* x x)) (* z z))))))
           25.0)
          (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2))))
   (if (<= z -5e+141)
     t_0
     (if (<= z 1.22e+146)
       (fmax
        (- (sqrt (fma 900.0 (pow y 2.0) (* 900.0 (pow z 2.0)))) 25.0)
        (- (fabs (+ (sin (* 30.0 z)) (* 30.0 x))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((((fabs(z) * 30.0) * sqrt((1.0 - -(fma(y, y, (x * x)) / (z * z))))) - 25.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	double tmp;
	if (z <= -5e+141) {
		tmp = t_0;
	} else if (z <= 1.22e+146) {
		tmp = fmax((sqrt(fma(900.0, pow(y, 2.0), (900.0 * pow(z, 2.0)))) - 25.0), (fabs((sin((30.0 * z)) + (30.0 * x))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(Float64(Float64(abs(z) * 30.0) * sqrt(Float64(1.0 - Float64(-Float64(fma(y, y, Float64(x * x)) / Float64(z * z)))))) - 25.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2))
	tmp = 0.0
	if (z <= -5e+141)
		tmp = t_0;
	elseif (z <= 1.22e+146)
		tmp = fmax(Float64(sqrt(fma(900.0, (y ^ 2.0), Float64(900.0 * (z ^ 2.0)))) - 25.0), Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * x))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(N[(N[(N[Abs[z], $MachinePrecision] * 30.0), $MachinePrecision] * N[Sqrt[N[(1.0 - (-N[(N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -5e+141], t$95$0, If[LessEqual[z, 1.22e+146], N[Max[N[(N[Sqrt[N[(900.0 * N[Power[y, 2.0], $MachinePrecision] + N[(900.0 * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000003e141 or 1.2199999999999999e146 < z

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

       1. lift-sqrt.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. distribute-lft-in N/A

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

       6. lift-*.f64 N/A

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

       7. metadata-eval N/A

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

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

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

       9. lift-*.f64 N/A

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

       10. sub-to-mult-rev N/A

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

       11. lift-/.f64 N/A

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

       12. lift--.f64 N/A

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

       13. *-commutative N/A

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

       14. sqrt-prod N/A

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

   11. Applied rewrites 45.2%

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

   if -5.0000000000000003e141 < z < 1.2199999999999999e146

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {y}^{2} + 900 \cdot {z}^{2}}} - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 57.7%

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

   10. Applied rewrites 57.7%

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

Alternative 10: 67.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} t_0 := \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\\ t_1 := \mathsf{max}\left(\left(\left|z\right| \cdot 30\right) \cdot \sqrt{1 - \left(-\frac{\mathsf{fma}\left(y, y, x \cdot x\right)}{z \cdot z}\right)} - 25, t\_0\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot {y}^{2}} - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2))
        (t_1
         (fmax
          (-
           (*
            (* (fabs z) 30.0)
            (sqrt (- 1.0 (- (/ (fma y y (* x x)) (* z z))))))
           25.0)
          t_0)))
   (if (<= z -3.9e+52)
     t_1
     (if (<= z 2.05e+91)
       (fmax (- (sqrt (* 900.0 (pow y 2.0))) 25.0) t_0)
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2;
	double t_1 = fmax((((fabs(z) * 30.0) * sqrt((1.0 - -(fma(y, y, (x * x)) / (z * z))))) - 25.0), t_0);
	double tmp;
	if (z <= -3.9e+52) {
		tmp = t_1;
	} else if (z <= 2.05e+91) {
		tmp = fmax((sqrt((900.0 * pow(y, 2.0))) - 25.0), t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2)
	t_1 = fmax(Float64(Float64(Float64(abs(z) * 30.0) * sqrt(Float64(1.0 - Float64(-Float64(fma(y, y, Float64(x * x)) / Float64(z * z)))))) - 25.0), t_0)
	tmp = 0.0
	if (z <= -3.9e+52)
		tmp = t_1;
	elseif (z <= 2.05e+91)
		tmp = fmax(Float64(sqrt(Float64(900.0 * (y ^ 2.0))) - 25.0), t_0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$1 = N[Max[N[(N[(N[(N[Abs[z], $MachinePrecision] * 30.0), $MachinePrecision] * N[Sqrt[N[(1.0 - (-N[(N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]}, If[LessEqual[z, -3.9e+52], t$95$1, If[LessEqual[z, 2.05e+91], N[Max[N[(N[Sqrt[N[(900.0 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e52 or 2.0500000000000001e91 < z

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

       1. lift-sqrt.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. distribute-lft-in N/A

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

       6. lift-*.f64 N/A

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

       7. metadata-eval N/A

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

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

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

       9. lift-*.f64 N/A

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

       10. sub-to-mult-rev N/A

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

       11. lift-/.f64 N/A

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

       12. lift--.f64 N/A

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

       13. *-commutative N/A

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

       14. sqrt-prod N/A

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

   11. Applied rewrites 45.2%

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

   if -3.9e52 < z < 2.0500000000000001e91

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

   10. Taylor expanded in y around inf

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

       1. lower-*.f64 N/A

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

       2. lower-pow.f64 50.7%

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

   12. Applied rewrites 50.7%

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

Alternative 11: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \left|\mathsf{fma}\left(30, x, t\_0\right)\right| - 0.2\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 4 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(z, z, \mathsf{fma}\left(y, y, x \cdot x\right)\right)} \cdot \sqrt{900} - 25, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot {y}^{2}} - 25, t\_1\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))) (t_1 (- (fabs (fma 30.0 x t_0)) 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))))
            (* t_0 (cos (* x 30.0)))))
          0.2))
        4e+149)
     (fmax (- (* (sqrt (fma z z (fma y y (* x x)))) (sqrt 900.0)) 25.0) t_1)
     (fmax (- (sqrt (* 900.0 (pow y 2.0))) 25.0) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fabs(fma(30.0, x, t_0)) - 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)))) + (t_0 * cos((x * 30.0))))) - 0.2)) <= 4e+149) {
		tmp = fmax(((sqrt(fma(z, z, fma(y, y, (x * x)))) * sqrt(900.0)) - 25.0), t_1);
	} else {
		tmp = fmax((sqrt((900.0 * pow(y, 2.0))) - 25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = Float64(abs(fma(30.0, x, t_0)) - 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(t_0 * cos(Float64(x * 30.0))))) - 0.2)) <= 4e+149)
		tmp = fmax(Float64(Float64(sqrt(fma(z, z, fma(y, y, Float64(x * x)))) * sqrt(900.0)) - 25.0), t_1);
	else
		tmp = fmax(Float64(sqrt(Float64(900.0 * (y ^ 2.0))) - 25.0), t_1);
	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[(N[Abs[N[(30.0 * x + t$95$0), $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[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 4e+149], N[Max[N[(N[(N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[900.0], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], N[Max[N[(N[Sqrt[N[(900.0 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $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))) < 4.0000000000000002e149

   1. Initial program 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

       1. lift-sqrt.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. sqrt-prod N/A

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

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

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

       6. lower-unsound-sqrt.f64 N/A

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

       7. lower-unsound-sqrt.f64 45.6%

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

   11. Applied rewrites 45.6%

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

   if 4.0000000000000002e149 < (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 45.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 45.1%

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

   7. Applied rewrites 45.1%

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

   9. Applied rewrites 45.0%

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

   10. Taylor expanded in y around inf

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

       1. lower-*.f64 N/A

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

       2. lower-pow.f64 50.7%

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

   12. Applied rewrites 50.7%

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

Alternative 12: 45.6% accurate, 4.3× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (* (sqrt (fma z z (fma y y (* x x)))) (sqrt 900.0)) 25.0)
  (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax(((sqrt(fma(z, z, fma(y, y, (x * x)))) * sqrt(900.0)) - 25.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(Float64(Float64(sqrt(fma(z, z, fma(y, y, Float64(x * x)))) * sqrt(900.0)) - 25.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[(N[Sqrt[N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[900.0], $MachinePrecision]), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 45.9%

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

2. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
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 45.6%

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

4. Applied rewrites 45.6%

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

5. Taylor expanded in x around 0

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

   1. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 45.1%

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

7. Applied rewrites 45.1%

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

9. Applied rewrites 45.0%

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

    1. lift-sqrt.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. *-commutative N/A

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

    4. sqrt-prod N/A

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

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

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

    6. lower-unsound-sqrt.f64 N/A

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

    7. lower-unsound-sqrt.f64 45.6%

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

11. Applied rewrites 45.6%

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

Alternative 13: 45.0% accurate, 4.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (sqrt (* 900.0 (fma y y (fma x x (* z z))))) 25.0)
  (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((sqrt((900.0 * fma(y, y, fma(x, x, (z * z))))) - 25.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(Float64(sqrt(Float64(900.0 * fma(y, y, fma(x, x, Float64(z * z))))) - 25.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(900.0 * N[(y * y + N[(x * x + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 45.9%

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

2. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
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 45.6%

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

4. Applied rewrites 45.6%

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

5. Taylor expanded in x around 0

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

   1. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 45.1%

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

7. Applied rewrites 45.1%

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

9. Applied rewrites 45.0%

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

    1. lift-fma.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. +-commutative N/A

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

    4. lift-fma.f64 N/A

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

    5. associate-+l+ N/A

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

    6. lower-fma.f64 N/A

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

    7. lift-*.f64 N/A

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

    8. lower-fma.f64 45.0%

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

11. Applied rewrites 45.0%

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

Alternative 14: 44.5% accurate, 8.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (- (sqrt (* 900.0 (fma z z (fma y y (* x x))))) 25.0)
  (- (fabs (fma 30.0 x (* 30.0 z))) 0.2)))

C

double code(double x, double y, double z) {
	return fmax((sqrt((900.0 * fma(z, z, fma(y, y, (x * x))))) - 25.0), (fabs(fma(30.0, x, (30.0 * z))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(Float64(sqrt(Float64(900.0 * fma(z, z, fma(y, y, Float64(x * x))))) - 25.0), Float64(abs(fma(30.0, x, Float64(30.0 * z))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(900.0 * N[(z * z + N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 45.9%

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

2. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot x\right) + \cos \left(30 \cdot x\right) \cdot \sin \left(30 \cdot z\right)}\right| - 0.2\right) \]
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 45.6%

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

4. Applied rewrites 45.6%

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

5. Taylor expanded in x around 0

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

   1. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 45.1%

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

7. Applied rewrites 45.1%

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

9. Applied rewrites 45.0%

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

10. Taylor expanded in z around 0

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

    1. lower-fma.f64 N/A

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

    2. lower-*.f64 44.5%

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

12. Applied rewrites 44.5%

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

Reproduce

herbie shell --seed 2025207 
(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)))