Gyroid sphere

Percentage Accurate: 46.6% → 71.6%

Time: 5.0s

Alternatives: 7

Speedup: 18.2×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 46.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(z \cdot 30\right)\\ t_1 := \sin \left(30 \cdot x\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, \left|t\_1\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot z, \left|\mathsf{fma}\left(t\_0 \cdot y, 30, t\_1\right) + \frac{\mathsf{fma}\left(\sin \left(-30 \cdot x\right), t\_0, \cos \left(-30 \cdot x\right) \cdot \sin \left(z \cdot 30\right)\right) + \sin \left(\mathsf{fma}\left(z, 30, 30 \cdot x\right)\right)}{2}\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (cos (* z 30.0))) (t_1 (sin (* 30.0 x))))
   (if (<= z -1.6e+72)
     (fmax (* -30.0 z) (- (fabs t_1) 0.2))
     (if (<= z 7.5e+116)
       (fmax (- (* -30.0 y) 25.0) (- (fabs (* 30.0 x)) 0.2))
       (fmax
        (* 30.0 z)
        (-
         (fabs
          (+
           (fma (* t_0 y) 30.0 t_1)
           (/
            (+
             (fma (sin (* -30.0 x)) t_0 (* (cos (* -30.0 x)) (sin (* z 30.0))))
             (sin (fma z 30.0 (* 30.0 x))))
            2.0)))
         0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = cos((z * 30.0));
	double t_1 = sin((30.0 * x));
	double tmp;
	if (z <= -1.6e+72) {
		tmp = fmax((-30.0 * z), (fabs(t_1) - 0.2));
	} else if (z <= 7.5e+116) {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((30.0 * z), (fabs((fma((t_0 * y), 30.0, t_1) + ((fma(sin((-30.0 * x)), t_0, (cos((-30.0 * x)) * sin((z * 30.0)))) + sin(fma(z, 30.0, (30.0 * x)))) / 2.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = cos(Float64(z * 30.0))
	t_1 = sin(Float64(30.0 * x))
	tmp = 0.0
	if (z <= -1.6e+72)
		tmp = fmax(Float64(-30.0 * z), Float64(abs(t_1) - 0.2));
	elseif (z <= 7.5e+116)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(30.0 * z), Float64(abs(Float64(fma(Float64(t_0 * y), 30.0, t_1) + Float64(Float64(fma(sin(Float64(-30.0 * x)), t_0, Float64(cos(Float64(-30.0 * x)) * sin(Float64(z * 30.0)))) + sin(fma(z, 30.0, Float64(30.0 * x)))) / 2.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1.6e+72], N[Max[N[(-30.0 * z), $MachinePrecision], N[(N[Abs[t$95$1], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 7.5e+116], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(30.0 * z), $MachinePrecision], N[(N[Abs[N[(N[(N[(t$95$0 * y), $MachinePrecision] * 30.0 + t$95$1), $MachinePrecision] + N[(N[(N[(N[Sin[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * t$95$0 + N[(N[Cos[N[(-30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Sin[N[(z * 30.0 + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e72

   1. Initial program 24.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 24.1

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

   4. Applied rewrites 24.1%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 24.1

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

   7. Applied rewrites 24.1%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 67.2

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

   10. Applied rewrites 67.2%

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

   if -1.6000000000000001e72 < z < 7.5e116

   1. Initial program 60.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 59.4

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 58.9

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in y around -inf

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

      1. lower-*.f64 38.2

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

   10. Applied rewrites 38.2%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 72.6

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

   13. Applied rewrites 72.6%

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

   if 7.5e116 < z

   1. Initial program 19.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-cos.f64 N/A

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

      6. sin-cos-mult N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-sin.f64 N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 19.1

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

   3. Applied rewrites 19.1%

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. sin-sum N/A

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

      10. metadata-eval N/A

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

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

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

      12. metadata-eval N/A

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

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

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

      14. cos-neg-rev N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. sin-cos-mult-rev N/A

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

   5. Applied rewrites 19.1%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-*.f64 19.1

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

   8. Applied rewrites 19.1%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 73.2

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

   11. Applied rewrites 73.2%

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

Alternative 2: 71.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, t\_0\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= z -1.6e+72)
     (fmax (* -30.0 z) t_0)
     (if (<= z 2.55e+117)
       (fmax (- (* -30.0 y) 25.0) (- (fabs (* 30.0 x)) 0.2))
       (fmax (* z 30.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -1.6e+72) {
		tmp = fmax((-30.0 * z), t_0);
	} else if (z <= 2.55e+117) {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((z * 30.0), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(sin((30.0d0 * x))) - 0.2d0
    if (z <= (-1.6d+72)) then
        tmp = fmax(((-30.0d0) * z), t_0)
    else if (z <= 2.55d+117) then
        tmp = fmax((((-30.0d0) * y) - 25.0d0), (abs((30.0d0 * x)) - 0.2d0))
    else
        tmp = fmax((z * 30.0d0), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(Math.sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -1.6e+72) {
		tmp = fmax((-30.0 * z), t_0);
	} else if (z <= 2.55e+117) {
		tmp = fmax(((-30.0 * y) - 25.0), (Math.abs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((z * 30.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if z <= -1.6e+72:
		tmp = fmax((-30.0 * z), t_0)
	elif z <= 2.55e+117:
		tmp = fmax(((-30.0 * y) - 25.0), (math.fabs((30.0 * x)) - 0.2))
	else:
		tmp = fmax((z * 30.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (z <= -1.6e+72)
		tmp = fmax(Float64(-30.0 * z), t_0);
	elseif (z <= 2.55e+117)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(z * 30.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (z <= -1.6e+72)
		tmp = max((-30.0 * z), t_0);
	elseif (z <= 2.55e+117)
		tmp = max(((-30.0 * y) - 25.0), (abs((30.0 * x)) - 0.2));
	else
		tmp = max((z * 30.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -1.6e+72], N[Max[N[(-30.0 * z), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 2.55e+117], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * 30.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e72

   1. Initial program 24.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 24.1

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

   4. Applied rewrites 24.1%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 24.1

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

   7. Applied rewrites 24.1%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 67.2

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

   10. Applied rewrites 67.2%

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

   if -1.6000000000000001e72 < z < 2.5499999999999998e117

   1. Initial program 60.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 59.4

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 58.9

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in y around -inf

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

      1. lower-*.f64 38.2

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

   10. Applied rewrites 38.2%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 72.6

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

   13. Applied rewrites 72.6%

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

   if 2.5499999999999998e117 < z

   1. Initial program 19.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 19.0

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

   4. Applied rewrites 19.0%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 19.0

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

   7. Applied rewrites 19.0%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 70.7

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

   10. Applied rewrites 70.7%

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

Alternative 3: 64.9% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.5e+122)
   (fmax (- (* -30.0 y) 25.0) (- (fabs (* 30.0 x)) 0.2))
   (fmax (* y 30.0) (- (fabs (sin (* 30.0 x))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5e+122) {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), (fabs(sin((30.0 * x))) - 0.2));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 5.5d+122) then
        tmp = fmax((((-30.0d0) * y) - 25.0d0), (abs((30.0d0 * x)) - 0.2d0))
    else
        tmp = fmax((y * 30.0d0), (abs(sin((30.0d0 * x))) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5e+122) {
		tmp = fmax(((-30.0 * y) - 25.0), (Math.abs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), (Math.abs(Math.sin((30.0 * x))) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.5e+122:
		tmp = fmax(((-30.0 * y) - 25.0), (math.fabs((30.0 * x)) - 0.2))
	else:
		tmp = fmax((y * 30.0), (math.fabs(math.sin((30.0 * x))) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.5e+122)
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.5e+122)
		tmp = max(((-30.0 * y) - 25.0), (abs((30.0 * x)) - 0.2));
	else
		tmp = max((y * 30.0), (abs(sin((30.0 * x))) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.5e+122], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.4999999999999998e122

   1. Initial program 51.4%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 51.0

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

   4. Applied rewrites 51.0%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 50.6

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

   7. Applied rewrites 50.6%

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

   8. Taylor expanded in y around -inf

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

      1. lower-*.f64 33.4

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

   10. Applied rewrites 33.4%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 63.5

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

   13. Applied rewrites 63.5%

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

   if 5.4999999999999998e122 < y

   1. Initial program 18.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 18.3

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

   4. Applied rewrites 18.3%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 18.3

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

   7. Applied rewrites 18.3%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 72.8

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

   10. Applied rewrites 72.8%

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

Alternative 4: 64.2% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|30 \cdot x\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6e+72)
   (fmax (* -30.0 z) (- (fabs (sin (* 30.0 x))) 0.2))
   (fmax (- (* -30.0 y) 25.0) (- (fabs (* 30.0 x)) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e+72) {
		tmp = fmax((-30.0 * z), (fabs(sin((30.0 * x))) - 0.2));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.6d+72)) then
        tmp = fmax(((-30.0d0) * z), (abs(sin((30.0d0 * x))) - 0.2d0))
    else
        tmp = fmax((((-30.0d0) * y) - 25.0d0), (abs((30.0d0 * x)) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e+72) {
		tmp = fmax((-30.0 * z), (Math.abs(Math.sin((30.0 * x))) - 0.2));
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (Math.abs((30.0 * x)) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.6e+72:
		tmp = fmax((-30.0 * z), (math.fabs(math.sin((30.0 * x))) - 0.2))
	else:
		tmp = fmax(((-30.0 * y) - 25.0), (math.fabs((30.0 * x)) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.6e+72)
		tmp = fmax(Float64(-30.0 * z), Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.6e+72)
		tmp = max((-30.0 * z), (abs(sin((30.0 * x))) - 0.2));
	else
		tmp = max(((-30.0 * y) - 25.0), (abs((30.0 * x)) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.6e+72], N[Max[N[(-30.0 * z), $MachinePrecision], N[(N[Abs[N[Sin[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[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e72

   1. Initial program 24.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 24.1

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

   4. Applied rewrites 24.1%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 24.1

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

   7. Applied rewrites 24.1%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 67.2

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

   10. Applied rewrites 67.2%

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

   if -1.6000000000000001e72 < z

   1. Initial program 52.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 51.6

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

   4. Applied rewrites 51.6%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 51.2

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in y around -inf

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

      1. lower-*.f64 32.9

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

   10. Applied rewrites 32.9%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 63.4

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

   13. Applied rewrites 63.4%

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

Alternative 5: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|30 \cdot x\right| - 0.2\\ \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 2 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{900 \cdot \mathsf{fma}\left(x, x, z \cdot z\right)} - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (* 30.0 x)) 0.2)))
   (if (<=
        (fmax
         (-
          (sqrt
           (+
            (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
            (pow (* z 30.0) 2.0)))
          25.0)
         (-
          (fabs
           (+
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))
            (* (sin (* z 30.0)) (cos (* x 30.0)))))
          0.2))
        2e+153)
     (fmax (- (sqrt (* 900.0 (fma x x (* z z)))) 25.0) t_0)
     (fmax (- (* -30.0 y) 25.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((30.0 * x)) - 0.2;
	double tmp;
	if (fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (sin((z * 30.0)) * cos((x * 30.0))))) - 0.2)) <= 2e+153) {
		tmp = fmax((sqrt((900.0 * fma(x, x, (z * z)))) - 25.0), t_0);
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(30.0 * x)) - 0.2)
	tmp = 0.0
	if (fmax(Float64(sqrt(Float64(Float64((Float64(x * 30.0) ^ 2.0) + (Float64(y * 30.0) ^ 2.0)) + (Float64(z * 30.0) ^ 2.0))) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))))) - 0.2)) <= 2e+153)
		tmp = fmax(Float64(sqrt(Float64(900.0 * fma(x, x, Float64(z * z)))) - 25.0), t_0);
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), t_0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[N[Max[N[(N[Sqrt[N[(N[(N[Power[N[(x * 30.0), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(y * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[N[(z * 30.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], 2e+153], N[Max[N[(N[Sqrt[N[(900.0 * N[(x * x + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 2e153

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 98.3

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

   7. Applied rewrites 98.3%

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

   8. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. pow2 N/A

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

      4. lower-fma.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 74.3

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

   10. Applied rewrites 74.3%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 73.5

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

   13. Applied rewrites 73.5%

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

   if 2e153 < (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 8.7%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-sin.f64 N/A

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

      13. lift-*.f64 8.7

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

   4. Applied rewrites 8.7%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 8.7

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

   7. Applied rewrites 8.7%

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

   8. Taylor expanded in y around -inf

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

      1. lower-*.f64 19.7

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

   10. Applied rewrites 19.7%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 52.6

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

   13. Applied rewrites 52.6%

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

Alternative 6: 56.5% accurate, 18.2× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

public static double code(double x, double y, double z) {
	return fmax(((-30.0 * y) - 25.0), (Math.abs((30.0 * x)) - 0.2));
}

Python

def code(x, y, z):
	return fmax(((-30.0 * y) - 25.0), (math.fabs((30.0 * x)) - 0.2))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = max(((-30.0 * y) - 25.0), (abs((30.0 * x)) - 0.2));
end

Wolfram

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

Derivation

1. Initial program 46.6%

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

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-sin.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-cos.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lift-sin.f64 N/A

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

   13. lift-*.f64 46.2

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

4. Applied rewrites 46.2%

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

5. Taylor expanded in y around 0

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

   1. lift-sin.f64 N/A

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

   2. lift-*.f64 45.9

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

7. Applied rewrites 45.9%

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

8. Taylor expanded in y around -inf

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

   1. lower-*.f64 28.8

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

10. Applied rewrites 28.8%

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

11. Taylor expanded in x around 0

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

    1. lift-*.f64 56.5

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

13. Applied rewrites 56.5%

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

Alternative 7: 31.5% accurate, 21.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

public static double code(double x, double y, double z) {
	return fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
}

Python

def code(x, y, z):
	return fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 46.6%

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

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-sin.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-cos.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lift-sin.f64 N/A

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

   13. lift-*.f64 46.2

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

4. Applied rewrites 46.2%

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

5. Taylor expanded in y around 0

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

   1. lift-sin.f64 N/A

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

   2. lift-*.f64 45.9

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

7. Applied rewrites 45.9%

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

8. Taylor expanded in x around -inf

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

   1. lift-*.f64 17.1

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

10. Applied rewrites 17.1%

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

11. Taylor expanded in x around 0

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

    1. lift-*.f64 31.5

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

13. Applied rewrites 31.5%

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025120 
(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)))