Gyroid sphere

Percentage Accurate: 45.8% → 90.4%

Time: 5.8s

Alternatives: 14

Speedup: 7.4×

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: 45.8% 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: 90.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, z \cdot 30\right) - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1
         (fmax
          (- (hypot (* y 30.0) (* z 30.0)) 25.0)
          (- (fabs (fma t_0 (cos (* 30.0 x)) (sin (* 30.0 x)))) 0.2))))
   (if (<= z -1.85e+58)
     t_1
     (if (<= z 1.8e+17)
       (fmax
        (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
        (-
         (fabs
          (+
           (+
            (* (sin (* x 30.0)) (cos (* y 30.0)))
            (* (sin (* y 30.0)) (cos (* z 30.0))))
           (* t_0 (cos (* x 30.0)))))
         0.2))
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fmax((hypot((y * 30.0), (z * 30.0)) - 25.0), (fabs(fma(t_0, cos((30.0 * x)), sin((30.0 * x)))) - 0.2));
	double tmp;
	if (z <= -1.85e+58) {
		tmp = t_1;
	} else if (z <= 1.8e+17) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs((((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))) + (t_0 * cos((x * 30.0))))) - 0.2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = fmax(Float64(hypot(Float64(y * 30.0), Float64(z * 30.0)) - 25.0), Float64(abs(fma(t_0, cos(Float64(30.0 * x)), sin(Float64(30.0 * x)))) - 0.2))
	tmp = 0.0
	if (z <= -1.85e+58)
		tmp = t_1;
	elseif (z <= 1.8e+17)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))) + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1.85e+58], t$95$1, If[LessEqual[z, 1.8e+17], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e58 or 1.8e17 < z

   1. Initial program 30.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 40.3

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

   4. Applied rewrites 40.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 40.3

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

   7. Applied rewrites 40.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 82.0%

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

   if -1.8500000000000001e58 < z < 1.8e17

   1. Initial program 58.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 97.0

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

   4. Applied rewrites 97.0%

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

Alternative 2: 90.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\mathsf{fma}\left(\sin \left(z \cdot 30\right), \cos \left(30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\\ t_1 := \mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, z \cdot 30\right) - 25, t\_0\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs (fma (sin (* z 30.0)) (cos (* 30.0 x)) (sin (* 30.0 x))))
          0.2))
        (t_1 (fmax (- (hypot (* y 30.0) (* z 30.0)) 25.0) t_0)))
   (if (<= z -1.85e+58)
     t_1
     (if (<= z 1.8e+17)
       (fmax (- (hypot (* y 30.0) (* 30.0 x)) 25.0) t_0)
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(sin((z * 30.0)), cos((30.0 * x)), sin((30.0 * x)))) - 0.2;
	double t_1 = fmax((hypot((y * 30.0), (z * 30.0)) - 25.0), t_0);
	double tmp;
	if (z <= -1.85e+58) {
		tmp = t_1;
	} else if (z <= 1.8e+17) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(sin(Float64(z * 30.0)), cos(Float64(30.0 * x)), sin(Float64(30.0 * x)))) - 0.2)
	t_1 = fmax(Float64(hypot(Float64(y * 30.0), Float64(z * 30.0)) - 25.0), t_0)
	tmp = 0.0
	if (z <= -1.85e+58)
		tmp = t_1;
	elseif (z <= 1.8e+17)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), t_0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, Block[{t$95$1 = N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]}, If[LessEqual[z, -1.85e+58], t$95$1, If[LessEqual[z, 1.8e+17], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e58 or 1.8e17 < z

   1. Initial program 30.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 40.3

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

   4. Applied rewrites 40.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 40.3

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

   7. Applied rewrites 40.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 82.0%

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

   if -1.8500000000000001e58 < z < 1.8e17

   1. Initial program 58.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 97.0

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 96.6

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

   7. Applied rewrites 96.6%

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

Alternative 3: 90.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, z \cdot 30\right) - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(30 \cdot x\right), \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y, x\right) \cdot 30 - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1
         (fmax
          (- (hypot (* y 30.0) (* z 30.0)) 25.0)
          (- (fabs (fma t_0 (cos (* 30.0 x)) (sin (* 30.0 x)))) 0.2))))
   (if (<= z -1.85e+58)
     t_1
     (if (<= z 1.8e+17)
       (fmax
        (- (* (hypot y x) 30.0) 25.0)
        (- (fabs (fma (sin (* y 30.0)) (cos (* z 30.0)) t_0)) 0.2))
       t_1))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = fmax((hypot((y * 30.0), (z * 30.0)) - 25.0), (fabs(fma(t_0, cos((30.0 * x)), sin((30.0 * x)))) - 0.2));
	double tmp;
	if (z <= -1.85e+58) {
		tmp = t_1;
	} else if (z <= 1.8e+17) {
		tmp = fmax(((hypot(y, x) * 30.0) - 25.0), (fabs(fma(sin((y * 30.0)), cos((z * 30.0)), t_0)) - 0.2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = fmax(Float64(hypot(Float64(y * 30.0), Float64(z * 30.0)) - 25.0), Float64(abs(fma(t_0, cos(Float64(30.0 * x)), sin(Float64(30.0 * x)))) - 0.2))
	tmp = 0.0
	if (z <= -1.85e+58)
		tmp = t_1;
	elseif (z <= 1.8e+17)
		tmp = fmax(Float64(Float64(hypot(y, x) * 30.0) - 25.0), Float64(abs(fma(sin(Float64(y * 30.0)), cos(Float64(z * 30.0)), t_0)) - 0.2));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -1.85e+58], t$95$1, If[LessEqual[z, 1.8e+17], N[Max[N[(N[(N[Sqrt[y ^ 2 + x ^ 2], $MachinePrecision] * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e58 or 1.8e17 < z

   1. Initial program 30.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 40.3

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

   4. Applied rewrites 40.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 40.3

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

   7. Applied rewrites 40.3%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 82.0%

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

   if -1.8500000000000001e58 < z < 1.8e17

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 57.6

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

   4. Applied rewrites 57.6%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. +-commutative N/A

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

      10. unpow-prod-down N/A

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

      11. metadata-eval N/A

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

      12. unpow-prod-down N/A

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. unpow-prod-down N/A

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 N/A

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

      21. distribute-lft-out N/A

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

   6. Applied rewrites 57.6%

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

   7. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. lower-hypot.f64 96.5

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

   9. Applied rewrites 96.5%

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

Alternative 4: 86.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, \left|\sin \left(30 \cdot x\right) + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 4.6:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y, x\right) \cdot 30 - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), t\_0\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30, \left|\mathsf{fma}\left(30, x, t\_0\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))))
   (if (<= z -4.8e+159)
     (fmax
      (* -30.0 z)
      (- (fabs (+ (sin (* 30.0 x)) (* t_0 (cos (* x 30.0))))) 0.2))
     (if (<= z 4.6)
       (fmax
        (- (* (hypot y x) 30.0) 25.0)
        (- (fabs (fma (sin (* y 30.0)) (cos (* z 30.0)) t_0)) 0.2))
       (fmax (* z 30.0) (- (fabs (fma 30.0 x t_0)) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double tmp;
	if (z <= -4.8e+159) {
		tmp = fmax((-30.0 * z), (fabs((sin((30.0 * x)) + (t_0 * cos((x * 30.0))))) - 0.2));
	} else if (z <= 4.6) {
		tmp = fmax(((hypot(y, x) * 30.0) - 25.0), (fabs(fma(sin((y * 30.0)), cos((z * 30.0)), t_0)) - 0.2));
	} else {
		tmp = fmax((z * 30.0), (fabs(fma(30.0, x, t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	tmp = 0.0
	if (z <= -4.8e+159)
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(sin(Float64(30.0 * x)) + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2));
	elseif (z <= 4.6)
		tmp = fmax(Float64(Float64(hypot(y, x) * 30.0) - 25.0), Float64(abs(fma(sin(Float64(y * 30.0)), cos(Float64(z * 30.0)), t_0)) - 0.2));
	else
		tmp = fmax(Float64(z * 30.0), Float64(abs(fma(30.0, x, t_0)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -4.8e+159], N[Max[N[(-30.0 * z), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 4.6], N[Max[N[(N[(N[Sqrt[y ^ 2 + x ^ 2], $MachinePrecision] * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * 30.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e159

   1. Initial program 9.2%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 77.8

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 77.8

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

   7. Applied rewrites 77.8%

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

   if -4.8e159 < z < 4.5999999999999996

   1. Initial program 57.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 57.1

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

   4. Applied rewrites 57.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. +-commutative N/A

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

      10. unpow-prod-down N/A

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

      11. metadata-eval N/A

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

      12. unpow-prod-down N/A

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. unpow-prod-down N/A

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

      16. metadata-eval N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. unpow2 N/A

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

      20. lower-*.f64 N/A

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

      21. distribute-lft-out N/A

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

   6. Applied rewrites 57.1%

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

   7. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. lower-hypot.f64 91.8

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

   9. Applied rewrites 91.8%

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

   if 4.5999999999999996 < z

   1. Initial program 34.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 43.3

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

   4. Applied rewrites 43.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 43.3

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

   7. Applied rewrites 43.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 60.8%

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

   11. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-sin.f64 N/A

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

       5. lift-*.f64 78.5

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

   13. Applied rewrites 78.5%

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

Alternative 5: 86.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \sin \left(30 \cdot x\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z, \left|t\_1 + t\_0 \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 4.6:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|t\_1\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30, \left|\mathsf{fma}\left(30, x, t\_0\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0))) (t_1 (sin (* 30.0 x))))
   (if (<= z -4.8e+159)
     (fmax (* -30.0 z) (- (fabs (+ t_1 (* t_0 (cos (* x 30.0))))) 0.2))
     (if (<= z 4.6)
       (fmax (- (hypot (* y 30.0) (* 30.0 x)) 25.0) (- (fabs t_1) 0.2))
       (fmax (* z 30.0) (- (fabs (fma 30.0 x t_0)) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = sin((30.0 * x));
	double tmp;
	if (z <= -4.8e+159) {
		tmp = fmax((-30.0 * z), (fabs((t_1 + (t_0 * cos((x * 30.0))))) - 0.2));
	} else if (z <= 4.6) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs(t_1) - 0.2));
	} else {
		tmp = fmax((z * 30.0), (fabs(fma(30.0, x, t_0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = sin(Float64(30.0 * x))
	tmp = 0.0
	if (z <= -4.8e+159)
		tmp = fmax(Float64(-30.0 * z), Float64(abs(Float64(t_1 + Float64(t_0 * cos(Float64(x * 30.0))))) - 0.2));
	elseif (z <= 4.6)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(t_1) - 0.2));
	else
		tmp = fmax(Float64(z * 30.0), Float64(abs(fma(30.0, x, t_0)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -4.8e+159], N[Max[N[(-30.0 * z), $MachinePrecision], N[(N[Abs[N[(t$95$1 + N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 4.6], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[t$95$1], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * 30.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + t$95$0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e159

   1. Initial program 9.2%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 77.8

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 77.8

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

   7. Applied rewrites 77.8%

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

   if -4.8e159 < z < 4.5999999999999996

   1. Initial program 57.6%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 92.3

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

   4. Applied rewrites 92.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 91.9

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

   7. Applied rewrites 91.9%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 91.3

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

   10. Applied rewrites 91.3%

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

   if 4.5999999999999996 < z

   1. Initial program 34.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 43.3

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

   4. Applied rewrites 43.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 43.3

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

   7. Applied rewrites 43.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 60.8%

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

   11. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-sin.f64 N/A

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

       5. lift-*.f64 78.5

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

   13. Applied rewrites 78.5%

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

Alternative 6: 85.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 4.6:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(y \cdot 30, 30 \cdot x\right) - 25, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.8e+159)
   (fmax
    (- (sqrt (* (* x x) 900.0)) 25.0)
    (- (fabs (fma z 30.0 (sin (* y 30.0)))) 0.2))
   (if (<= z 4.6)
     (fmax
      (- (hypot (* y 30.0) (* 30.0 x)) 25.0)
      (- (fabs (sin (* 30.0 x))) 0.2))
     (fmax (* z 30.0) (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e+159) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs(fma(z, 30.0, sin((y * 30.0)))) - 0.2));
	} else if (z <= 4.6) {
		tmp = fmax((hypot((y * 30.0), (30.0 * x)) - 25.0), (fabs(sin((30.0 * x))) - 0.2));
	} else {
		tmp = fmax((z * 30.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.8e+159)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(fma(z, 30.0, sin(Float64(y * 30.0)))) - 0.2));
	elseif (z <= 4.6)
		tmp = fmax(Float64(hypot(Float64(y * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(sin(Float64(30.0 * x))) - 0.2));
	else
		tmp = fmax(Float64(z * 30.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.8e+159], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0 + N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 4.6], N[Max[N[(N[Sqrt[N[(y * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * 30.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e159

   1. Initial program 9.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 9.2

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

   4. Applied rewrites 9.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 9.2

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

   7. Applied rewrites 9.2%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 9.2

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

   10. Applied rewrites 9.2%

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

   11. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. pow2 N/A

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

       4. lower-*.f64 69.4

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

   13. Applied rewrites 69.4%

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

   if -4.8e159 < z < 4.5999999999999996

   1. Initial program 57.6%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 92.3

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

   4. Applied rewrites 92.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 91.9

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

   7. Applied rewrites 91.9%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 91.3

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

   10. Applied rewrites 91.3%

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

   if 4.5999999999999996 < z

   1. Initial program 34.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 43.3

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

   4. Applied rewrites 43.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 43.3

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

   7. Applied rewrites 43.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 60.8%

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

   11. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-sin.f64 N/A

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

       5. lift-*.f64 78.5

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

   13. Applied rewrites 78.5%

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

Alternative 7: 74.4% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{if}\;y \leq -1050000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(y, y, x \cdot x\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* 30.0 x)))) 0.2))))
   (if (<= y -1050000000000.0)
     t_0
     (if (<= y 4.7e+125)
       (fmax
        (- (sqrt (* (fma y y (* x x)) 900.0)) 25.0)
        (- (fabs (fma z 30.0 (sin (* y 30.0)))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((30.0 * x)))) - 0.2));
	double tmp;
	if (y <= -1050000000000.0) {
		tmp = t_0;
	} else if (y <= 4.7e+125) {
		tmp = fmax((sqrt((fma(y, y, (x * x)) * 900.0)) - 25.0), (fabs(fma(z, 30.0, sin((y * 30.0)))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(30.0 * x)))) - 0.2))
	tmp = 0.0
	if (y <= -1050000000000.0)
		tmp = t_0;
	elseif (y <= 4.7e+125)
		tmp = fmax(Float64(sqrt(Float64(fma(y, y, Float64(x * x)) * 900.0)) - 25.0), Float64(abs(fma(z, 30.0, sin(Float64(y * 30.0)))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -1050000000000.0], t$95$0, If[LessEqual[y, 4.7e+125], N[Max[N[(N[Sqrt[N[(N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0 + N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e12 or 4.69999999999999972e125 < y

   1. Initial program 26.2%

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

   2. Taylor expanded in x around -inf

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

      1. lower-*.f64 12.7

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

   4. Applied rewrites 12.7%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-sin.f64 N/A

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

      11. lift-*.f64 12.7

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

   7. Applied rewrites 12.7%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 74.3

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

   10. Applied rewrites 74.3%

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

   if -1.05e12 < y < 4.69999999999999972e125

   1. Initial program 58.4%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 58.0

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

   4. Applied rewrites 58.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 37.1

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 36.6

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

   10. Applied rewrites 36.6%

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

   11. Taylor expanded in z around 0

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

       1. distribute-lft-in N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 N/A

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

       4. +-commutative N/A

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

       5. pow2 N/A

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

       6. lower-fma.f64 N/A

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

       7. pow2 N/A

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

       8. lower-*.f64 74.5

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

   13. Applied rewrites 74.5%

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

Alternative 8: 72.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{if}\;y \leq -480000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* 30.0 x)))) 0.2))))
   (if (<= y -480000000000.0)
     t_0
     (if (<= y 1.1e+61)
       (fmax
        (- (sqrt (* (* x x) 900.0)) 25.0)
        (- (fabs (fma z 30.0 (sin (* y 30.0)))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((30.0 * x)))) - 0.2));
	double tmp;
	if (y <= -480000000000.0) {
		tmp = t_0;
	} else if (y <= 1.1e+61) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs(fma(z, 30.0, sin((y * 30.0)))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(30.0 * x)))) - 0.2))
	tmp = 0.0
	if (y <= -480000000000.0)
		tmp = t_0;
	elseif (y <= 1.1e+61)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(fma(z, 30.0, sin(Float64(y * 30.0)))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -480000000000.0], t$95$0, If[LessEqual[y, 1.1e+61], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0 + N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e11 or 1.1e61 < y

   1. Initial program 30.0%

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

   2. Taylor expanded in x around -inf

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

      1. lower-*.f64 13.6

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

   4. Applied rewrites 13.6%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-sin.f64 N/A

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

      11. lift-*.f64 13.6

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

   7. Applied rewrites 13.6%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 72.7

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

   10. Applied rewrites 72.7%

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

   if -4.8e11 < y < 1.1e61

   1. Initial program 58.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 57.7

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

   4. Applied rewrites 57.7%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 39.3

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

   7. Applied rewrites 39.3%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 38.7

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

   10. Applied rewrites 38.7%

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

   11. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. pow2 N/A

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

       4. lower-*.f64 72.0

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

   13. Applied rewrites 72.0%

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

Alternative 9: 73.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot \left(y + z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.05e-18)
   (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* 30.0 x)))) 0.2))
   (if (<= x 1.95e-5)
     (fmax (- (sqrt (* (* z z) 900.0)) 25.0) (- (fabs (* 30.0 (+ y z))) 0.2))
     (fmax (* z 30.0) (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.05e-18) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((30.0 * x)))) - 0.2));
	} else if (x <= 1.95e-5) {
		tmp = fmax((sqrt(((z * z) * 900.0)) - 25.0), (fabs((30.0 * (y + z))) - 0.2));
	} else {
		tmp = fmax((z * 30.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.05e-18)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(30.0 * x)))) - 0.2));
	elseif (x <= 1.95e-5)
		tmp = fmax(Float64(sqrt(Float64(Float64(z * z) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * Float64(y + z))) - 0.2));
	else
		tmp = fmax(Float64(z * 30.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.05e-18], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(y * 30.0 + N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.95e-5], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(z * 30.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0499999999999999e-18

   1. Initial program 35.5%

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

   2. Taylor expanded in x around -inf

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

      1. lower-*.f64 58.1

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

   4. Applied rewrites 58.1%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-sin.f64 N/A

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

      11. lift-*.f64 58.1

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

   7. Applied rewrites 58.1%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 77.6

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

   10. Applied rewrites 77.6%

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

   if -2.0499999999999999e-18 < x < 1.95e-5

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 58.0

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

   4. Applied rewrites 58.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 42.9

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

   7. Applied rewrites 42.9%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 42.2

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

   10. Applied rewrites 42.2%

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

   11. Taylor expanded in y around 0

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

       1. distribute-lft-out N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 73.6

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

   13. Applied rewrites 73.6%

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

   if 1.95e-5 < x

   1. Initial program 33.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 79.3

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

   7. Applied rewrites 79.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 14.9%

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

   11. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-sin.f64 N/A

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

       5. lift-*.f64 69.6

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

   13. Applied rewrites 69.6%

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

Alternative 10: 71.9% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(z \cdot 30, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{if}\;x \leq -450000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot \left(y + z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* z 30.0) (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2))))
   (if (<= x -450000.0)
     t_0
     (if (<= x 1.95e-5)
       (fmax (- (sqrt (* (* z z) 900.0)) 25.0) (- (fabs (* 30.0 (+ y z))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((z * 30.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	double tmp;
	if (x <= -450000.0) {
		tmp = t_0;
	} else if (x <= 1.95e-5) {
		tmp = fmax((sqrt(((z * z) * 900.0)) - 25.0), (fabs((30.0 * (y + z))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(z * 30.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2))
	tmp = 0.0
	if (x <= -450000.0)
		tmp = t_0;
	elseif (x <= 1.95e-5)
		tmp = fmax(Float64(sqrt(Float64(Float64(z * z) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * Float64(y + z))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(z * 30.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -450000.0], t$95$0, If[LessEqual[x, 1.95e-5], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e5 or 1.95e-5 < x

   1. Initial program 33.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 80.3

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

   4. Applied rewrites 80.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 80.3

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

   7. Applied rewrites 80.3%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 14.5%

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

   11. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-sin.f64 N/A

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

       5. lift-*.f64 70.6

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

   13. Applied rewrites 70.6%

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

   if -4.5e5 < x < 1.95e-5

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 57.6

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

   4. Applied rewrites 57.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 42.2

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 41.5

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

   10. Applied rewrites 41.5%

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

   11. Taylor expanded in y around 0

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

       1. distribute-lft-out N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 73.1

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

   13. Applied rewrites 73.1%

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

Alternative 11: 68.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;x \leq -450000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, y \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))))
   (if (<= x -450000.0)
     t_0
     (if (<= x 5e+48)
       (fmax
        (- (sqrt (* (* z z) 900.0)) 25.0)
        (- (fabs (fma z 30.0 (* y 30.0))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	double tmp;
	if (x <= -450000.0) {
		tmp = t_0;
	} else if (x <= 5e+48) {
		tmp = fmax((sqrt(((z * z) * 900.0)) - 25.0), (fabs(fma(z, 30.0, (y * 30.0))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2))
	tmp = 0.0
	if (x <= -450000.0)
		tmp = t_0;
	elseif (x <= 5e+48)
		tmp = fmax(Float64(sqrt(Float64(Float64(z * z) * 900.0)) - 25.0), Float64(abs(fma(z, 30.0, Float64(y * 30.0))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -450000.0], t$95$0, If[LessEqual[x, 5e+48], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0 + N[(y * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e5 or 4.99999999999999973e48 < x

   1. Initial program 31.0%

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

   2. Taylor expanded in x around -inf

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

      1. lower-*.f64 34.9

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

   4. Applied rewrites 34.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sin.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-sin.f64 N/A

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

      11. lift-*.f64 34.9

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

   7. Applied rewrites 34.9%

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

   8. Taylor expanded in y around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 34.9

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

   10. Applied rewrites 34.9%

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

   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 64.2

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

   13. Applied rewrites 64.2%

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

   if -4.5e5 < x < 4.99999999999999973e48

   1. Initial program 58.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 57.7

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

   4. Applied rewrites 57.7%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 40.4

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

   7. Applied rewrites 40.4%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 39.8

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

   10. Applied rewrites 39.8%

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

   11. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 71.2

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

   13. Applied rewrites 71.2%

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

Alternative 12: 68.0% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;x \leq -450000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot \left(y + z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))))
   (if (<= x -450000.0)
     t_0
     (if (<= x 5e+48)
       (fmax (- (sqrt (* (* z z) 900.0)) 25.0) (- (fabs (* 30.0 (+ y z))) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	double tmp;
	if (x <= -450000.0) {
		tmp = t_0;
	} else if (x <= 5e+48) {
		tmp = fmax((sqrt(((z * z) * 900.0)) - 25.0), (fabs((30.0 * (y + z))) - 0.2));
	} else {
		tmp = 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 = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    if (x <= (-450000.0d0)) then
        tmp = t_0
    else if (x <= 5d+48) then
        tmp = fmax((sqrt(((z * z) * 900.0d0)) - 25.0d0), (abs((30.0d0 * (y + z))) - 0.2d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	double tmp;
	if (x <= -450000.0) {
		tmp = t_0;
	} else if (x <= 5e+48) {
		tmp = fmax((Math.sqrt(((z * z) * 900.0)) - 25.0), (Math.abs((30.0 * (y + z))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	tmp = 0
	if x <= -450000.0:
		tmp = t_0
	elif x <= 5e+48:
		tmp = fmax((math.sqrt(((z * z) * 900.0)) - 25.0), (math.fabs((30.0 * (y + z))) - 0.2))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2))
	tmp = 0.0
	if (x <= -450000.0)
		tmp = t_0;
	elseif (x <= 5e+48)
		tmp = fmax(Float64(sqrt(Float64(Float64(z * z) * 900.0)) - 25.0), Float64(abs(Float64(30.0 * Float64(y + z))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	tmp = 0.0;
	if (x <= -450000.0)
		tmp = t_0;
	elseif (x <= 5e+48)
		tmp = max((sqrt(((z * z) * 900.0)) - 25.0), (abs((30.0 * (y + z))) - 0.2));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -450000.0], t$95$0, If[LessEqual[x, 5e+48], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e5 or 4.99999999999999973e48 < x

   1. Initial program 31.0%

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

   2. Taylor expanded in x around -inf

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

      1. lower-*.f64 34.9

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

   4. Applied rewrites 34.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) \cdot \cos \left(30 \cdot y\right) + \sin \color{blue}{\left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \color{blue}{\cos \left(30 \cdot y\right)}, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \color{blue}{\left(30 \cdot y\right)}, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(\color{blue}{30} \cdot y\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      7. lift-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      10. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      11. lift-*.f64 34.9

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]

   7. Applied rewrites 34.9%

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)}\right| - 0.2\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lift-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 34.9

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]

   10. Applied rewrites 34.9%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]

   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 64.2

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]

   13. Applied rewrites 64.2%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]

   if -4.5e5 < x < 4.99999999999999973e48

   1. Initial program 58.2%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot y\right) \cdot \cos \left(30 \cdot z\right) + \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(\color{blue}{30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      5. lift-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \color{blue}{\left(30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(\color{blue}{30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      8. lift-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      11. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      12. lift-*.f64 57.7

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - 0.2\right) \]

   4. Applied rewrites 57.7%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {z}^{2}}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{z}^{2} \cdot \color{blue}{900}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{z}^{2} \cdot \color{blue}{900}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 40.4

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - 0.2\right) \]

   7. Applied rewrites 40.4%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\left(z \cdot z\right) \cdot 900}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\sin \left(30 \cdot y\right) + \color{blue}{30 \cdot z}\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot z + \sin \left(30 \cdot y\right)\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|z \cdot 30 + \sin \left(30 \cdot y\right)\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      5. lift-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      6. lift-*.f64 39.8

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 39.8%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, \color{blue}{30}, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot y + 30 \cdot \color{blue}{z}\right| - \frac{1}{5}\right) \]
   12. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot \left(y + z\right)\right| - \frac{1}{5}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot \left(y + z\right)\right| - \frac{1}{5}\right) \]

       3. lower-+.f64 71.2

          \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot \left(y + z\right)\right| - 0.2\right) \]

   13. Applied rewrites 71.2%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot \left(y + \color{blue}{z}\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 50.6% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;x \leq -62:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))))
   (if (<= x -62.0)
     t_0
     (if (<= x 2.7e+17)
       (fmax (- (sqrt (* (* z z) 900.0)) 25.0) (- (fabs (* z 30.0)) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	double tmp;
	if (x <= -62.0) {
		tmp = t_0;
	} else if (x <= 2.7e+17) {
		tmp = fmax((sqrt(((z * z) * 900.0)) - 25.0), (fabs((z * 30.0)) - 0.2));
	} else {
		tmp = 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 = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    if (x <= (-62.0d0)) then
        tmp = t_0
    else if (x <= 2.7d+17) then
        tmp = fmax((sqrt(((z * z) * 900.0d0)) - 25.0d0), (abs((z * 30.0d0)) - 0.2d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	double tmp;
	if (x <= -62.0) {
		tmp = t_0;
	} else if (x <= 2.7e+17) {
		tmp = fmax((Math.sqrt(((z * z) * 900.0)) - 25.0), (Math.abs((z * 30.0)) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	tmp = 0
	if x <= -62.0:
		tmp = t_0
	elif x <= 2.7e+17:
		tmp = fmax((math.sqrt(((z * z) * 900.0)) - 25.0), (math.fabs((z * 30.0)) - 0.2))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2))
	tmp = 0.0
	if (x <= -62.0)
		tmp = t_0;
	elseif (x <= 2.7e+17)
		tmp = fmax(Float64(sqrt(Float64(Float64(z * z) * 900.0)) - 25.0), Float64(abs(Float64(z * 30.0)) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	tmp = 0.0;
	if (x <= -62.0)
		tmp = t_0;
	elseif (x <= 2.7e+17)
		tmp = max((sqrt(((z * z) * 900.0)) - 25.0), (abs((z * 30.0)) - 0.2));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -62.0], t$95$0, If[LessEqual[x, 2.7e+17], N[Max[N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -62 or 2.7e17 < x

   1. Initial program 32.7%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in x around -inf

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 33.2

         \[\leadsto \mathsf{max}\left(-30 \cdot \color{blue}{x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   4. Applied rewrites 33.2%

      \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot y\right) + \cos \left(30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)}\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\cos \left(30 \cdot y\right) \cdot \sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) \cdot \cos \left(30 \cdot y\right) + \sin \color{blue}{\left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \color{blue}{\cos \left(30 \cdot y\right)}, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \color{blue}{\left(30 \cdot y\right)}, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(\color{blue}{30} \cdot y\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      7. lift-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      10. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      11. lift-*.f64 33.2

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]

   7. Applied rewrites 33.2%

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)}\right| - 0.2\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. lift-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]

      2. lift-*.f64 33.2

         \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]

   10. Applied rewrites 33.2%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]

   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 62.2

          \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]

   13. Applied rewrites 62.2%

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]

   if -62 < x < 2.7e17

   1. Initial program 58.2%

      \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\sin \left(30 \cdot z\right) + \cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\cos \left(30 \cdot z\right) \cdot \sin \left(30 \cdot y\right) + \color{blue}{\sin \left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(30 \cdot y\right) \cdot \cos \left(30 \cdot z\right) + \sin \color{blue}{\left(30 \cdot z\right)}\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), \color{blue}{\cos \left(30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(\color{blue}{30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      5. lift-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \color{blue}{\left(30 \cdot z\right)}, \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(\color{blue}{30} \cdot z\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      8. lift-cos.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(30 \cdot z\right)\right)\right| - \frac{1}{5}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      11. lift-sin.f64 N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      12. lift-*.f64 57.6

          \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - 0.2\right) \]

   4. Applied rewrites 57.6%

      \[\leadsto \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\color{blue}{\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)}\right| - 0.2\right) \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{900 \cdot {z}^{2}}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{z}^{2} \cdot \color{blue}{900}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{{z}^{2} \cdot \color{blue}{900}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      4. lower-*.f64 41.7

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - 0.2\right) \]

   7. Applied rewrites 41.7%

      \[\leadsto \mathsf{max}\left(\sqrt{\color{blue}{\left(z \cdot z\right) \cdot 900}} - 25, \left|\mathsf{fma}\left(\sin \left(y \cdot 30\right), \cos \left(z \cdot 30\right), \sin \left(z \cdot 30\right)\right)\right| - 0.2\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\sin \left(30 \cdot y\right) + \color{blue}{30 \cdot z}\right| - \frac{1}{5}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot z + \sin \left(30 \cdot y\right)\right| - \frac{1}{5}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|z \cdot 30 + \sin \left(30 \cdot y\right)\right| - \frac{1}{5}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      5. lift-sin.f64 N/A

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

      6. lift-*.f64 41.0

         \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, 30, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]

   10. Applied rewrites 41.0%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|\mathsf{fma}\left(z, \color{blue}{30}, \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|30 \cdot z\right| - \frac{1}{5}\right) \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|z \cdot 30\right| - \frac{1}{5}\right) \]

       2. lift-*.f64 39.7

          \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right) \]

   13. Applied rewrites 39.7%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(z \cdot z\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 31.8% accurate, 9.4× 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 45.8%

   \[\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

2. Taylor expanded in x around -inf

   \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - \frac{1}{5}\right) \]
3. Step-by-step derivation

   1. lower-*.f64 18.6

      \[\leadsto \mathsf{max}\left(-30 \cdot \color{blue}{x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

4. Applied rewrites 18.6%

   \[\leadsto \mathsf{max}\left(\color{blue}{-30 \cdot x}, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]

5. Taylor expanded in z around 0

   \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\sin \left(30 \cdot y\right) + \cos \left(30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)}\right| - \frac{1}{5}\right) \]
6. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\cos \left(30 \cdot y\right) \cdot \sin \left(30 \cdot x\right) + \color{blue}{\sin \left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) \cdot \cos \left(30 \cdot y\right) + \sin \color{blue}{\left(30 \cdot y\right)}\right| - \frac{1}{5}\right) \]

   3. lower-fma.f64 N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \color{blue}{\cos \left(30 \cdot y\right)}, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

   4. lower-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \color{blue}{\left(30 \cdot y\right)}, \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(\color{blue}{30} \cdot y\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

   7. lift-cos.f64 N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(30 \cdot y\right)\right)\right| - \frac{1}{5}\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

   10. lift-sin.f64 N/A

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - \frac{1}{5}\right) \]

   11. lift-*.f64 18.2

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)\right| - 0.2\right) \]

7. Applied rewrites 18.2%

   \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\color{blue}{\mathsf{fma}\left(\sin \left(30 \cdot x\right), \cos \left(y \cdot 30\right), \sin \left(y \cdot 30\right)\right)}\right| - 0.2\right) \]

8. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]
9. Step-by-step derivation

   1. lift-sin.f64 N/A

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]

   2. lift-*.f64 17.6

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]

10. Applied rewrites 17.6%

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - 0.2\right) \]

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 31.8

       \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]

13. Applied rewrites 31.8%

    \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right) \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025095 
(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)))