Gyroid sphere

Percentage Accurate: 46.3% → 98.7%

Time: 9.6s

Alternatives: 4

Speedup: 4.7×

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: 46.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 3.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 47.5%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-sin.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. cos-neg-rev N/A

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

   9. lower-cos.f64 N/A

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

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

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

   11. metadata-eval N/A

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

   12. lower-*.f64 N/A

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

   13. lower-sin.f64 N/A

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

   14. lower-*.f64 47.5

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

5. Applied rewrites 47.5%

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

6. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. unpow2 N/A

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

   4. metadata-eval N/A

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

   5. swap-sqr N/A

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

   6. sqr-neg-rev N/A

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

   7. unpow2 N/A

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

   8. metadata-eval N/A

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

   9. swap-sqr N/A

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

   10. sqr-neg-rev N/A

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

   11. lower-hypot.f64 N/A

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

   12. *-commutative N/A

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

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

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

   14. metadata-eval N/A

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

   15. lower-*.f64 N/A

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

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

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

   17. metadata-eval N/A

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

   18. lower-*.f64 72.6

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

8. Applied rewrites 72.6%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 72.6%

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

12. Taylor expanded in z around 0

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

    1. *-commutative N/A

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

    2. lower-*.f64 98.2

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

14. Applied rewrites 98.2%

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

Alternative 2: 75.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(30 \cdot y\right)\\ t_1 := -30 \cdot x - 25\\ t_2 := \mathsf{max}\left(t\_1, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-296}:\\ \;\;\;\;\mathsf{max}\left(30 \cdot x - 25, \left|\mathsf{fma}\left(t\_0, \cos \left(-30 \cdot z\right), z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{max}\left(t\_1, \left|\mathsf{fma}\left(t\_0, 1, z \cdot 30\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (sin (* 30.0 y)))
        (t_1 (- (* -30.0 x) 25.0))
        (t_2 (fmax t_1 (- (fabs (fma (* y 30.0) 1.0 (sin (* 30.0 z)))) 0.2))))
   (if (<= y -4.8e+26)
     t_2
     (if (<= y 3.4e-296)
       (fmax
        (- (* 30.0 x) 25.0)
        (- (fabs (fma t_0 (cos (* -30.0 z)) (* z 30.0))) 0.2))
       (if (<= y 7e+63)
         (fmax t_1 (- (fabs (fma t_0 1.0 (* z 30.0))) 0.2))
         t_2)))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * y));
	double t_1 = (-30.0 * x) - 25.0;
	double t_2 = fmax(t_1, (fabs(fma((y * 30.0), 1.0, sin((30.0 * z)))) - 0.2));
	double tmp;
	if (y <= -4.8e+26) {
		tmp = t_2;
	} else if (y <= 3.4e-296) {
		tmp = fmax(((30.0 * x) - 25.0), (fabs(fma(t_0, cos((-30.0 * z)), (z * 30.0))) - 0.2));
	} else if (y <= 7e+63) {
		tmp = fmax(t_1, (fabs(fma(t_0, 1.0, (z * 30.0))) - 0.2));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * y))
	t_1 = Float64(Float64(-30.0 * x) - 25.0)
	t_2 = fmax(t_1, Float64(abs(fma(Float64(y * 30.0), 1.0, sin(Float64(30.0 * z)))) - 0.2))
	tmp = 0.0
	if (y <= -4.8e+26)
		tmp = t_2;
	elseif (y <= 3.4e-296)
		tmp = fmax(Float64(Float64(30.0 * x) - 25.0), Float64(abs(fma(t_0, cos(Float64(-30.0 * z)), Float64(z * 30.0))) - 0.2));
	elseif (y <= 7e+63)
		tmp = fmax(t_1, Float64(abs(fma(t_0, 1.0, Float64(z * 30.0))) - 0.2));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(-30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision]}, Block[{t$95$2 = N[Max[t$95$1, N[(N[Abs[N[(N[(y * 30.0), $MachinePrecision] * 1.0 + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -4.8e+26], t$95$2, If[LessEqual[y, 3.4e-296], N[Max[N[(N[(30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 * N[Cos[N[(-30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 7e+63], N[Max[t$95$1, N[(N[Abs[N[(t$95$0 * 1.0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000009e26 or 7.00000000000000059e63 < y

   1. Initial program 35.2%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. cos-neg-rev N/A

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

      9. lower-cos.f64 N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-*.f64 35.2

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

   5. Applied rewrites 35.2%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 13.9

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

   8. Applied rewrites 13.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 13.8%

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

   12. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 76.5

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

   14. Applied rewrites 76.5%

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

   if -4.80000000000000009e26 < y < 3.39999999999999997e-296

   1. Initial program 58.1%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. cos-neg-rev N/A

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

      9. lower-cos.f64 N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 53.1

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

   8. Applied rewrites 53.1%

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

   9. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 87.1

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

   11. Applied rewrites 87.1%

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

   if 3.39999999999999997e-296 < y < 7.00000000000000059e63

   1. Initial program 55.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. cos-neg-rev N/A

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

      9. lower-cos.f64 N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-*.f64 55.7

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

   5. Applied rewrites 55.7%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 50.2

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

   8. Applied rewrites 50.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 50.2%

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

   12. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 88.1

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

   14. Applied rewrites 88.1%

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

Alternative 3: 75.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -30 \cdot x - 25\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+55} \lor \neg \left(y \leq 7 \cdot 10^{+63}\right):\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_0, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* -30.0 x) 25.0)))
   (if (or (<= y -1.75e+55) (not (<= y 7e+63)))
     (fmax t_0 (- (fabs (fma (* y 30.0) 1.0 (sin (* 30.0 z)))) 0.2))
     (fmax t_0 (- (fabs (fma (sin (* 30.0 y)) 1.0 (* z 30.0))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = (-30.0 * x) - 25.0;
	double tmp;
	if ((y <= -1.75e+55) || !(y <= 7e+63)) {
		tmp = fmax(t_0, (fabs(fma((y * 30.0), 1.0, sin((30.0 * z)))) - 0.2));
	} else {
		tmp = fmax(t_0, (fabs(fma(sin((30.0 * y)), 1.0, (z * 30.0))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-30.0 * x) - 25.0)
	tmp = 0.0
	if ((y <= -1.75e+55) || !(y <= 7e+63))
		tmp = fmax(t_0, Float64(abs(fma(Float64(y * 30.0), 1.0, sin(Float64(30.0 * z)))) - 0.2));
	else
		tmp = fmax(t_0, Float64(abs(fma(sin(Float64(30.0 * y)), 1.0, Float64(z * 30.0))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-30.0 * x), $MachinePrecision] - 25.0), $MachinePrecision]}, If[Or[LessEqual[y, -1.75e+55], N[Not[LessEqual[y, 7e+63]], $MachinePrecision]], N[Max[t$95$0, N[(N[Abs[N[(N[(y * 30.0), $MachinePrecision] * 1.0 + N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[t$95$0, N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] * 1.0 + N[(z * 30.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75000000000000005e55 or 7.00000000000000059e63 < y

   1. Initial program 35.1%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. cos-neg-rev N/A

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

      9. lower-cos.f64 N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-*.f64 35.1

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

   5. Applied rewrites 35.1%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 12.5

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

   8. Applied rewrites 12.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 12.5%

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

   12. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 77.9

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

   14. Applied rewrites 77.9%

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

   if -1.75000000000000005e55 < y < 7.00000000000000059e63

   1. Initial program 56.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-sin.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. cos-neg-rev N/A

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

      9. lower-cos.f64 N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. lower-sin.f64 N/A

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

      14. lower-*.f64 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in x around -inf

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

      1. lower-*.f64 46.5

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

   8. Applied rewrites 46.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 46.5%

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

   12. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 82.8

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

   14. Applied rewrites 82.8%

       \[\leadsto \mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+55} \lor \neg \left(y \leq 7 \cdot 10^{+63}\right):\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(y \cdot 30, 1, \sin \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x - 25, \left|\mathsf{fma}\left(\sin \left(30 \cdot y\right), 1, z \cdot 30\right)\right| - 0.2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.8% accurate, 4.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fmax(((-30.0 * x) - 25.0), (fabs(fma((y * 30.0), 1.0, sin((30.0 * z)))) - 0.2));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 47.5%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-sin.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. cos-neg-rev N/A

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

   9. lower-cos.f64 N/A

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

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

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

   11. metadata-eval N/A

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

   12. lower-*.f64 N/A

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

   13. lower-sin.f64 N/A

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

   14. lower-*.f64 47.5

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

5. Applied rewrites 47.5%

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

6. Taylor expanded in x around -inf

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

   1. lower-*.f64 32.7

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

8. Applied rewrites 32.7%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 32.7%

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

12. Taylor expanded in y around 0

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

    1. *-commutative N/A

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

    2. lower-*.f64 60.0

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

14. Applied rewrites 60.0%

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

Reproduce

herbie shell --seed 2025026 
(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)))