Gyroid sphere

Percentage Accurate: 46.6% → 94.4%

Time: 28.2s

Alternatives: 3

Speedup: 19.2×

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: 46.6% 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: 94.4% accurate, 8.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \cdot 30 \leq 4 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z - 25, \left|\mathsf{fma}\left(30, x, 30 \cdot y\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(y \cdot \left(30 - 25 \cdot \frac{1}{y}\right), \left|\mathsf{fma}\left(30, x, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= (* z 30.0) 4e-46)
  (fmax (- (* -30.0 z) 25.0) (- (fabs (fma 30.0 x (* 30.0 y))) 0.2))
  (fmax
   (* y (- 30.0 (* 25.0 (/ 1.0 y))))
   (- (fabs (fma 30.0 x (* 30.0 z))) 0.2))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * 30.0) <= 4e-46) {
		tmp = fmax(((-30.0 * z) - 25.0), (fabs(fma(30.0, x, (30.0 * y))) - 0.2));
	} else {
		tmp = fmax((y * (30.0 - (25.0 * (1.0 / y)))), (fabs(fma(30.0, x, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * 30.0) <= 4e-46)
		tmp = fmax(Float64(Float64(-30.0 * z) - 25.0), Float64(abs(fma(30.0, x, Float64(30.0 * y))) - 0.2));
	else
		tmp = fmax(Float64(y * Float64(30.0 - Float64(25.0 * Float64(1.0 / y)))), Float64(abs(fma(30.0, x, Float64(30.0 * z))) - 0.2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * 30.0), $MachinePrecision], 4e-46], N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[(30.0 * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[N[(y * N[(30.0 - N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[(30.0 * z), $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_2 = IF ((((-30) * z) - (25)) > ((abs((((30) * x) + ((30) * y)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (((-30) * z) - (25)) ELSE ((abs((((30) * x) + ((30) * y)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	LET tmp_3 = IF ((y * ((30) - ((25) * ((1) / y)))) > ((abs((((30) * x) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (y * ((30) - ((25) * ((1) / y)))) ELSE ((abs((((30) * x) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	LET tmp_1 = IF ((z * (30)) <= (40000000000000000919961738156528673140238465635323379551573975153410589607508903666295307727068461781844315680136997710747426282296146382577717304229736328125e-203)) THEN tmp_2 ELSE tmp_3 ENDIF IN
	tmp_1
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 30 binary64)) < 4.0000000000000001e-46

   1. Initial program 46.6%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 31.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 49.5%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 56.8%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 83.3%

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

   if 4.0000000000000001e-46 < (*.f64 z #s(literal 30 binary64))

   1. Initial program 46.6%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 46.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.8%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 57.2%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 84.3%

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

Alternative 2: 83.3% accurate, 14.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * x + N[(30.0 * y), $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) * z) - (25)) > ((abs((((30) * x) + ((30) * y)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (((-30) * z) - (25)) ELSE ((abs((((30) * x) + ((30) * y)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	tmp
END code

Derivation

1. Initial program 46.6%

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

2. Taylor expanded in z around -inf

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

4. Applied rewrites 31.0%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 49.5%

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

8. Taylor expanded in z around 0

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

10. Applied rewrites 56.8%

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

11. Taylor expanded in x around 0

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

13. Applied rewrites 83.3%

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

Alternative 3: 55.9% accurate, 19.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(30.0 * y), $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) * z) - (25)) > ((abs(((30) * y))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (((-30) * z) - (25)) ELSE ((abs(((30) * y))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	tmp
END code

Derivation

1. Initial program 46.6%

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

2. Taylor expanded in z around -inf

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

4. Applied rewrites 31.0%

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

5. Taylor expanded in y around 0

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

7. Applied rewrites 49.5%

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

8. Taylor expanded in z around 0

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

10. Applied rewrites 56.8%

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

11. Taylor expanded in x around 0

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

13. Applied rewrites 55.9%

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

Reproduce

herbie shell --seed 2026089 +o generate:egglog
(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)))