Gyroid sphere

Percentage Accurate: 46.5% → 99.9%

Time: 10.0s

Alternatives: 8

Speedup: N/A×

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: 46.5% 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: 99.9% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(\mathsf{hypot}\left(\mathsf{hypot}\left({\left(30 \cdot y\right)}^{1}, {\left(30 \cdot x\right)}^{1}\right), z \cdot 30\right) + -1 \cdot 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (+
   (hypot (hypot (pow (* 30.0 y) 1.0) (pow (* 30.0 x) 1.0)) (* z 30.0))
   (* -1.0 25.0))
  (-
   (fabs
    (fma
     (sin (* 30.0 x))
     (sin (fma y 30.0 (/ PI 2.0)))
     (fma
      (sin (* y 30.0))
      (sin (fma z 30.0 (/ PI 2.0)))
      (* (sin (* z 30.0)) (sin (fma 30.0 x (/ PI 2.0)))))))
   0.2)))

C

double code(double x, double y, double z) {
	return fmax((hypot(hypot(pow((30.0 * y), 1.0), pow((30.0 * x), 1.0)), (z * 30.0)) + (-1.0 * 25.0)), (fabs(fma(sin((30.0 * x)), sin(fma(y, 30.0, (((double) M_PI) / 2.0))), fma(sin((y * 30.0)), sin(fma(z, 30.0, (((double) M_PI) / 2.0))), (sin((z * 30.0)) * sin(fma(30.0, x, (((double) M_PI) / 2.0))))))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(Float64(hypot(hypot((Float64(30.0 * y) ^ 1.0), (Float64(30.0 * x) ^ 1.0)), Float64(z * 30.0)) + Float64(-1.0 * 25.0)), Float64(abs(fma(sin(Float64(30.0 * x)), sin(fma(y, 30.0, Float64(pi / 2.0))), fma(sin(Float64(y * 30.0)), sin(fma(z, 30.0, Float64(pi / 2.0))), Float64(sin(Float64(z * 30.0)) * sin(fma(30.0, x, Float64(pi / 2.0))))))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[Sqrt[N[Power[N[(30.0 * y), $MachinePrecision], 1.0], $MachinePrecision] ^ 2 + N[Power[N[(30.0 * x), $MachinePrecision], 1.0], $MachinePrecision] ^ 2], $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y * 30.0 + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(z * 30.0 + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(30.0 * x + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 42.0%

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

4. Applied rewrites 54.3%

   \[\leadsto \color{blue}{\mathsf{max}\left(\mathsf{hypot}\left({\left(\mathsf{fma}\left(y \cdot y, 900, \left(x \cdot x\right) \cdot 900\right)\right)}^{0.5}, z \cdot 30\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right)\right| - 0.2\right)} \]
5. Step-by-step derivation

   1. lift-pow.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-fma.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. unpow1/2 N/A

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

   7. pow2 N/A

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

   8. metadata-eval N/A

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

   9. unpow-prod-down N/A

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

   10. pow2 N/A

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

   11. metadata-eval N/A

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

   12. unpow-prod-down N/A

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

   13. sqr-pow N/A

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

   14. sqr-pow N/A

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

   15. lower-hypot.f64 N/A

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

   16. *-commutative N/A

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

   17. metadata-eval N/A

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

   18. lower-pow.f64 N/A

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

   19. lower-*.f64 N/A

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

6. Applied rewrites 99.9%

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

7. Final simplification 99.9%

   \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(\mathsf{hypot}\left({\left(30 \cdot y\right)}^{1}, {\left(30 \cdot x\right)}^{1}\right), z \cdot 30\right) + -1 \cdot 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right)\right| - 0.2\right) \]
8. Add Preprocessing

Alternative 2: 99.6% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(\mathsf{hypot}\left(\mathsf{hypot}\left({\left(30 \cdot y\right)}^{1}, {\left(30 \cdot x\right)}^{1}\right), z \cdot 30\right) + -1 \cdot 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(30, y \cdot \sin \left(\mathsf{fma}\left(0.5, \pi, 30 \cdot z\right)\right), \sin \left(30 \cdot z\right) \cdot \sin \left(\mathsf{fma}\left(0.5, \pi, 30 \cdot x\right)\right)\right)\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (+
   (hypot (hypot (pow (* 30.0 y) 1.0) (pow (* 30.0 x) 1.0)) (* z 30.0))
   (* -1.0 25.0))
  (-
   (fabs
    (fma
     (sin (* 30.0 x))
     (sin (fma y 30.0 (/ PI 2.0)))
     (fma
      30.0
      (* y (sin (fma 0.5 PI (* 30.0 z))))
      (* (sin (* 30.0 z)) (sin (fma 0.5 PI (* 30.0 x)))))))
   0.2)))

C

double code(double x, double y, double z) {
	return fmax((hypot(hypot(pow((30.0 * y), 1.0), pow((30.0 * x), 1.0)), (z * 30.0)) + (-1.0 * 25.0)), (fabs(fma(sin((30.0 * x)), sin(fma(y, 30.0, (((double) M_PI) / 2.0))), fma(30.0, (y * sin(fma(0.5, ((double) M_PI), (30.0 * z)))), (sin((30.0 * z)) * sin(fma(0.5, ((double) M_PI), (30.0 * x))))))) - 0.2));
}

Julia

function code(x, y, z)
	return fmax(Float64(hypot(hypot((Float64(30.0 * y) ^ 1.0), (Float64(30.0 * x) ^ 1.0)), Float64(z * 30.0)) + Float64(-1.0 * 25.0)), Float64(abs(fma(sin(Float64(30.0 * x)), sin(fma(y, 30.0, Float64(pi / 2.0))), fma(30.0, Float64(y * sin(fma(0.5, pi, Float64(30.0 * z)))), Float64(sin(Float64(30.0 * z)) * sin(fma(0.5, pi, Float64(30.0 * x))))))) - 0.2))
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[Sqrt[N[Sqrt[N[Power[N[(30.0 * y), $MachinePrecision], 1.0], $MachinePrecision] ^ 2 + N[Power[N[(30.0 * x), $MachinePrecision], 1.0], $MachinePrecision] ^ 2], $MachinePrecision] ^ 2 + N[(z * 30.0), $MachinePrecision] ^ 2], $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y * 30.0 + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(30.0 * N[(y * N[Sin[N[(0.5 * Pi + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(0.5 * Pi + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 42.0%

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

4. Applied rewrites 54.3%

   \[\leadsto \color{blue}{\mathsf{max}\left(\mathsf{hypot}\left({\left(\mathsf{fma}\left(y \cdot y, 900, \left(x \cdot x\right) \cdot 900\right)\right)}^{0.5}, z \cdot 30\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right)\right| - 0.2\right)} \]
5. Step-by-step derivation

   1. lift-pow.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-fma.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. unpow1/2 N/A

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

   7. pow2 N/A

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

   8. metadata-eval N/A

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

   9. unpow-prod-down N/A

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

   10. pow2 N/A

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

   11. metadata-eval N/A

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

   12. unpow-prod-down N/A

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

   13. sqr-pow N/A

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

   14. sqr-pow N/A

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

   15. lower-hypot.f64 N/A

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

   16. *-commutative N/A

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

   17. metadata-eval N/A

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

   18. lower-pow.f64 N/A

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

   19. lower-*.f64 N/A

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

6. Applied rewrites 99.9%

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

7. Taylor expanded in y around 0

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

   1. lower-fma.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-sin.f64 N/A

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

   4. lower-fma.f64 N/A

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

   5. lift-PI.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lift-sin.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. lower-sin.f64 N/A

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

   11. lower-fma.f64 N/A

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

9. Applied rewrites 99.6%

   \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(\mathsf{hypot}\left({\left(30 \cdot y\right)}^{1}, {\left(30 \cdot x\right)}^{1}\right), z \cdot 30\right) - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \color{blue}{\mathsf{fma}\left(30, y \cdot \sin \left(\mathsf{fma}\left(0.5, \pi, 30 \cdot z\right)\right), \sin \left(30 \cdot z\right) \cdot \sin \left(\mathsf{fma}\left(0.5, \pi, 30 \cdot x\right)\right)\right)}\right)\right| - 0.2\right) \]

10. Final simplification 99.6%

    \[\leadsto \mathsf{max}\left(\mathsf{hypot}\left(\mathsf{hypot}\left({\left(30 \cdot y\right)}^{1}, {\left(30 \cdot x\right)}^{1}\right), z \cdot 30\right) + -1 \cdot 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(30, y \cdot \sin \left(\mathsf{fma}\left(0.5, \pi, 30 \cdot z\right)\right), \sin \left(30 \cdot z\right) \cdot \sin \left(\mathsf{fma}\left(0.5, \pi, 30 \cdot x\right)\right)\right)\right)\right| - 0.2\right) \]
11. Add Preprocessing

Alternative 3: 58.7% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(z \cdot 30\right)\\ t_1 := \sin \left(y \cdot 30\right)\\ t_2 := \mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(t\_1, \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), t\_0 \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right)\\ t_3 := \left|t\_2\right|\\ t_4 := \left|t\_0 \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + t\_1 \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, t\_4\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, t\_4\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \frac{{t\_3}^{3} - 0.008}{t\_2 \cdot t\_2 + \left(0.04 + t\_3 \cdot 0.2\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x + -1 \cdot 25, t\_4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* z 30.0)))
        (t_1 (sin (* y 30.0)))
        (t_2
         (fma
          (sin (* 30.0 x))
          (sin (fma y 30.0 (/ PI 2.0)))
          (fma
           t_1
           (sin (fma z 30.0 (/ PI 2.0)))
           (* t_0 (sin (fma 30.0 x (/ PI 2.0)))))))
        (t_3 (fabs t_2))
        (t_4
         (-
          (fabs
           (+
            (* t_0 (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* t_1 (cos (* z 30.0))))))
          0.2)))
   (if (<= x -1.15e+112)
     (fmax (+ (* -30.0 x) (* -1.0 25.0)) t_4)
     (if (<= x -2.1e-131)
       (fmax (+ (* -30.0 y) (* -1.0 25.0)) t_4)
       (if (<= x 6.5e+148)
         (fmax
          (-
           (sqrt
            (+
             (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
             (pow (* z 30.0) 2.0)))
           25.0)
          (/ (- (pow t_3 3.0) 0.008) (+ (* t_2 t_2) (+ 0.04 (* t_3 0.2)))))
         (fmax (+ (* 30.0 x) (* -1.0 25.0)) t_4))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((z * 30.0));
	double t_1 = sin((y * 30.0));
	double t_2 = fma(sin((30.0 * x)), sin(fma(y, 30.0, (((double) M_PI) / 2.0))), fma(t_1, sin(fma(z, 30.0, (((double) M_PI) / 2.0))), (t_0 * sin(fma(30.0, x, (((double) M_PI) / 2.0))))));
	double t_3 = fabs(t_2);
	double t_4 = fabs(((t_0 * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (t_1 * cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_4);
	} else if (x <= -2.1e-131) {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_4);
	} else if (x <= 6.5e+148) {
		tmp = fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), ((pow(t_3, 3.0) - 0.008) / ((t_2 * t_2) + (0.04 + (t_3 * 0.2)))));
	} else {
		tmp = fmax(((30.0 * x) + (-1.0 * 25.0)), t_4);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(z * 30.0))
	t_1 = sin(Float64(y * 30.0))
	t_2 = fma(sin(Float64(30.0 * x)), sin(fma(y, 30.0, Float64(pi / 2.0))), fma(t_1, sin(fma(z, 30.0, Float64(pi / 2.0))), Float64(t_0 * sin(fma(30.0, x, Float64(pi / 2.0))))))
	t_3 = abs(t_2)
	t_4 = Float64(abs(Float64(Float64(t_0 * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(t_1 * cos(Float64(z * 30.0)))))) - 0.2)
	tmp = 0.0
	if (x <= -1.15e+112)
		tmp = fmax(Float64(Float64(-30.0 * x) + Float64(-1.0 * 25.0)), t_4);
	elseif (x <= -2.1e-131)
		tmp = fmax(Float64(Float64(-30.0 * y) + Float64(-1.0 * 25.0)), t_4);
	elseif (x <= 6.5e+148)
		tmp = 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(Float64((t_3 ^ 3.0) - 0.008) / Float64(Float64(t_2 * t_2) + Float64(0.04 + Float64(t_3 * 0.2)))));
	else
		tmp = fmax(Float64(Float64(30.0 * x) + Float64(-1.0 * 25.0)), t_4);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y * 30.0 + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(t$95$1 * N[Sin[N[(z * 30.0 + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(t$95$0 * N[Sin[N[(30.0 * x + N[(Pi / 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Abs[t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[(N[Abs[N[(N[(t$95$0 * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sin[N[(x * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(y * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[Cos[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.15e+112], N[Max[N[(N[(-30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$4], $MachinePrecision], If[LessEqual[x, -2.1e-131], N[Max[N[(N[(-30.0 * y), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$4], $MachinePrecision], If[LessEqual[x, 6.5e+148], 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[(N[Power[t$95$3, 3.0], $MachinePrecision] - 0.008), $MachinePrecision] / N[(N[(t$95$2 * t$95$2), $MachinePrecision] + N[(0.04 + N[(t$95$3 * 0.2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$4], $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.15e112

   1. Initial program 12.3%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -1.15e112 < x < -2.09999999999999997e-131

   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 y around -inf

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

      1. lower-*.f64 56.7

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

   5. Applied rewrites 56.7%

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

   if -2.09999999999999997e-131 < x < 6.49999999999999947e148

   1. Initial program 59.6%

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

   4. Applied rewrites 59.6%

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

   if 6.49999999999999947e148 < x

   1. Initial program 11.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \frac{{\left(\left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right)\right|\right)}^{3} - 0.008}{\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right) \cdot \mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right) + \left(0.04 + \left|\mathsf{fma}\left(\sin \left(30 \cdot x\right), \sin \left(\mathsf{fma}\left(y, 30, \frac{\pi}{2}\right)\right), \mathsf{fma}\left(\sin \left(y \cdot 30\right), \sin \left(\mathsf{fma}\left(z, 30, \frac{\pi}{2}\right)\right), \sin \left(z \cdot 30\right) \cdot \sin \left(\mathsf{fma}\left(30, x, \frac{\pi}{2}\right)\right)\right)\right)\right| \cdot 0.2\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.7% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, t\_0\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, t\_0\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x + -1 \cdot 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs
           (+
            (* (sin (* z 30.0)) (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))))
          0.2)))
   (if (<= x -1.15e+112)
     (fmax (+ (* -30.0 x) (* -1.0 25.0)) t_0)
     (if (<= x -2.1e-131)
       (fmax (+ (* -30.0 y) (* -1.0 25.0)) t_0)
       (if (<= x 6.5e+148)
         (fmax
          (-
           (sqrt
            (+
             (+ (pow (* x 30.0) 2.0) (pow (* y 30.0) 2.0))
             (pow (* z 30.0) 2.0)))
           25.0)
          t_0)
         (fmax (+ (* 30.0 x) (* -1.0 25.0)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else if (x <= -2.1e-131) {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	} else if (x <= 6.5e+148) {
		tmp = fmax((sqrt(((pow((x * 30.0), 2.0) + pow((y * 30.0), 2.0)) + pow((z * 30.0), 2.0))) - 25.0), t_0);
	} else {
		tmp = fmax(((30.0 * x) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(((sin((z * 30.0d0)) * cos((x * 30.0d0))) + ((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))))) - 0.2d0
    if (x <= (-1.15d+112)) then
        tmp = fmax((((-30.0d0) * x) + ((-1.0d0) * 25.0d0)), t_0)
    else if (x <= (-2.1d-131)) then
        tmp = fmax((((-30.0d0) * y) + ((-1.0d0) * 25.0d0)), t_0)
    else if (x <= 6.5d+148) then
        tmp = fmax((sqrt(((((x * 30.0d0) ** 2.0d0) + ((y * 30.0d0) ** 2.0d0)) + ((z * 30.0d0) ** 2.0d0))) - 25.0d0), t_0)
    else
        tmp = fmax(((30.0d0 * x) + ((-1.0d0) * 25.0d0)), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(((Math.sin((z * 30.0)) * Math.cos((x * 30.0))) + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else if (x <= -2.1e-131) {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	} else if (x <= 6.5e+148) {
		tmp = 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), t_0);
	} else {
		tmp = fmax(((30.0 * x) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((math.sin((z * 30.0)) * math.cos((x * 30.0))) + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2
	tmp = 0
	if x <= -1.15e+112:
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0)
	elif x <= -2.1e-131:
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0)
	elif x <= 6.5e+148:
		tmp = 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), t_0)
	else:
		tmp = fmax(((30.0 * x) + (-1.0 * 25.0)), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2)
	tmp = 0.0
	if (x <= -1.15e+112)
		tmp = fmax(Float64(Float64(-30.0 * x) + Float64(-1.0 * 25.0)), t_0);
	elseif (x <= -2.1e-131)
		tmp = fmax(Float64(Float64(-30.0 * y) + Float64(-1.0 * 25.0)), t_0);
	elseif (x <= 6.5e+148)
		tmp = 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), t_0);
	else
		tmp = fmax(Float64(Float64(30.0 * x) + Float64(-1.0 * 25.0)), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	tmp = 0.0;
	if (x <= -1.15e+112)
		tmp = max(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	elseif (x <= -2.1e-131)
		tmp = max(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	elseif (x <= 6.5e+148)
		tmp = max((sqrt(((((x * 30.0) ^ 2.0) + ((y * 30.0) ^ 2.0)) + ((z * 30.0) ^ 2.0))) - 25.0), t_0);
	else
		tmp = max(((30.0 * x) + (-1.0 * 25.0)), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.15e+112], N[Max[N[(N[(-30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, -2.1e-131], N[Max[N[(N[(-30.0 * y), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 6.5e+148], 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], t$95$0], $MachinePrecision], N[Max[N[(N[(30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.15e112

   1. Initial program 12.3%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -1.15e112 < x < -2.09999999999999997e-131

   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 y around -inf

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

      1. lower-*.f64 56.7

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

   5. Applied rewrites 56.7%

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

   if -2.09999999999999997e-131 < x < 6.49999999999999947e148

   1. Initial program 59.6%

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

   if 6.49999999999999947e148 < x

   1. Initial program 11.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, t\_0\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-220}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, t\_0\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z + -1 \cdot 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x + -1 \cdot 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs
           (+
            (* (sin (* z 30.0)) (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))))
          0.2)))
   (if (<= x -1.15e+112)
     (fmax (+ (* -30.0 x) (* -1.0 25.0)) t_0)
     (if (<= x -3.5e-220)
       (fmax (+ (* -30.0 y) (* -1.0 25.0)) t_0)
       (if (<= x 1.3e+68)
         (fmax (+ (* -30.0 z) (* -1.0 25.0)) t_0)
         (fmax (+ (* 30.0 x) (* -1.0 25.0)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else if (x <= -3.5e-220) {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	} else if (x <= 1.3e+68) {
		tmp = fmax(((-30.0 * z) + (-1.0 * 25.0)), t_0);
	} else {
		tmp = fmax(((30.0 * x) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(((sin((z * 30.0d0)) * cos((x * 30.0d0))) + ((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))))) - 0.2d0
    if (x <= (-1.15d+112)) then
        tmp = fmax((((-30.0d0) * x) + ((-1.0d0) * 25.0d0)), t_0)
    else if (x <= (-3.5d-220)) then
        tmp = fmax((((-30.0d0) * y) + ((-1.0d0) * 25.0d0)), t_0)
    else if (x <= 1.3d+68) then
        tmp = fmax((((-30.0d0) * z) + ((-1.0d0) * 25.0d0)), t_0)
    else
        tmp = fmax(((30.0d0 * x) + ((-1.0d0) * 25.0d0)), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(((Math.sin((z * 30.0)) * Math.cos((x * 30.0))) + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else if (x <= -3.5e-220) {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	} else if (x <= 1.3e+68) {
		tmp = fmax(((-30.0 * z) + (-1.0 * 25.0)), t_0);
	} else {
		tmp = fmax(((30.0 * x) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((math.sin((z * 30.0)) * math.cos((x * 30.0))) + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2
	tmp = 0
	if x <= -1.15e+112:
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0)
	elif x <= -3.5e-220:
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0)
	elif x <= 1.3e+68:
		tmp = fmax(((-30.0 * z) + (-1.0 * 25.0)), t_0)
	else:
		tmp = fmax(((30.0 * x) + (-1.0 * 25.0)), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2)
	tmp = 0.0
	if (x <= -1.15e+112)
		tmp = fmax(Float64(Float64(-30.0 * x) + Float64(-1.0 * 25.0)), t_0);
	elseif (x <= -3.5e-220)
		tmp = fmax(Float64(Float64(-30.0 * y) + Float64(-1.0 * 25.0)), t_0);
	elseif (x <= 1.3e+68)
		tmp = fmax(Float64(Float64(-30.0 * z) + Float64(-1.0 * 25.0)), t_0);
	else
		tmp = fmax(Float64(Float64(30.0 * x) + Float64(-1.0 * 25.0)), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	tmp = 0.0;
	if (x <= -1.15e+112)
		tmp = max(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	elseif (x <= -3.5e-220)
		tmp = max(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	elseif (x <= 1.3e+68)
		tmp = max(((-30.0 * z) + (-1.0 * 25.0)), t_0);
	else
		tmp = max(((30.0 * x) + (-1.0 * 25.0)), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.15e+112], N[Max[N[(N[(-30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, -3.5e-220], N[Max[N[(N[(-30.0 * y), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, 1.3e+68], N[Max[N[(N[(-30.0 * z), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.15e112

   1. Initial program 12.3%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -1.15e112 < x < -3.49999999999999988e-220

   1. Initial program 48.9%

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

   3. Taylor expanded in y around -inf

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

      1. lower-*.f64 54.5

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

   5. Applied rewrites 54.5%

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

   if -3.49999999999999988e-220 < x < 1.2999999999999999e68

   1. Initial program 58.4%

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

   3. Taylor expanded in z around -inf

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

      1. lower-*.f64 50.8

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

   5. Applied rewrites 50.8%

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

   if 1.2999999999999999e68 < x

   1. Initial program 27.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-220}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.0% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, t\_0\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-220}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z + -1 \cdot 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs
           (+
            (* (sin (* z 30.0)) (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))))
          0.2)))
   (if (<= x -1.15e+112)
     (fmax (+ (* -30.0 x) (* -1.0 25.0)) t_0)
     (if (<= x -3.5e-220)
       (fmax (+ (* -30.0 y) (* -1.0 25.0)) t_0)
       (fmax (+ (* -30.0 z) (* -1.0 25.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else if (x <= -3.5e-220) {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	} else {
		tmp = fmax(((-30.0 * z) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(((sin((z * 30.0d0)) * cos((x * 30.0d0))) + ((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))))) - 0.2d0
    if (x <= (-1.15d+112)) then
        tmp = fmax((((-30.0d0) * x) + ((-1.0d0) * 25.0d0)), t_0)
    else if (x <= (-3.5d-220)) then
        tmp = fmax((((-30.0d0) * y) + ((-1.0d0) * 25.0d0)), t_0)
    else
        tmp = fmax((((-30.0d0) * z) + ((-1.0d0) * 25.0d0)), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(((Math.sin((z * 30.0)) * Math.cos((x * 30.0))) + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else if (x <= -3.5e-220) {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	} else {
		tmp = fmax(((-30.0 * z) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((math.sin((z * 30.0)) * math.cos((x * 30.0))) + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2
	tmp = 0
	if x <= -1.15e+112:
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0)
	elif x <= -3.5e-220:
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0)
	else:
		tmp = fmax(((-30.0 * z) + (-1.0 * 25.0)), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2)
	tmp = 0.0
	if (x <= -1.15e+112)
		tmp = fmax(Float64(Float64(-30.0 * x) + Float64(-1.0 * 25.0)), t_0);
	elseif (x <= -3.5e-220)
		tmp = fmax(Float64(Float64(-30.0 * y) + Float64(-1.0 * 25.0)), t_0);
	else
		tmp = fmax(Float64(Float64(-30.0 * z) + Float64(-1.0 * 25.0)), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	tmp = 0.0;
	if (x <= -1.15e+112)
		tmp = max(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	elseif (x <= -3.5e-220)
		tmp = max(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	else
		tmp = max(((-30.0 * z) + (-1.0 * 25.0)), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.15e+112], N[Max[N[(N[(-30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[x, -3.5e-220], N[Max[N[(N[(-30.0 * y), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(-30.0 * z), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e112

   1. Initial program 12.3%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -1.15e112 < x < -3.49999999999999988e-220

   1. Initial program 48.9%

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

   3. Taylor expanded in y around -inf

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

      1. lower-*.f64 54.5

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

   5. Applied rewrites 54.5%

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

   if -3.49999999999999988e-220 < x

   1. Initial program 45.8%

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

   3. Taylor expanded in z around -inf

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

      1. lower-*.f64 35.7

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

   5. Applied rewrites 35.7%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-220}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (fabs
           (+
            (* (sin (* z 30.0)) (cos (* x 30.0)))
            (+
             (* (sin (* x 30.0)) (cos (* y 30.0)))
             (* (sin (* y 30.0)) (cos (* z 30.0))))))
          0.2)))
   (if (<= x -1.15e+112)
     (fmax (+ (* -30.0 x) (* -1.0 25.0)) t_0)
     (fmax (+ (* -30.0 y) (* -1.0 25.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs(((sin((z * 30.0d0)) * cos((x * 30.0d0))) + ((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))))) - 0.2d0
    if (x <= (-1.15d+112)) then
        tmp = fmax((((-30.0d0) * x) + ((-1.0d0) * 25.0d0)), t_0)
    else
        tmp = fmax((((-30.0d0) * y) + ((-1.0d0) * 25.0d0)), t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(((Math.sin((z * 30.0)) * Math.cos((x * 30.0))) + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2;
	double tmp;
	if (x <= -1.15e+112) {
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	} else {
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((math.sin((z * 30.0)) * math.cos((x * 30.0))) + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2
	tmp = 0
	if x <= -1.15e+112:
		tmp = fmax(((-30.0 * x) + (-1.0 * 25.0)), t_0)
	else:
		tmp = fmax(((-30.0 * y) + (-1.0 * 25.0)), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2)
	tmp = 0.0
	if (x <= -1.15e+112)
		tmp = fmax(Float64(Float64(-30.0 * x) + Float64(-1.0 * 25.0)), t_0);
	else
		tmp = fmax(Float64(Float64(-30.0 * y) + Float64(-1.0 * 25.0)), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2;
	tmp = 0.0;
	if (x <= -1.15e+112)
		tmp = max(((-30.0 * x) + (-1.0 * 25.0)), t_0);
	else
		tmp = max(((-30.0 * y) + (-1.0 * 25.0)), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[x, -1.15e+112], N[Max[N[(N[(-30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision], N[Max[N[(N[(-30.0 * y), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], t$95$0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e112

   1. Initial program 12.3%

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

   3. Taylor expanded in x around -inf

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

      1. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -1.15e112 < x

   1. Initial program 46.8%

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

   3. Taylor expanded in y around -inf

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

      1. lower-*.f64 35.4

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

   5. Applied rewrites 35.4%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \mathsf{max}\left(-30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fmax
  (+ (* -30.0 x) (* -1.0 25.0))
  (-
   (fabs
    (+
     (* (sin (* z 30.0)) (cos (* x 30.0)))
     (+
      (* (sin (* x 30.0)) (cos (* y 30.0)))
      (* (sin (* y 30.0)) (cos (* z 30.0))))))
   0.2)))

C

double code(double x, double y, double z) {
	return fmax(((-30.0 * x) + (-1.0 * 25.0)), (fabs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 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((((-30.0d0) * x) + ((-1.0d0) * 25.0d0)), (abs(((sin((z * 30.0d0)) * cos((x * 30.0d0))) + ((sin((x * 30.0d0)) * cos((y * 30.0d0))) + (sin((y * 30.0d0)) * cos((z * 30.0d0)))))) - 0.2d0))
end function

Java

public static double code(double x, double y, double z) {
	return fmax(((-30.0 * x) + (-1.0 * 25.0)), (Math.abs(((Math.sin((z * 30.0)) * Math.cos((x * 30.0))) + ((Math.sin((x * 30.0)) * Math.cos((y * 30.0))) + (Math.sin((y * 30.0)) * Math.cos((z * 30.0)))))) - 0.2));
}

Python

def code(x, y, z):
	return fmax(((-30.0 * x) + (-1.0 * 25.0)), (math.fabs(((math.sin((z * 30.0)) * math.cos((x * 30.0))) + ((math.sin((x * 30.0)) * math.cos((y * 30.0))) + (math.sin((y * 30.0)) * math.cos((z * 30.0)))))) - 0.2))

Julia

function code(x, y, z)
	return fmax(Float64(Float64(-30.0 * x) + Float64(-1.0 * 25.0)), Float64(abs(Float64(Float64(sin(Float64(z * 30.0)) * cos(Float64(x * 30.0))) + Float64(Float64(sin(Float64(x * 30.0)) * cos(Float64(y * 30.0))) + Float64(sin(Float64(y * 30.0)) * cos(Float64(z * 30.0)))))) - 0.2))
end

MATLAB

function tmp = code(x, y, z)
	tmp = max(((-30.0 * x) + (-1.0 * 25.0)), (abs(((sin((z * 30.0)) * cos((x * 30.0))) + ((sin((x * 30.0)) * cos((y * 30.0))) + (sin((y * 30.0)) * cos((z * 30.0)))))) - 0.2));
end

Wolfram

code[x_, y_, z_] := N[Max[N[(N[(-30.0 * x), $MachinePrecision] + N[(-1.0 * 25.0), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[(N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(x * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 42.0%

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

3. Taylor expanded in x around -inf

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

   1. lower-*.f64 27.4

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

5. Applied rewrites 27.4%

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

6. Final simplification 27.4%

   \[\leadsto \mathsf{max}\left(-30 \cdot x + -1 \cdot 25, \left|\sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right) + \left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right)\right| - 0.2\right) \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025065 
(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)))