Gyroid sphere

Percentage Accurate: 46.2% → 87.4%

Time: 3.4s

Alternatives: 5

Speedup: 10.0×

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: 46.2% 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: 87.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} t_0 := \sin \left(30 \cdot y\right)\\ t_1 := -1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right)\\ \mathbf{if}\;y \cdot 30 \leq -5 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{max}\left(t\_1, \left|t\_0 + 30 \cdot z\right| - 0.2\right)\\ \mathbf{elif}\;y \cdot 30 \leq 5000:\\ \;\;\;\;\mathsf{max}\left(-30 \cdot z - 25, \left|t\_0 + \mathsf{fma}\left(30, z, 30 \cdot \left(x \cdot \cos \left(30 \cdot y\right)\right)\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(t\_1, \left|\mathsf{fma}\left(30, y, 30 \cdot z\right)\right| - 0.2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (sin (* 30.0 y)))
       (t_1 (* -1.0 (* y (+ 30.0 (* 25.0 (/ 1.0 y)))))))
  (if (<= (* y 30.0) -5e+44)
    (fmax t_1 (- (fabs (+ t_0 (* 30.0 z))) 0.2))
    (if (<= (* y 30.0) 5000.0)
      (fmax
       (- (* -30.0 z) 25.0)
       (-
        (fabs (+ t_0 (fma 30.0 z (* 30.0 (* x (cos (* 30.0 y)))))))
        0.2))
      (fmax t_1 (- (fabs (fma 30.0 y (* 30.0 z))) 0.2))))))

C

double code(double x, double y, double z) {
	double t_0 = sin((30.0 * y));
	double t_1 = -1.0 * (y * (30.0 + (25.0 * (1.0 / y))));
	double tmp;
	if ((y * 30.0) <= -5e+44) {
		tmp = fmax(t_1, (fabs((t_0 + (30.0 * z))) - 0.2));
	} else if ((y * 30.0) <= 5000.0) {
		tmp = fmax(((-30.0 * z) - 25.0), (fabs((t_0 + fma(30.0, z, (30.0 * (x * cos((30.0 * y))))))) - 0.2));
	} else {
		tmp = fmax(t_1, (fabs(fma(30.0, y, (30.0 * z))) - 0.2));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = sin(Float64(30.0 * y))
	t_1 = Float64(-1.0 * Float64(y * Float64(30.0 + Float64(25.0 * Float64(1.0 / y)))))
	tmp = 0.0
	if (Float64(y * 30.0) <= -5e+44)
		tmp = fmax(t_1, Float64(abs(Float64(t_0 + Float64(30.0 * z))) - 0.2));
	elseif (Float64(y * 30.0) <= 5000.0)
		tmp = fmax(Float64(Float64(-30.0 * z) - 25.0), Float64(abs(Float64(t_0 + fma(30.0, z, Float64(30.0 * Float64(x * cos(Float64(30.0 * y))))))) - 0.2));
	else
		tmp = fmax(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[Sin[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 * N[(y * N[(30.0 + N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * 30.0), $MachinePrecision], -5e+44], N[Max[t$95$1, N[(N[Abs[N[(t$95$0 + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(y * 30.0), $MachinePrecision], 5000.0], N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(t$95$0 + N[(30.0 * z + N[(30.0 * N[(x * N[Cos[N[(30.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], N[Max[t$95$1, N[(N[Abs[N[(30.0 * y + 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 t_0 = (sin(((30) * y))) IN
		LET t_1 = ((-1) * (y * ((30) + ((25) * ((1) / y))))) IN
			LET tmp_2 = IF (t_1 > ((abs((t_0 + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN t_1 ELSE ((abs((t_0 + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
			LET tmp_5 = IF ((((-30) * z) - (25)) > ((abs((t_0 + (((30) * z) + ((30) * (x * (cos(((30) * y))))))))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (((-30) * z) - (25)) ELSE ((abs((t_0 + (((30) * z) + ((30) * (x * (cos(((30) * y))))))))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
			LET tmp_6 = IF (t_1 > ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN t_1 ELSE ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
			LET tmp_4 = IF ((y * (30)) <= (5000)) THEN tmp_5 ELSE tmp_6 ENDIF IN
			LET tmp_1 = IF ((y * (30)) <= (-499999999999999964878644512267775609965379584)) THEN tmp_2 ELSE tmp_4 ENDIF IN
	tmp_1
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 y #s(literal 30 binary64)) < -4.9999999999999996e44

   1. Initial program 46.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 45.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in y around -inf

      \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.2%

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

   if -4.9999999999999996e44 < (*.f64 y #s(literal 30 binary64)) < 5e3

   1. Initial program 46.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 30.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 39.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 63.2%

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

   if 5e3 < (*.f64 y #s(literal 30 binary64))

   1. Initial program 46.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 45.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in y around -inf

      \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.2%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|30 \cdot y + 30 \cdot z\right| - 0.2\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 69.0%

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

Alternative 2: 84.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(-30 \cdot z - 25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;x \cdot 30 \leq -1 \cdot 10^{+85}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \cdot 30 \leq 5 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\mathsf{fma}\left(30, y, 30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (fmax
         (- (* -30.0 z) 25.0)
         (- (fabs (+ (sin (* 30.0 z)) (* 30.0 x))) 0.2))))
  (if (<= (* x 30.0) -1e+85)
    t_0
    (if (<= (* x 30.0) 5e+133)
      (fmax
       (* -1.0 (* y (+ 30.0 (* 25.0 (/ 1.0 y)))))
       (- (fabs (fma 30.0 y (* 30.0 z))) 0.2))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax(((-30.0 * z) - 25.0), (fabs((sin((30.0 * z)) + (30.0 * x))) - 0.2));
	double tmp;
	if ((x * 30.0) <= -1e+85) {
		tmp = t_0;
	} else if ((x * 30.0) <= 5e+133) {
		tmp = fmax((-1.0 * (y * (30.0 + (25.0 * (1.0 / y))))), (fabs(fma(30.0, y, (30.0 * z))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(Float64(-30.0 * z) - 25.0), Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * x))) - 0.2))
	tmp = 0.0
	if (Float64(x * 30.0) <= -1e+85)
		tmp = t_0;
	elseif (Float64(x * 30.0) <= 5e+133)
		tmp = fmax(Float64(-1.0 * Float64(y * Float64(30.0 + Float64(25.0 * Float64(1.0 / y))))), Float64(abs(fma(30.0, y, Float64(30.0 * z))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(N[(-30.0 * z), $MachinePrecision] - 25.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x * 30.0), $MachinePrecision], -1e+85], t$95$0, If[LessEqual[N[(x * 30.0), $MachinePrecision], 5e+133], N[Max[N[(-1.0 * N[(y * N[(30.0 + N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * y + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

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(((sin(((30) * z))) + ((30) * x)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (((-30) * z) - (25)) ELSE ((abs(((sin(((30) * z))) + ((30) * x)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	LET t_0 = tmp IN
		LET tmp_4 = IF (((-1) * (y * ((30) + ((25) * ((1) / y))))) > ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN ((-1) * (y * ((30) + ((25) * ((1) / y))))) ELSE ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
		LET tmp_3 = IF ((x * (30)) <= (49999999999999996074101824835349657503774913686486230752187555524924150803830162236428630807572544714024682228918922745266209965473792)) THEN tmp_4 ELSE t_0 ENDIF IN
		LET tmp_1 = IF ((x * (30)) <= (-10000000000000000146306952306748730309700429878646550592786107871697963642511482159104)) THEN t_0 ELSE tmp_3 ENDIF IN
	tmp_1
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 30 binary64)) < -1e85 or 4.9999999999999996e133 < (*.f64 x #s(literal 30 binary64))

   1. Initial program 46.2%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.5%

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

   8. Taylor expanded in z around -inf

      \[\leadsto \mathsf{max}\left(-1 \cdot \left(z \cdot \left(30 + 25 \cdot \frac{1}{z}\right)\right), \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 57.4%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 57.4%

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

   if -1e85 < (*.f64 x #s(literal 30 binary64)) < 4.9999999999999996e133

   1. Initial program 46.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 45.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in y around -inf

      \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.2%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|30 \cdot y + 30 \cdot z\right| - 0.2\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 69.0%

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

Alternative 3: 83.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(y \cdot 30, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;x \cdot 30 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \cdot 30 \leq 10^{+175}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\mathsf{fma}\left(30, y, 30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (fmax
         (* y 30.0)
         (- (fabs (+ (sin (* 30.0 z)) (* 30.0 x))) 0.2))))
  (if (<= (* x 30.0) -5e+100)
    t_0
    (if (<= (* x 30.0) 1e+175)
      (fmax
       (* -1.0 (* y (+ 30.0 (* 25.0 (/ 1.0 y)))))
       (- (fabs (fma 30.0 y (* 30.0 z))) 0.2))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax((y * 30.0), (fabs((sin((30.0 * z)) + (30.0 * x))) - 0.2));
	double tmp;
	if ((x * 30.0) <= -5e+100) {
		tmp = t_0;
	} else if ((x * 30.0) <= 1e+175) {
		tmp = fmax((-1.0 * (y * (30.0 + (25.0 * (1.0 / y))))), (fabs(fma(30.0, y, (30.0 * z))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(Float64(y * 30.0), Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * x))) - 0.2))
	tmp = 0.0
	if (Float64(x * 30.0) <= -5e+100)
		tmp = t_0;
	elseif (Float64(x * 30.0) <= 1e+175)
		tmp = fmax(Float64(-1.0 * Float64(y * Float64(30.0 + Float64(25.0 * Float64(1.0 / y))))), Float64(abs(fma(30.0, y, Float64(30.0 * z))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[(y * 30.0), $MachinePrecision], N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x * 30.0), $MachinePrecision], -5e+100], t$95$0, If[LessEqual[N[(x * 30.0), $MachinePrecision], 1e+175], N[Max[N[(-1.0 * N[(y * N[(30.0 + N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * y + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

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 ((y * (30)) > ((abs(((sin(((30) * z))) + ((30) * x)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (y * (30)) ELSE ((abs(((sin(((30) * z))) + ((30) * x)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	LET t_0 = tmp IN
		LET tmp_4 = IF (((-1) * (y * ((30) + ((25) * ((1) / y))))) > ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN ((-1) * (y * ((30) + ((25) * ((1) / y))))) ELSE ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
		LET tmp_3 = IF ((x * (30)) <= (9999999999999999371534524623368764100273307559896873275206250678451924602685103382037576783819090846734548822294900033162112051840457868829614121240178061963384891963422539776)) THEN tmp_4 ELSE t_0 ENDIF IN
		LET tmp_1 = IF ((x * (30)) <= (-49999999999999998852475663262266831422342135996207500306499798736599672609039495565163064724075577344)) THEN t_0 ELSE tmp_3 ENDIF IN
	tmp_1
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 30 binary64)) < -4.9999999999999999e100 or 9.9999999999999994e174 < (*.f64 x #s(literal 30 binary64))

   1. Initial program 46.2%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.5%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 57.5%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 45.9%

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

   if -4.9999999999999999e100 < (*.f64 x #s(literal 30 binary64)) < 9.9999999999999994e174

   1. Initial program 46.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 45.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in y around -inf

      \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.2%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|30 \cdot y + 30 \cdot z\right| - 0.2\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 69.0%

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

Alternative 4: 82.1% accurate, 4.9× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(-25, \left|\sin \left(30 \cdot z\right) + 30 \cdot x\right| - 0.2\right)\\ \mathbf{if}\;x \cdot 30 \leq -1 \cdot 10^{+158}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \cdot 30 \leq 10^{+175}:\\ \;\;\;\;\mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\mathsf{fma}\left(30, y, 30 \cdot z\right)\right| - 0.2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0
        (fmax -25.0 (- (fabs (+ (sin (* 30.0 z)) (* 30.0 x))) 0.2))))
  (if (<= (* x 30.0) -1e+158)
    t_0
    (if (<= (* x 30.0) 1e+175)
      (fmax
       (* -1.0 (* y (+ 30.0 (* 25.0 (/ 1.0 y)))))
       (- (fabs (fma 30.0 y (* 30.0 z))) 0.2))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fmax(-25.0, (fabs((sin((30.0 * z)) + (30.0 * x))) - 0.2));
	double tmp;
	if ((x * 30.0) <= -1e+158) {
		tmp = t_0;
	} else if ((x * 30.0) <= 1e+175) {
		tmp = fmax((-1.0 * (y * (30.0 + (25.0 * (1.0 / y))))), (fabs(fma(30.0, y, (30.0 * z))) - 0.2));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fmax(-25.0, Float64(abs(Float64(sin(Float64(30.0 * z)) + Float64(30.0 * x))) - 0.2))
	tmp = 0.0
	if (Float64(x * 30.0) <= -1e+158)
		tmp = t_0;
	elseif (Float64(x * 30.0) <= 1e+175)
		tmp = fmax(Float64(-1.0 * Float64(y * Float64(30.0 + Float64(25.0 * Float64(1.0 / y))))), Float64(abs(fma(30.0, y, Float64(30.0 * z))) - 0.2));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[-25.0, N[(N[Abs[N[(N[Sin[N[(30.0 * z), $MachinePrecision]], $MachinePrecision] + N[(30.0 * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x * 30.0), $MachinePrecision], -1e+158], t$95$0, If[LessEqual[N[(x * 30.0), $MachinePrecision], 1e+175], N[Max[N[(-1.0 * N[(y * N[(30.0 + N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * y + N[(30.0 * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - 0.2), $MachinePrecision]], $MachinePrecision], t$95$0]]]

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 ((-25) > ((abs(((sin(((30) * z))) + ((30) * x)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN (-25) ELSE ((abs(((sin(((30) * z))) + ((30) * x)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	LET t_0 = tmp IN
		LET tmp_4 = IF (((-1) * (y * ((30) + ((25) * ((1) / y))))) > ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN ((-1) * (y * ((30) + ((25) * ((1) / y))))) ELSE ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
		LET tmp_3 = IF ((x * (30)) <= (9999999999999999371534524623368764100273307559896873275206250678451924602685103382037576783819090846734548822294900033162112051840457868829614121240178061963384891963422539776)) THEN tmp_4 ELSE t_0 ENDIF IN
		LET tmp_1 = IF ((x * (30)) <= (-99999999999999995287335453651211007997446182781858083179085387749785952239205787068995699003416510776387310061494932420984963311567802202010637287727642443776)) THEN t_0 ELSE tmp_3 ENDIF IN
	tmp_1
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 30 binary64)) < -9.9999999999999995e157 or 9.9999999999999994e174 < (*.f64 x #s(literal 30 binary64))

   1. Initial program 46.2%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 45.5%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 57.5%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 43.7%

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

   if -9.9999999999999995e157 < (*.f64 x #s(literal 30 binary64)) < 9.9999999999999994e174

   1. Initial program 46.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 45.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in y around -inf

      \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.2%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|30 \cdot y + 30 \cdot z\right| - 0.2\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 69.0%

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

Alternative 5: 69.0% accurate, 10.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[Max[N[(-1.0 * N[(y * N[(30.0 + N[(25.0 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(30.0 * y + 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 = IF (((-1) * (y * ((30) + ((25) * ((1) / y))))) > ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54))) THEN ((-1) * (y * ((30) + ((25) * ((1) / y))))) ELSE ((abs((((30) * y) + ((30) * z)))) - (200000000000000011102230246251565404236316680908203125e-54)) ENDIF IN
	tmp
END code

Derivation

1. Initial program 46.2%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 45.8%

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

5. Taylor expanded in z around 0

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

7. Applied rewrites 45.4%

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

8. Taylor expanded in y around -inf

   \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|\sin \left(30 \cdot y\right) + 30 \cdot z\right| - 0.2\right) \]
9. Step-by-step derivation

10. Applied rewrites 56.2%

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

11. Taylor expanded in y around 0

    \[\leadsto \mathsf{max}\left(-1 \cdot \left(y \cdot \left(30 + 25 \cdot \frac{1}{y}\right)\right), \left|30 \cdot y + 30 \cdot z\right| - 0.2\right) \]
12. Step-by-step derivation

13. Applied rewrites 69.0%

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

Reproduce

herbie shell --seed 2026084 
(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)))