Gyroid sphere

Percentage Accurate: 46.2% → 98.3%

Time: 5.4s

Alternatives: 6

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: 46.2% 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: 98.3% accurate, 3.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 45.5%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. metadata-eval N/A

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

   4. unpow-prod-down N/A

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

   5. unpow2 N/A

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

   6. *-commutative N/A

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

   7. metadata-eval N/A

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

   8. unpow-prod-down N/A

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

   9. unpow2 N/A

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

   10. lower-hypot.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-*.f64 75.3

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

5. Applied rewrites 75.3%

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

6. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. sin-+PI/2-rev N/A

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

   3. sin-mult-rev N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

8. Applied rewrites 75.0%

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

9. Taylor expanded in x around 0

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

    1. +-commutative N/A

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

    2. lower-fma.f64 N/A

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

    3. *-commutative N/A

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

    4. lift-sin.f64 N/A

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

    5. lift-*.f64 98.8

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

11. Applied rewrites 98.8%

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

Alternative 2: 69.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+158} \lor \neg \left(y \leq 5.1 \cdot 10^{+73}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e+158) (not (<= y 5.1e+73)))
   (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* 30.0 x)))) 0.2))
   (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* z 30.0)) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e+158) || !(y <= 5.1e+73)) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((30.0 * x)))) - 0.2));
	} else {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((z * 30.0)) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e+158) || !(y <= 5.1e+73))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(30.0 * x)))) - 0.2));
	else
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(z * 30.0)) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e+158], N[Not[LessEqual[y, 5.1e+73]], $MachinePrecision]], 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], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999993e158 or 5.10000000000000024e73 < y

   1. Initial program 18.7%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 7.7

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

   5. Applied rewrites 7.7%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. sin-+PI/2-rev N/A

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

      3. sin-mult-rev N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

   8. Applied rewrites 7.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{30 \cdot y}\right| - \frac{1}{5}\right) \]
   10. 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 76.9

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

   11. Applied rewrites 76.9%

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

   if -1.14999999999999993e158 < y < 5.10000000000000024e73

   1. Initial program 56.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 38.0

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

   5. Applied rewrites 38.0%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. sin-+PI/2-rev N/A

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

      3. sin-mult-rev N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

   8. Applied rewrites 37.3%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. lift-sin.f64 N/A

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

       3. lift-*.f64 35.9

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

   11. Applied rewrites 35.9%

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

   12. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 69.9

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

   14. Applied rewrites 69.9%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+158} \lor \neg \left(y \leq 5.1 \cdot 10^{+73}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.0% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-77}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\mathsf{fma}\left(y, 30, \sin \left(30 \cdot x\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e-77)
   (fmax (* -30.0 x) (- (fabs (fma y 30.0 (sin (* 30.0 x)))) 0.2))
   (if (<= x 4.5e+152)
     (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* z 30.0)) 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 <= -5.5e-77) {
		tmp = fmax((-30.0 * x), (fabs(fma(y, 30.0, sin((30.0 * x)))) - 0.2));
	} else if (x <= 4.5e+152) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((z * 30.0)) - 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 <= -5.5e-77)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(fma(y, 30.0, sin(Float64(30.0 * x)))) - 0.2));
	elseif (x <= 4.5e+152)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(z * 30.0)) - 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, -5.5e-77], 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, 4.5e+152], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $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 < -5.49999999999999998e-77

   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. Add Preprocessing

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 46.6

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

   5. Applied rewrites 46.6%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. sin-+PI/2-rev N/A

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

      3. sin-mult-rev N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

   8. Applied rewrites 46.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right) + \color{blue}{30 \cdot y}\right| - \frac{1}{5}\right) \]
   10. 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 73.4

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

   11. Applied rewrites 73.4%

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

   if -5.49999999999999998e-77 < x < 4.5000000000000001e152

   1. Initial program 57.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 33.9

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

   5. Applied rewrites 33.9%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. sin-+PI/2-rev N/A

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

      3. sin-mult-rev N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

   8. Applied rewrites 32.9%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. lift-sin.f64 N/A

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

       3. lift-*.f64 31.5

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

   11. Applied rewrites 31.5%

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

   12. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 71.3

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

   14. Applied rewrites 71.3%

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

   if 4.5000000000000001e152 < x

   1. Initial program 7.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 43.3

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

   5. Applied rewrites 43.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. sin-+PI/2-rev N/A

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

      3. sin-mult-rev N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

   8. Applied rewrites 43.3%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-sin.f64 N/A

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

       5. lift-*.f64 100.0

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

   11. Applied rewrites 100.0%

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

   12. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 93.1

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

   14. Applied rewrites 93.1%

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

Alternative 4: 97.9% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(y * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 45.5%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. metadata-eval N/A

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

   4. unpow-prod-down N/A

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

   5. unpow2 N/A

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

   6. *-commutative N/A

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

   7. metadata-eval N/A

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

   8. unpow-prod-down N/A

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

   9. unpow2 N/A

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

   10. lower-hypot.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-*.f64 75.3

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

5. Applied rewrites 75.3%

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

6. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. sin-+PI/2-rev N/A

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

   3. sin-mult-rev N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

8. Applied rewrites 75.0%

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

9. Taylor expanded in x around 0

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

    1. +-commutative N/A

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

    2. lower-fma.f64 N/A

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

    3. *-commutative N/A

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

    4. lift-sin.f64 N/A

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

    5. lift-*.f64 98.8

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

11. Applied rewrites 98.8%

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

12. Taylor expanded in x around inf

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

    1. lift-*.f64 97.9

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

14. Applied rewrites 97.9%

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

Alternative 5: 66.0% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+156} \lor \neg \left(x \leq 5.8 \cdot 10^{+187}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e+156) (not (<= x 5.8e+187)))
   (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))
   (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* z 30.0)) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+156) || !(x <= 5.8e+187)) {
		tmp = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((z * 30.0)) - 0.2));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.7d+156)) .or. (.not. (x <= 5.8d+187))) then
        tmp = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    else
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((z * 30.0d0)) - 0.2d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+156) || !(x <= 5.8e+187)) {
		tmp = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((Math.sqrt(((x * x) * 900.0)) - 25.0), (Math.abs((z * 30.0)) - 0.2));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e+156) or not (x <= 5.8e+187):
		tmp = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	else:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((z * 30.0)) - 0.2))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e+156) || !(x <= 5.8e+187))
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(z * 30.0)) - 0.2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.7e+156) || ~((x <= 5.8e+187)))
		tmp = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	else
		tmp = max((sqrt(((x * x) * 900.0)) - 25.0), (abs((z * 30.0)) - 0.2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e+156], N[Not[LessEqual[x, 5.8e+187]], $MachinePrecision]], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e156 or 5.8000000000000002e187 < x

   1. Initial program 7.5%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 44.6

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

   5. Applied rewrites 44.6%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. sin-+PI/2-rev N/A

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

      3. sin-mult-rev N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

   8. Applied rewrites 44.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]
   10. 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 44.6

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

   11. Applied rewrites 44.6%

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

   12. Taylor expanded in x around 0

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

       1. lift-*.f64 77.8

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

   14. Applied rewrites 77.8%

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

   if -1.7e156 < x < 5.8000000000000002e187

   1. Initial program 54.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 33.2

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

   5. Applied rewrites 33.2%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. sin-+PI/2-rev N/A

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

      3. sin-mult-rev N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

   8. Applied rewrites 32.3%

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

   9. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. lift-sin.f64 N/A

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

       3. lift-*.f64 31.0

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

   11. Applied rewrites 31.0%

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

   12. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 65.4

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

   14. Applied rewrites 65.4%

       \[\leadsto \mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+156} \lor \neg \left(x \leq 5.8 \cdot 10^{+187}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|z \cdot 30\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.8% 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 45.5%

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

3. Taylor expanded in x around -inf

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

   1. lower-*.f64 16.4

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

5. Applied rewrites 16.4%

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

6. Taylor expanded in z around 0

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

   1. *-commutative N/A

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

   2. sin-+PI/2-rev N/A

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

   3. sin-mult-rev N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

8. Applied rewrites 16.1%

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

9. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot x\right)\right| - \frac{1}{5}\right) \]
10. 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 15.3

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

11. Applied rewrites 15.3%

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

12. Taylor expanded in x around 0

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

    1. lift-*.f64 28.7

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

14. Applied rewrites 28.7%

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

Reproduce

herbie shell --seed 2025085 
(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)))