Gyroid sphere

Percentage Accurate: 45.8% → 98.8%

Time: 3.7s

Alternatives: 2

Speedup: 11.9×

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (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

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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF (((sqrt(((((x * (30)) ^ (2)) + ((y * (30)) ^ (2))) + ((z * (30)) ^ (2))))) - (25)) > ((abs(((((sin((x * (30)))) * (cos((y * (30))))) + ((sin((y * (30)))) * (cos((z * (30)))))) + ((sin((z * (30)))) * (cos((x * (30)))))))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN ((sqrt(((((x * (30)) ^ (2)) + ((y * (30)) ^ (2))) + ((z * (30)) ^ (2))))) - (25)) ELSE ((abs(((((sin((x * (30)))) * (cos((y * (30))))) + ((sin((y * (30)))) * (cos((z * (30)))))) + ((sin((z * (30)))) * (cos((x * (30)))))))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	tmp
END code

Initial Program: 45.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (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

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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF (((sqrt(((((x * (30)) ^ (2)) + ((y * (30)) ^ (2))) + ((z * (30)) ^ (2))))) - (25)) > ((abs(((((sin((x * (30)))) * (cos((y * (30))))) + ((sin((y * (30)))) * (cos((z * (30)))))) + ((sin((z * (30)))) * (cos((x * (30)))))))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN ((sqrt(((((x * (30)) ^ (2)) + ((y * (30)) ^ (2))) + ((z * (30)) ^ (2))))) - (25)) ELSE ((abs(((((sin((x * (30)))) * (cos((y * (30))))) + ((sin((y * (30)))) * (cos((z * (30)))))) + ((sin((z * (30)))) * (cos((x * (30)))))))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	tmp
END code

Alternative 1: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\sqrt{\left({\left(x \cdot 30\right)}^{2} + {\left(y \cdot 30\right)}^{2}\right) + {\left(z \cdot 30\right)}^{2}} - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right)\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+143}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot y - 25, \left|\mathsf{fma}\left(30, x, \mathsf{fma}\left(30, y, 30 \cdot z\right)\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (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))))
  (if (<= t_0 2e+143)
    t_0
    (fmax
     (- (* -30.0 y) 25.0)
     (- (fabs (fma 30.0 x (fma 30.0 y (* 30.0 z)))) 0.2)))))

C

double code(double x, double y, double z) {
	double t_0 = 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));
	double tmp;
	if (t_0 <= 2e+143) {
		tmp = t_0;
	} else {
		tmp = fmax(((-30.0 * y) - 25.0), (fabs(fma(30.0, x, fma(30.0, y, (30.0 * z)))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= 2e+143)
		tmp = t_0;
	else
		tmp = fmax(Float64(Float64(-30.0 * y) - 25.0), Float64(abs(fma(30.0, x, fma(30.0, y, Float64(30.0 * z)))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, 2e+143], t$95$0, N[Max[N[(N[(-30.0 * y), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[(30.0 * y + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF (((sqrt(((((x * (30)) ^ (2)) + ((y * (30)) ^ (2))) + ((z * (30)) ^ (2))))) - (25)) > ((abs(((((sin((x * (30)))) * (cos((y * (30))))) + ((sin((y * (30)))) * (cos((z * (30)))))) + ((sin((z * (30)))) * (cos((x * (30)))))))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN ((sqrt(((((x * (30)) ^ (2)) + ((y * (30)) ^ (2))) + ((z * (30)) ^ (2))))) - (25)) ELSE ((abs(((((sin((x * (30)))) * (cos((y * (30))))) + ((sin((y * (30)))) * (cos((z * (30)))))) + ((sin((z * (30)))) * (cos((x * (30)))))))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	LET t_0 = tmp IN
		LET tmp_2 = IF ((((-30) * y) - (25)) > ((abs((((30) * x) + (((30) * y) + ((30) * z))))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (((-30) * y) - (25)) ELSE ((abs((((30) * x) + (((30) * y) + ((30) * z))))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
		LET tmp_1 = IF (t_0 <= (200000000000000004749086471730221071481731585565736437494692997734047485908404114513635525643216658825869193826768023215158682633978016314687488)) THEN t_0 ELSE tmp_2 ENDIF IN
	tmp_1
END code

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))) < 2e143

   1. Initial program 45.8%

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

   if 2e143 < (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 45.8%

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

   2. Taylor expanded in y around -inf

      \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 29.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|\sin \left(30 \cdot y\right) + \left(30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right) + \cos \left(30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 49.0%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|\sin \left(30 \cdot x\right) + \left(30 \cdot y + 30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right)\right)\right| - 0.2\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 61.8%

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

   11. Taylor expanded in x around 0

       \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|30 \cdot x + \left(30 \cdot y + 30 \cdot z\right)\right| - 0.2\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 96.7%

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

Alternative 2: 96.7% accurate, 11.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp = IF ((((-30) * y) - (25)) > ((abs((((30) * x) + (((30) * y) + ((30) * z))))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (((-30) * y) - (25)) ELSE ((abs((((30) * x) + (((30) * y) + ((30) * z))))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	tmp
END code

Derivation

1. Initial program 45.8%

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

2. Taylor expanded in y around -inf

   \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|\left(\sin \left(x \cdot 30\right) \cdot \cos \left(y \cdot 30\right) + \sin \left(y \cdot 30\right) \cdot \cos \left(z \cdot 30\right)\right) + \sin \left(z \cdot 30\right) \cdot \cos \left(x \cdot 30\right)\right| - 0.2\right) \]
3. Step-by-step derivation

4. Applied rewrites 29.8%

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

5. Taylor expanded in z around 0

   \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|\sin \left(30 \cdot y\right) + \left(30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right) + \cos \left(30 \cdot y\right) \cdot \sin \left(30 \cdot x\right)\right)\right| - 0.2\right) \]
6. Step-by-step derivation

7. Applied rewrites 49.0%

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

8. Taylor expanded in y around 0

   \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|\sin \left(30 \cdot x\right) + \left(30 \cdot y + 30 \cdot \left(z \cdot \cos \left(30 \cdot x\right)\right)\right)\right| - 0.2\right) \]
9. Step-by-step derivation

10. Applied rewrites 61.8%

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

11. Taylor expanded in x around 0

    \[\leadsto \mathsf{max}\left(-30 \cdot y - 25, \left|30 \cdot x + \left(30 \cdot y + 30 \cdot z\right)\right| - 0.2\right) \]
12. Step-by-step derivation

13. Applied rewrites 96.7%

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

Reproduce

herbie shell --seed 2026086 
(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)))