Gyroid sphere

Percentage Accurate: 46.8% → 93.3%

Time: 6.9s

Alternatives: 5

Speedup: 13.1×

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: 46.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(900 \cdot z, z, 900 \cdot \mathsf{fma}\left(y, y, x \cdot x\right)\right)\\ t_1 := 25 \cdot \frac{1}{x}\\ \mathbf{if}\;x \leq -1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(x \cdot \left(30 + t\_1\right)\right), \left|\sin \left(30 \cdot z\right) + 30 \cdot \left(y \cdot \cos \left(30 \cdot z\right)\right)\right| - 0.2\right)\\ \mathbf{elif}\;x \leq -0.94:\\ \;\;\;\;\mathsf{max}\left(\frac{t\_0 - 625}{\sqrt{t\_0} - -25}, \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - t\_1\right), \left|\mathsf{fma}\left(30, y, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* 900.0 z) z (* 900.0 (fma y y (* x x)))))
        (t_1 (* 25.0 (/ 1.0 x))))
   (if (<= x -1e+139)
     (fmax
      (* -1.0 (* x (+ 30.0 t_1)))
      (- (fabs (+ (sin (* 30.0 z)) (* 30.0 (* y (cos (* 30.0 z)))))) 0.2))
     (if (<= x -0.94)
       (fmax
        (/ (- t_0 625.0) (- (sqrt t_0) -25.0))
        (- (fabs (+ (sin (* 30.0 y)) (* 30.0 z))) 0.2))
       (fmax (* x (- 30.0 t_1)) (- (fabs (fma 30.0 y (* 30.0 z))) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = fma((900.0 * z), z, (900.0 * fma(y, y, (x * x))));
	double t_1 = 25.0 * (1.0 / x);
	double tmp;
	if (x <= -1e+139) {
		tmp = fmax((-1.0 * (x * (30.0 + t_1))), (fabs((sin((30.0 * z)) + (30.0 * (y * cos((30.0 * z)))))) - 0.2));
	} else if (x <= -0.94) {
		tmp = fmax(((t_0 - 625.0) / (sqrt(t_0) - -25.0)), (fabs((sin((30.0 * y)) + (30.0 * z))) - 0.2));
	} else {
		tmp = fmax((x * (30.0 - t_1)), (fabs(fma(30.0, y, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(900.0 * z), z, Float64(900.0 * fma(y, y, Float64(x * x))))
	t_1 = Float64(25.0 * Float64(1.0 / x))
	tmp = 0.0
	if (x <= -1e+139)
		tmp = fmax(Float64(-1.0 * Float64(x * Float64(30.0 + t_1))), Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * Float64(y * cos(Float64(30.0 * z)))))) - 0.2));
	elseif (x <= -0.94)
		tmp = fmax(Float64(Float64(t_0 - 625.0) / Float64(sqrt(t_0) - -25.0)), Float64(abs(Float64(sin(Float64(30.0 * y)) + Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(x * Float64(30.0 - t_1)), Float64(abs(fma(30.0, y, Float64(30.0 * z))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(900.0 * z), $MachinePrecision] * z + N[(900.0 * N[(y * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+139], N[Max[N[(-1.0 * N[(x * N[(30.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * N[(y * N[Cos[N[(30.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, -0.94], N[Max[N[(N[(t$95$0 - 625.0), $MachinePrecision] / N[(N[Sqrt[t$95$0], $MachinePrecision] - -25.0), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(x * N[(30.0 - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * y + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.00000000000000003e139

   1. Initial program 46.8%

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

   2. 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. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 29.3

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

   7. Applied rewrites 29.3%

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

   8. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-*.f64 49.2

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

   10. Applied rewrites 49.2%

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

   if -1.00000000000000003e139 < x < -0.93999999999999995

   1. Initial program 46.8%

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

   2. 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. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 46.2

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

   7. Applied rewrites 46.2%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 61.6%

      \[\leadsto \mathsf{max}\left(\color{blue}{\frac{\mathsf{fma}\left(900 \cdot z, z, 900 \cdot \mathsf{fma}\left(y, y, x \cdot x\right)\right) - 625}{\sqrt{\mathsf{fma}\left(900 \cdot z, z, 900 \cdot \mathsf{fma}\left(y, y, x \cdot x\right)\right)} - -25}}, \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]

   if -0.93999999999999995 < x

   1. Initial program 46.8%

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

   2. 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. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 46.2

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

   7. Applied rewrites 46.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 57.3

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

   10. Applied rewrites 57.3%

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

   11. Taylor expanded in y around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 84.2

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

   13. Applied rewrites 84.2%

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

Alternative 2: 92.7% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot x, \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\mathsf{fma}\left(30, y, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.02e+18)
   (fmax (* -30.0 x) (- (fabs (+ (sin (* 30.0 y)) (* 30.0 z))) 0.2))
   (fmax
    (* x (- 30.0 (* 25.0 (/ 1.0 x))))
    (- (fabs (fma 30.0 y (* 30.0 z))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.02e+18) {
		tmp = fmax((-30.0 * x), (fabs((sin((30.0 * y)) + (30.0 * z))) - 0.2));
	} else {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (fabs(fma(30.0, y, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.02e+18)
		tmp = fmax(Float64(-30.0 * x), Float64(abs(Float64(sin(Float64(30.0 * y)) + Float64(30.0 * z))) - 0.2));
	else
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), Float64(abs(fma(30.0, y, Float64(30.0 * z))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.02e+18], N[Max[N[(-30.0 * x), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision] + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * y + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e18

   1. Initial program 46.8%

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

   2. 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. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 46.2

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

   7. Applied rewrites 46.2%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 61.6%

      \[\leadsto \mathsf{max}\left(\color{blue}{\frac{\mathsf{fma}\left(900 \cdot z, z, 900 \cdot \mathsf{fma}\left(y, y, x \cdot x\right)\right) - 625}{\sqrt{\mathsf{fma}\left(900 \cdot z, z, 900 \cdot \mathsf{fma}\left(y, y, x \cdot x\right)\right)} - -25}}, \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]

   10. Taylor expanded in x around -inf

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

       1. lower-*.f64 44.9

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

   12. Applied rewrites 44.9%

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

   if -1.02e18 < x

   1. Initial program 46.8%

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

   2. 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. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 46.2

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

   7. Applied rewrites 46.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 57.3

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

   10. Applied rewrites 57.3%

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

   11. Taylor expanded in y around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 84.2

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

   13. Applied rewrites 84.2%

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

Alternative 3: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \leq 10^{+154}:\\ \;\;\;\;\mathsf{max}\left(\sqrt{\mathsf{fma}\left(30 \cdot x, 30 \cdot x, 900 \cdot \mathsf{fma}\left(y, y, z \cdot z\right)\right)} - 25, \left|30 \cdot z\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x \cdot \left(30 - 25 \cdot \frac{1}{x}\right), \left|\mathsf{fma}\left(30, y, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (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))
      1e+154)
   (fmax
    (- (sqrt (fma (* 30.0 x) (* 30.0 x) (* 900.0 (fma y y (* z z))))) 25.0)
    (- (fabs (* 30.0 z)) 0.2))
   (fmax
    (* x (- 30.0 (* 25.0 (/ 1.0 x))))
    (- (fabs (fma 30.0 y (* 30.0 z))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (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)) <= 1e+154) {
		tmp = fmax((sqrt(fma((30.0 * x), (30.0 * x), (900.0 * fma(y, y, (z * z))))) - 25.0), (fabs((30.0 * z)) - 0.2));
	} else {
		tmp = fmax((x * (30.0 - (25.0 * (1.0 / x)))), (fabs(fma(30.0, y, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (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)) <= 1e+154)
		tmp = fmax(Float64(sqrt(fma(Float64(30.0 * x), Float64(30.0 * x), Float64(900.0 * fma(y, y, Float64(z * z))))) - 25.0), Float64(abs(Float64(30.0 * z)) - 0.2));
	else
		tmp = fmax(Float64(x * Float64(30.0 - Float64(25.0 * Float64(1.0 / x)))), Float64(abs(fma(30.0, y, Float64(30.0 * z))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[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], 1e+154], N[Max[N[(N[Sqrt[N[(N[(30.0 * x), $MachinePrecision] * N[(30.0 * x), $MachinePrecision] + N[(900.0 * N[(y * y + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(x * N[(30.0 - N[(25.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * y + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64))) < 1.00000000000000004e154

   1. Initial program 46.8%

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

   2. 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. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 46.2

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

   7. Applied rewrites 46.2%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-pow.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. unpow-prod-down N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. lift-pow.f64 N/A

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

      18. unpow-prod-down N/A

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

      19. pow2 N/A

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

      20. lift-*.f64 N/A

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

      21. metadata-eval N/A

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

      22. distribute-rgt-out N/A

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

      23. lower-*.f64 N/A

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

      24. unpow2 N/A

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

      25. lower-fma.f64 46.1

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in y around 0

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

       1. lower-*.f64 45.8

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

   12. Applied rewrites 45.8%

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

   if 1.00000000000000004e154 < (fmax.f64 (-.f64 (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 x #s(literal 30 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 y #s(literal 30 binary64)) #s(literal 2 binary64))) (pow.f64 (*.f64 z #s(literal 30 binary64)) #s(literal 2 binary64)))) #s(literal 25 binary64)) (-.f64 (fabs.f64 (+.f64 (+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal 30 binary64))) (cos.f64 (*.f64 y #s(literal 30 binary64)))) (*.f64 (sin.f64 (*.f64 y #s(literal 30 binary64))) (cos.f64 (*.f64 z #s(literal 30 binary64))))) (*.f64 (sin.f64 (*.f64 z #s(literal 30 binary64))) (cos.f64 (*.f64 x #s(literal 30 binary64)))))) #s(literal 1/5 binary64)))

   1. Initial program 46.8%

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

   2. 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. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-cos.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-sin.f64 N/A

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

      8. lower-*.f64 46.5

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

   4. Applied rewrites 46.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-sin.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 46.2

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

   7. Applied rewrites 46.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 57.3

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

   10. Applied rewrites 57.3%

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

   11. Taylor expanded in y around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 84.2

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

   13. Applied rewrites 84.2%

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

Alternative 4: 84.2% accurate, 10.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 46.8%

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

2. 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. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-cos.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-sin.f64 N/A

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

   8. lower-*.f64 46.5

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

4. Applied rewrites 46.5%

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

5. Taylor expanded in z around 0

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

   1. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 46.2

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

7. Applied rewrites 46.2%

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

8. Taylor expanded in x around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 57.3

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

10. Applied rewrites 57.3%

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

11. Taylor expanded in y around 0

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

    1. lower-fma.f64 N/A

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

    2. lower-*.f64 84.2

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

13. Applied rewrites 84.2%

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

Alternative 5: 56.3% accurate, 13.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 46.8%

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

2. 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. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-cos.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-sin.f64 N/A

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

   8. lower-*.f64 46.5

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

4. Applied rewrites 46.5%

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

5. Taylor expanded in z around 0

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

   1. lower-+.f64 N/A

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

   2. lower-sin.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 46.2

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

7. Applied rewrites 46.2%

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

8. Taylor expanded in x around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 57.3

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

10. Applied rewrites 57.3%

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

11. Taylor expanded in y around 0

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

    1. lower-*.f64 56.3

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

13. Applied rewrites 56.3%

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

Reproduce

herbie shell --seed 2025140 
(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)))