Gyroid sphere

Percentage Accurate: 46.7% → 98.4%

Time: 5.2s

Alternatives: 8

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 46.7% 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: 98.4% accurate, 3.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 46.7%

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

2. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. metadata-eval N/A

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

   4. unpow-prod-down N/A

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

   5. unpow2 N/A

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

   6. *-commutative N/A

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

   7. metadata-eval N/A

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

   8. unpow-prod-down N/A

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

   9. unpow2 N/A

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

   10. lower-hypot.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-*.f64 71.7

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

4. Applied rewrites 71.7%

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

5. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-sin.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lower-sin.f64 N/A

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

   10. lift-*.f64 71.5

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

7. Applied rewrites 71.5%

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

8. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-sin.f64 N/A

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

   5. lift-*.f64 98.4

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

10. Applied rewrites 98.4%

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

Alternative 2: 67.7% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot y, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ t_1 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;z \leq -9 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z - 25, t\_1\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-126}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|y \cdot 30\right| - 0.2\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+111}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30 - 25, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 y) (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2)))
        (t_1 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= z -9e+93)
     (fmax (- (* -30.0 z) 25.0) t_1)
     (if (<= z -2e-126)
       t_0
       (if (<= z 6.8e-6)
         (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* y 30.0)) 0.2))
         (if (<= z 3.1e+111) t_0 (fmax (- (* z 30.0) 25.0) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * y), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	double t_1 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -9e+93) {
		tmp = fmax(((-30.0 * z) - 25.0), t_1);
	} else if (z <= -2e-126) {
		tmp = t_0;
	} else if (z <= 6.8e-6) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((y * 30.0)) - 0.2));
	} else if (z <= 3.1e+111) {
		tmp = t_0;
	} else {
		tmp = fmax(((z * 30.0) - 25.0), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * y), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2))
	t_1 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (z <= -9e+93)
		tmp = fmax(Float64(Float64(-30.0 * z) - 25.0), t_1);
	elseif (z <= -2e-126)
		tmp = t_0;
	elseif (z <= 6.8e-6)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(y * 30.0)) - 0.2));
	elseif (z <= 3.1e+111)
		tmp = t_0;
	else
		tmp = fmax(Float64(Float64(z * 30.0) - 25.0), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * y), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -9e+93], N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision], If[LessEqual[z, -2e-126], t$95$0, If[LessEqual[z, 6.8e-6], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 3.1e+111], t$95$0, N[Max[N[(N[(z * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], t$95$1], $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999981e93

   1. Initial program 21.7%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 84.5

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

   7. Applied rewrites 84.5%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 84.5

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

   10. Applied rewrites 84.5%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 70.1

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

   13. Applied rewrites 70.1%

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

   if -8.99999999999999981e93 < z < -1.9999999999999999e-126 or 6.80000000000000012e-6 < z < 3.1e111

   1. Initial program 58.4%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 65.6

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

   4. Applied rewrites 65.6%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 65.4

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

   7. Applied rewrites 65.4%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 98.4

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

   10. Applied rewrites 98.4%

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

   11. Taylor expanded in y around -inf

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

   13. Applied rewrites 53.8%

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

   if -1.9999999999999999e-126 < z < 6.80000000000000012e-6

   1. Initial program 60.8%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 43.1

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

   7. Applied rewrites 43.1%

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

   8. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lift-sin.f64 N/A

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

      3. lift-*.f64 42.9

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

   10. Applied rewrites 42.9%

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

   11. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 74.4

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

   13. Applied rewrites 74.4%

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

   if 3.1e111 < z

   1. Initial program 18.5%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 85.9

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

   4. Applied rewrites 85.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 85.9

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

   7. Applied rewrites 85.9%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 85.9

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

   10. Applied rewrites 85.9%

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

   11. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 72.6

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

   13. Applied rewrites 72.6%

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

Alternative 3: 87.2% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y, t\_0\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{max}\left(\mathsf{hypot}\left(z \cdot 30, 30 \cdot x\right) - 25, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2)))
   (if (<= y -8.4e+99)
     (fmax (* -30.0 y) t_0)
     (if (<= y 6.8e+127)
       (fmax (- (hypot (* z 30.0) (* 30.0 x)) 25.0) (- (fabs (* 30.0 x)) 0.2))
       (fmax (* y 30.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2;
	double tmp;
	if (y <= -8.4e+99) {
		tmp = fmax((-30.0 * y), t_0);
	} else if (y <= 6.8e+127) {
		tmp = fmax((hypot((z * 30.0), (30.0 * x)) - 25.0), (fabs((30.0 * x)) - 0.2));
	} else {
		tmp = fmax((y * 30.0), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2)
	tmp = 0.0
	if (y <= -8.4e+99)
		tmp = fmax(Float64(-30.0 * y), t_0);
	elseif (y <= 6.8e+127)
		tmp = fmax(Float64(hypot(Float64(z * 30.0), Float64(30.0 * x)) - 25.0), Float64(abs(Float64(30.0 * x)) - 0.2));
	else
		tmp = fmax(Float64(y * 30.0), t_0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[y, -8.4e+99], N[Max[N[(-30.0 * y), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[y, 6.8e+127], N[Max[N[(N[Sqrt[N[(z * 30.0), $MachinePrecision] ^ 2 + N[(30.0 * x), $MachinePrecision] ^ 2], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * 30.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.40000000000000041e99

   1. Initial program 21.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 84.3

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

   4. Applied rewrites 84.3%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 84.3

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

   7. Applied rewrites 84.3%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 98.6

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

   10. Applied rewrites 98.6%

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

   11. Taylor expanded in y around -inf

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

   13. Applied rewrites 85.9%

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

   if -8.40000000000000041e99 < y < 6.79999999999999955e127

   1. Initial program 59.4%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 90.0

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

   4. Applied rewrites 90.0%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 89.2

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

   7. Applied rewrites 89.2%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 88.6

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

   10. Applied rewrites 88.6%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 88.0

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

   13. Applied rewrites 88.0%

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

   if 6.79999999999999955e127 < y

   1. Initial program 15.7%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 85.7

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

   4. Applied rewrites 85.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 85.7

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

   7. Applied rewrites 85.7%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 98.6

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

   10. Applied rewrites 98.6%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 84.8%

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

Alternative 4: 72.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z - 25, t\_0\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{max}\left(y \cdot 30 - 25, \left|\mathsf{fma}\left(30, x, \sin \left(z \cdot 30\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30 - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= z -5.1e+89)
     (fmax (- (* -30.0 z) 25.0) t_0)
     (if (<= z 2.75e+110)
       (fmax (- (* y 30.0) 25.0) (- (fabs (fma 30.0 x (sin (* z 30.0)))) 0.2))
       (fmax (- (* z 30.0) 25.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -5.1e+89) {
		tmp = fmax(((-30.0 * z) - 25.0), t_0);
	} else if (z <= 2.75e+110) {
		tmp = fmax(((y * 30.0) - 25.0), (fabs(fma(30.0, x, sin((z * 30.0)))) - 0.2));
	} else {
		tmp = fmax(((z * 30.0) - 25.0), t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (z <= -5.1e+89)
		tmp = fmax(Float64(Float64(-30.0 * z) - 25.0), t_0);
	elseif (z <= 2.75e+110)
		tmp = fmax(Float64(Float64(y * 30.0) - 25.0), Float64(abs(fma(30.0, x, sin(Float64(z * 30.0)))) - 0.2));
	else
		tmp = fmax(Float64(Float64(z * 30.0) - 25.0), t_0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -5.1e+89], N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 2.75e+110], N[Max[N[(N[(y * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[Sin[N[(z * 30.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(z * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.10000000000000027e89

   1. Initial program 22.3%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 84.1

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 84.1

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

   7. Applied rewrites 84.1%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 84.1

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

   10. Applied rewrites 84.1%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 69.6

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

   13. Applied rewrites 69.6%

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

   if -5.10000000000000027e89 < z < 2.74999999999999998e110

   1. Initial program 59.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 64.6

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

   4. Applied rewrites 64.6%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 64.2

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

   7. Applied rewrites 64.2%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-sin.f64 N/A

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

      5. lift-*.f64 98.2

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

   10. Applied rewrites 98.2%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 73.8

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

   13. Applied rewrites 73.8%

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

   if 2.74999999999999998e110 < z

   1. Initial program 18.7%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 85.9

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

   4. Applied rewrites 85.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 85.9

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

   7. Applied rewrites 85.9%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 85.9

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

   10. Applied rewrites 85.9%

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

   11. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 72.4

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

   13. Applied rewrites 72.4%

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

Alternative 5: 68.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\sin \left(30 \cdot x\right)\right| - 0.2\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z - 25, t\_0\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|y \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(z \cdot 30 - 25, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (fabs (sin (* 30.0 x))) 0.2)))
   (if (<= z -6.2e+93)
     (fmax (- (* -30.0 z) 25.0) t_0)
     (if (<= z 4.5e+55)
       (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* y 30.0)) 0.2))
       (fmax (- (* z 30.0) 25.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(sin((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -6.2e+93) {
		tmp = fmax(((-30.0 * z) - 25.0), t_0);
	} else if (z <= 4.5e+55) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((y * 30.0)) - 0.2));
	} else {
		tmp = fmax(((z * 30.0) - 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((30.0d0 * x))) - 0.2d0
    if (z <= (-6.2d+93)) then
        tmp = fmax((((-30.0d0) * z) - 25.0d0), t_0)
    else if (z <= 4.5d+55) then
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((y * 30.0d0)) - 0.2d0))
    else
        tmp = fmax(((z * 30.0d0) - 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((30.0 * x))) - 0.2;
	double tmp;
	if (z <= -6.2e+93) {
		tmp = fmax(((-30.0 * z) - 25.0), t_0);
	} else if (z <= 4.5e+55) {
		tmp = fmax((Math.sqrt(((x * x) * 900.0)) - 25.0), (Math.abs((y * 30.0)) - 0.2));
	} else {
		tmp = fmax(((z * 30.0) - 25.0), t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(math.sin((30.0 * x))) - 0.2
	tmp = 0
	if z <= -6.2e+93:
		tmp = fmax(((-30.0 * z) - 25.0), t_0)
	elif z <= 4.5e+55:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((y * 30.0)) - 0.2))
	else:
		tmp = fmax(((z * 30.0) - 25.0), t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(abs(sin(Float64(30.0 * x))) - 0.2)
	tmp = 0.0
	if (z <= -6.2e+93)
		tmp = fmax(Float64(Float64(-30.0 * z) - 25.0), t_0);
	elseif (z <= 4.5e+55)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(y * 30.0)) - 0.2));
	else
		tmp = fmax(Float64(Float64(z * 30.0) - 25.0), t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(sin((30.0 * x))) - 0.2;
	tmp = 0.0;
	if (z <= -6.2e+93)
		tmp = max(((-30.0 * z) - 25.0), t_0);
	elseif (z <= 4.5e+55)
		tmp = max((sqrt(((x * x) * 900.0)) - 25.0), (abs((y * 30.0)) - 0.2));
	else
		tmp = max(((z * 30.0) - 25.0), t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Abs[N[Sin[N[(30.0 * x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]}, If[LessEqual[z, -6.2e+93], N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision], If[LessEqual[z, 4.5e+55], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(N[(z * 30.0), $MachinePrecision] - 25.0), $MachinePrecision], t$95$0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.20000000000000038e93

   1. Initial program 21.7%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 84.4

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

   4. Applied rewrites 84.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 84.4

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

   7. Applied rewrites 84.4%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 84.4

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

   10. Applied rewrites 84.4%

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

   11. Taylor expanded in z around -inf

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

       1. lower-*.f64 70.0

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

   13. Applied rewrites 70.0%

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

   if -6.20000000000000038e93 < z < 4.49999999999999998e55

   1. Initial program 59.8%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 59.2

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

   4. Applied rewrites 59.2%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 38.6

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

   7. Applied rewrites 38.6%

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

   8. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lift-sin.f64 N/A

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

      3. lift-*.f64 37.7

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

   10. Applied rewrites 37.7%

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

   11. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 68.3

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

   13. Applied rewrites 68.3%

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

   if 4.49999999999999998e55 < z

   1. Initial program 28.0%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. unpow-prod-down N/A

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

      5. unpow2 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. unpow-prod-down N/A

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

      9. unpow2 N/A

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

      10. lower-hypot.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 83.4

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

   4. Applied rewrites 83.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 83.4

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 83.4

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

   10. Applied rewrites 83.4%

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

   11. Taylor expanded in x around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 66.2

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

   13. Applied rewrites 66.2%

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

Alternative 6: 98.0% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 46.7%

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

2. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. metadata-eval N/A

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

   4. unpow-prod-down N/A

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

   5. unpow2 N/A

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

   6. *-commutative N/A

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

   7. metadata-eval N/A

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

   8. unpow-prod-down N/A

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

   9. unpow2 N/A

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

   10. lower-hypot.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-*.f64 71.7

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

4. Applied rewrites 71.7%

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

5. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-sin.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lower-sin.f64 N/A

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

   10. lift-*.f64 71.5

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

7. Applied rewrites 71.5%

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

8. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-sin.f64 N/A

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

   5. lift-*.f64 98.4

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

10. Applied rewrites 98.4%

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

11. Taylor expanded in x around inf

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

    1. lift-*.f64 98.0

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

13. Applied rewrites 98.0%

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

Alternative 7: 67.8% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot x, \left|30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+152}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\left(x \cdot x\right) \cdot 900} - 25, \left|y \cdot 30\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fmax (* -30.0 x) (- (fabs (* 30.0 x)) 0.2))))
   (if (<= x -4.5e+152)
     t_0
     (if (<= x 2.3e+150)
       (fmax (- (sqrt (* (* x x) 900.0)) 25.0) (- (fabs (* y 30.0)) 0.2))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (fabs((30.0 * x)) - 0.2));
	double tmp;
	if (x <= -4.5e+152) {
		tmp = t_0;
	} else if (x <= 2.3e+150) {
		tmp = fmax((sqrt(((x * x) * 900.0)) - 25.0), (fabs((y * 30.0)) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = fmax(((-30.0d0) * x), (abs((30.0d0 * x)) - 0.2d0))
    if (x <= (-4.5d+152)) then
        tmp = t_0
    else if (x <= 2.3d+150) then
        tmp = fmax((sqrt(((x * x) * 900.0d0)) - 25.0d0), (abs((y * 30.0d0)) - 0.2d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = fmax((-30.0 * x), (Math.abs((30.0 * x)) - 0.2));
	double tmp;
	if (x <= -4.5e+152) {
		tmp = t_0;
	} else if (x <= 2.3e+150) {
		tmp = fmax((Math.sqrt(((x * x) * 900.0)) - 25.0), (Math.abs((y * 30.0)) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = fmax((-30.0 * x), (math.fabs((30.0 * x)) - 0.2))
	tmp = 0
	if x <= -4.5e+152:
		tmp = t_0
	elif x <= 2.3e+150:
		tmp = fmax((math.sqrt(((x * x) * 900.0)) - 25.0), (math.fabs((y * 30.0)) - 0.2))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = fmax(Float64(-30.0 * x), Float64(abs(Float64(30.0 * x)) - 0.2))
	tmp = 0.0
	if (x <= -4.5e+152)
		tmp = t_0;
	elseif (x <= 2.3e+150)
		tmp = fmax(Float64(sqrt(Float64(Float64(x * x) * 900.0)) - 25.0), Float64(abs(Float64(y * 30.0)) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = max((-30.0 * x), (abs((30.0 * x)) - 0.2));
	tmp = 0.0;
	if (x <= -4.5e+152)
		tmp = t_0;
	elseif (x <= 2.3e+150)
		tmp = max((sqrt(((x * x) * 900.0)) - 25.0), (abs((y * 30.0)) - 0.2));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(30.0 * x), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -4.5e+152], t$95$0, If[LessEqual[x, 2.3e+150], N[Max[N[(N[Sqrt[N[(N[(x * x), $MachinePrecision] * 900.0), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(y * 30.0), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000001e152 or 2.30000000000000001e150 < x

   1. Initial program 9.1%

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

   2. Taylor expanded in x around -inf

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

      1. lower-*.f64 40.5

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

   4. Applied rewrites 40.5%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-cos.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sin.f64 N/A

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

      10. lift-*.f64 40.5

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

   7. Applied rewrites 40.5%

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

   8. Taylor expanded in z around 0

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

      1. lift-sin.f64 N/A

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

      2. lift-*.f64 40.5

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

   10. Applied rewrites 40.5%

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

   11. Taylor expanded in x around 0

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

       1. lift-*.f64 77.0

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

   13. Applied rewrites 77.0%

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

   if -4.5000000000000001e152 < x < 2.30000000000000001e150

   1. Initial program 59.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-sin.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-sin.f64 N/A

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

      12. lift-*.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-*.f64 32.9

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

   7. Applied rewrites 32.9%

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

   8. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lift-sin.f64 N/A

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

      3. lift-*.f64 31.7

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

   10. Applied rewrites 31.7%

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

   11. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. lift-*.f64 64.6

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

   13. Applied rewrites 64.6%

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

Alternative 8: 31.6% accurate, 9.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 46.7%

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

2. Taylor expanded in x around -inf

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

   1. lower-*.f64 18.8

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

4. Applied rewrites 18.8%

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

5. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-sin.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-cos.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lower-sin.f64 N/A

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

   10. lift-*.f64 18.4

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

7. Applied rewrites 18.4%

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

8. Taylor expanded in z around 0

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

   1. lift-sin.f64 N/A

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

   2. lift-*.f64 17.8

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

10. Applied rewrites 17.8%

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

11. Taylor expanded in x around 0

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

    1. lift-*.f64 31.6

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

13. Applied rewrites 31.6%

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

Reproduce

herbie shell --seed 2025101 
(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)))