Main:z from

Percentage Accurate: 92.0% → 99.1%

Time: 13.6s

Alternatives: 33

Speedup: 0.6×

Specification

Math

\[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (+
 (+
  (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y)))
  (- (sqrt (+ z 1.0)) (sqrt z)))
 (- (sqrt (+ t 1.0)) (sqrt t))))

C

double code(double x, double y, double z, double t) {
	return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((z + 1.0d0)) - sqrt(z))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((Math.sqrt((x + 1.0)) - Math.sqrt(x)) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + (Math.sqrt((z + 1.0)) - Math.sqrt(z))) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}

Python

def code(x, y, z, t):
	return (((math.sqrt((x + 1.0)) - math.sqrt(x)) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + (math.sqrt((z + 1.0)) - math.sqrt(z))) + (math.sqrt((t + 1.0)) - math.sqrt(t))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) + Float64(sqrt(Float64(y + 1.0)) - sqrt(y))) + Float64(sqrt(Float64(z + 1.0)) - sqrt(z))) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((((sqrt((x + (1)))) - (sqrt(x))) + ((sqrt((y + (1)))) - (sqrt(y)))) + ((sqrt((z + (1)))) - (sqrt(z)))) + ((sqrt((t + (1)))) - (sqrt(t)))
END code

Initial Program: 92.0% accurate, 1.0× speedup

Math

\[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (+
 (+
  (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y)))
  (- (sqrt (+ z 1.0)) (sqrt z)))
 (- (sqrt (+ t 1.0)) (sqrt t))))

C

double code(double x, double y, double z, double t) {
	return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((z + 1.0d0)) - sqrt(z))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((Math.sqrt((x + 1.0)) - Math.sqrt(x)) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + (Math.sqrt((z + 1.0)) - Math.sqrt(z))) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}

Python

def code(x, y, z, t):
	return (((math.sqrt((x + 1.0)) - math.sqrt(x)) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + (math.sqrt((z + 1.0)) - math.sqrt(z))) + (math.sqrt((t + 1.0)) - math.sqrt(t))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) + Float64(sqrt(Float64(y + 1.0)) - sqrt(y))) + Float64(sqrt(Float64(z + 1.0)) - sqrt(z))) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((((sqrt((x + (1)))) - (sqrt(x))) + ((sqrt((y + (1)))) - (sqrt(y)))) + ((sqrt((z + (1)))) - (sqrt(z)))) + ((sqrt((t + (1)))) - (sqrt(t)))
END code

Alternative 1: 99.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_3 := \mathsf{max}\left(t\_2, t\right)\\ t_4 := \mathsf{min}\left(t\_2, t\right)\\ t_5 := \sqrt{t\_4}\\ t_6 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_7 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_8 := \mathsf{min}\left(t\_7, t\_3\right)\\ t_9 := \sqrt{t\_8 + 1} - \sqrt{t\_8}\\ t_10 := \mathsf{max}\left(t\_7, t\_3\right)\\ t_11 := \mathsf{min}\left(t\_6, t\_10\right)\\ t_12 := \sqrt{t\_11}\\ t_13 := \mathsf{max}\left(t\_6, t\_10\right)\\ t_14 := \sqrt{t\_13 + 1} - \sqrt{t\_13}\\ t_15 := \sqrt{t\_11 + 1}\\ \mathbf{if}\;t\_9 \leq 5 \cdot 10^{-5}:\\ \;\;\;\;\left(\mathsf{fma}\left(0.5, \frac{1}{t\_8 \cdot \sqrt{\frac{1}{t\_8}}}, \frac{1}{t\_5 + \sqrt{1 + t\_4}}\right) + \left(t\_15 - t\_12\right)\right) + t\_14\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\sqrt{t\_4 + 1} - t\_5\right) + t\_9\right) + \frac{1}{t\_12 + t\_15}\right) + t\_14\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmin (fmin x y) z))
       (t_3 (fmax t_2 t))
       (t_4 (fmin t_2 t))
       (t_5 (sqrt t_4))
       (t_6 (fmax (fmax x y) t_1))
       (t_7 (fmin (fmax x y) t_1))
       (t_8 (fmin t_7 t_3))
       (t_9 (- (sqrt (+ t_8 1.0)) (sqrt t_8)))
       (t_10 (fmax t_7 t_3))
       (t_11 (fmin t_6 t_10))
       (t_12 (sqrt t_11))
       (t_13 (fmax t_6 t_10))
       (t_14 (- (sqrt (+ t_13 1.0)) (sqrt t_13)))
       (t_15 (sqrt (+ t_11 1.0))))
  (if (<= t_9 5e-5)
    (+
     (+
      (fma
       0.5
       (/ 1.0 (* t_8 (sqrt (/ 1.0 t_8))))
       (/ 1.0 (+ t_5 (sqrt (+ 1.0 t_4)))))
      (- t_15 t_12))
     t_14)
    (+
     (+ (+ (- (sqrt (+ t_4 1.0)) t_5) t_9) (/ 1.0 (+ t_12 t_15)))
     t_14))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmin(fmin(x, y), z);
	double t_3 = fmax(t_2, t);
	double t_4 = fmin(t_2, t);
	double t_5 = sqrt(t_4);
	double t_6 = fmax(fmax(x, y), t_1);
	double t_7 = fmin(fmax(x, y), t_1);
	double t_8 = fmin(t_7, t_3);
	double t_9 = sqrt((t_8 + 1.0)) - sqrt(t_8);
	double t_10 = fmax(t_7, t_3);
	double t_11 = fmin(t_6, t_10);
	double t_12 = sqrt(t_11);
	double t_13 = fmax(t_6, t_10);
	double t_14 = sqrt((t_13 + 1.0)) - sqrt(t_13);
	double t_15 = sqrt((t_11 + 1.0));
	double tmp;
	if (t_9 <= 5e-5) {
		tmp = (fma(0.5, (1.0 / (t_8 * sqrt((1.0 / t_8)))), (1.0 / (t_5 + sqrt((1.0 + t_4))))) + (t_15 - t_12)) + t_14;
	} else {
		tmp = (((sqrt((t_4 + 1.0)) - t_5) + t_9) + (1.0 / (t_12 + t_15))) + t_14;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmin(fmin(x, y), z)
	t_3 = fmax(t_2, t)
	t_4 = fmin(t_2, t)
	t_5 = sqrt(t_4)
	t_6 = fmax(fmax(x, y), t_1)
	t_7 = fmin(fmax(x, y), t_1)
	t_8 = fmin(t_7, t_3)
	t_9 = Float64(sqrt(Float64(t_8 + 1.0)) - sqrt(t_8))
	t_10 = fmax(t_7, t_3)
	t_11 = fmin(t_6, t_10)
	t_12 = sqrt(t_11)
	t_13 = fmax(t_6, t_10)
	t_14 = Float64(sqrt(Float64(t_13 + 1.0)) - sqrt(t_13))
	t_15 = sqrt(Float64(t_11 + 1.0))
	tmp = 0.0
	if (t_9 <= 5e-5)
		tmp = Float64(Float64(fma(0.5, Float64(1.0 / Float64(t_8 * sqrt(Float64(1.0 / t_8)))), Float64(1.0 / Float64(t_5 + sqrt(Float64(1.0 + t_4))))) + Float64(t_15 - t_12)) + t_14);
	else
		tmp = Float64(Float64(Float64(Float64(sqrt(Float64(t_4 + 1.0)) - t_5) + t_9) + Float64(1.0 / Float64(t_12 + t_15))) + t_14);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$3 = N[Max[t$95$2, t], $MachinePrecision]}, Block[{t$95$4 = N[Min[t$95$2, t], $MachinePrecision]}, Block[{t$95$5 = N[Sqrt[t$95$4], $MachinePrecision]}, Block[{t$95$6 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$7 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$8 = N[Min[t$95$7, t$95$3], $MachinePrecision]}, Block[{t$95$9 = N[(N[Sqrt[N[(t$95$8 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$8], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[Max[t$95$7, t$95$3], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$6, t$95$10], $MachinePrecision]}, Block[{t$95$12 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$13 = N[Max[t$95$6, t$95$10], $MachinePrecision]}, Block[{t$95$14 = N[(N[Sqrt[N[(t$95$13 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$13], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$15 = N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$9, 5e-5], N[(N[(N[(0.5 * N[(1.0 / N[(t$95$8 * N[Sqrt[N[(1.0 / t$95$8), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$5 + N[Sqrt[N[(1.0 + t$95$4), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$15 - t$95$12), $MachinePrecision]), $MachinePrecision] + t$95$14), $MachinePrecision], N[(N[(N[(N[(N[Sqrt[N[(t$95$4 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$5), $MachinePrecision] + t$95$9), $MachinePrecision] + N[(1.0 / N[(t$95$12 + t$95$15), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$14), $MachinePrecision]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 < z) THEN tmp_7 ELSE z ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_8 = IF (t_2 > t) THEN t_2 ELSE t ENDIF IN
			LET t_3 = tmp_8 IN
				LET tmp_9 = IF (t_2 < t) THEN t_2 ELSE t ENDIF IN
				LET t_4 = tmp_9 IN
					LET t_5 = (sqrt(t_4)) IN
						LET tmp_12 = IF (x > y) THEN x ELSE y ENDIF IN
						LET tmp_13 = IF (x > y) THEN x ELSE y ENDIF IN
						LET tmp_11 = IF (tmp_12 > t_1) THEN tmp_13 ELSE t_1 ENDIF IN
						LET t_6 = tmp_11 IN
							LET tmp_16 = IF (x > y) THEN x ELSE y ENDIF IN
							LET tmp_17 = IF (x > y) THEN x ELSE y ENDIF IN
							LET tmp_15 = IF (tmp_16 < t_1) THEN tmp_17 ELSE t_1 ENDIF IN
							LET t_7 = tmp_15 IN
								LET tmp_18 = IF (t_7 < t_3) THEN t_7 ELSE t_3 ENDIF IN
								LET t_8 = tmp_18 IN
									LET t_9 = ((sqrt((t_8 + (1)))) - (sqrt(t_8))) IN
										LET tmp_19 = IF (t_7 > t_3) THEN t_7 ELSE t_3 ENDIF IN
										LET t_10 = tmp_19 IN
											LET tmp_20 = IF (t_6 < t_10) THEN t_6 ELSE t_10 ENDIF IN
											LET t_11 = tmp_20 IN
												LET t_12 = (sqrt(t_11)) IN
													LET tmp_21 = IF (t_6 > t_10) THEN t_6 ELSE t_10 ENDIF IN
													LET t_13 = tmp_21 IN
														LET t_14 = ((sqrt((t_13 + (1)))) - (sqrt(t_13))) IN
															LET t_15 = (sqrt((t_11 + (1)))) IN
																LET tmp_22 = IF (t_9 <= (500000000000000023960868011929647991564706899225711822509765625e-67)) THEN (((((5e-1) * ((1) / (t_8 * (sqrt(((1) / t_8)))))) + ((1) / (t_5 + (sqrt(((1) + t_4)))))) + (t_15 - t_12)) + t_14) ELSE (((((sqrt((t_4 + (1)))) - t_5) + t_9) + ((1) / (t_12 + t_15))) + t_14) ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y)) < 5.0000000000000002e-5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\left(\frac{1}{2} \cdot \frac{1}{y \cdot \sqrt{\frac{1}{y}}} + \frac{1}{\sqrt{x} + \sqrt{1 + x}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 49.2%

      \[\leadsto \left(\mathsf{fma}\left(0.5, \frac{1}{y \cdot \sqrt{\frac{1}{y}}}, \frac{1}{\sqrt{x} + \sqrt{1 + x}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 5.0000000000000002e-5 < (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{max}\left(t\_3, t\right)\\ t_5 := \mathsf{min}\left(t\_2, t\_4\right)\\ t_6 := \sqrt{t\_5 + 1}\\ t_7 := \sqrt{t\_5}\\ t_8 := \mathsf{min}\left(t\_3, t\right)\\ t_9 := \sqrt{t\_8}\\ t_10 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_11 := \sqrt{t\_10}\\ t_12 := \mathsf{max}\left(t\_2, t\_4\right)\\ t_13 := \sqrt{t\_12 + 1} - \sqrt{t\_12}\\ \mathbf{if}\;t\_8 \leq 38884565.37637351:\\ \;\;\;\;\left(\left(\left(\sqrt{t\_10 + 1} - t\_11\right) + \left(\sqrt{t\_8 + 1} - t\_9\right)\right) + \frac{1}{t\_7 + t\_6}\right) + t\_13\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{1}{\left(\sqrt{1 + t\_10} + t\_11\right) \cdot t\_9} + \frac{0.5}{t\_8}\right) \cdot t\_9 + \left(t\_6 - t\_7\right)\right) + t\_13\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmax t_3 t))
       (t_5 (fmin t_2 t_4))
       (t_6 (sqrt (+ t_5 1.0)))
       (t_7 (sqrt t_5))
       (t_8 (fmin t_3 t))
       (t_9 (sqrt t_8))
       (t_10 (fmin (fmin x y) z))
       (t_11 (sqrt t_10))
       (t_12 (fmax t_2 t_4))
       (t_13 (- (sqrt (+ t_12 1.0)) (sqrt t_12))))
  (if (<= t_8 38884565.37637351)
    (+
     (+
      (+ (- (sqrt (+ t_10 1.0)) t_11) (- (sqrt (+ t_8 1.0)) t_9))
      (/ 1.0 (+ t_7 t_6)))
     t_13)
    (+
     (+
      (*
       (+ (/ 1.0 (* (+ (sqrt (+ 1.0 t_10)) t_11) t_9)) (/ 0.5 t_8))
       t_9)
      (- t_6 t_7))
     t_13))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmax(t_3, t);
	double t_5 = fmin(t_2, t_4);
	double t_6 = sqrt((t_5 + 1.0));
	double t_7 = sqrt(t_5);
	double t_8 = fmin(t_3, t);
	double t_9 = sqrt(t_8);
	double t_10 = fmin(fmin(x, y), z);
	double t_11 = sqrt(t_10);
	double t_12 = fmax(t_2, t_4);
	double t_13 = sqrt((t_12 + 1.0)) - sqrt(t_12);
	double tmp;
	if (t_8 <= 38884565.37637351) {
		tmp = (((sqrt((t_10 + 1.0)) - t_11) + (sqrt((t_8 + 1.0)) - t_9)) + (1.0 / (t_7 + t_6))) + t_13;
	} else {
		tmp = ((((1.0 / ((sqrt((1.0 + t_10)) + t_11) * t_9)) + (0.5 / t_8)) * t_9) + (t_6 - t_7)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmax(t_3, t)
    t_5 = fmin(t_2, t_4)
    t_6 = sqrt((t_5 + 1.0d0))
    t_7 = sqrt(t_5)
    t_8 = fmin(t_3, t)
    t_9 = sqrt(t_8)
    t_10 = fmin(fmin(x, y), z)
    t_11 = sqrt(t_10)
    t_12 = fmax(t_2, t_4)
    t_13 = sqrt((t_12 + 1.0d0)) - sqrt(t_12)
    if (t_8 <= 38884565.37637351d0) then
        tmp = (((sqrt((t_10 + 1.0d0)) - t_11) + (sqrt((t_8 + 1.0d0)) - t_9)) + (1.0d0 / (t_7 + t_6))) + t_13
    else
        tmp = ((((1.0d0 / ((sqrt((1.0d0 + t_10)) + t_11) * t_9)) + (0.5d0 / t_8)) * t_9) + (t_6 - t_7)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmax(t_3, t);
	double t_5 = fmin(t_2, t_4);
	double t_6 = Math.sqrt((t_5 + 1.0));
	double t_7 = Math.sqrt(t_5);
	double t_8 = fmin(t_3, t);
	double t_9 = Math.sqrt(t_8);
	double t_10 = fmin(fmin(x, y), z);
	double t_11 = Math.sqrt(t_10);
	double t_12 = fmax(t_2, t_4);
	double t_13 = Math.sqrt((t_12 + 1.0)) - Math.sqrt(t_12);
	double tmp;
	if (t_8 <= 38884565.37637351) {
		tmp = (((Math.sqrt((t_10 + 1.0)) - t_11) + (Math.sqrt((t_8 + 1.0)) - t_9)) + (1.0 / (t_7 + t_6))) + t_13;
	} else {
		tmp = ((((1.0 / ((Math.sqrt((1.0 + t_10)) + t_11) * t_9)) + (0.5 / t_8)) * t_9) + (t_6 - t_7)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmax(t_3, t)
	t_5 = fmin(t_2, t_4)
	t_6 = math.sqrt((t_5 + 1.0))
	t_7 = math.sqrt(t_5)
	t_8 = fmin(t_3, t)
	t_9 = math.sqrt(t_8)
	t_10 = fmin(fmin(x, y), z)
	t_11 = math.sqrt(t_10)
	t_12 = fmax(t_2, t_4)
	t_13 = math.sqrt((t_12 + 1.0)) - math.sqrt(t_12)
	tmp = 0
	if t_8 <= 38884565.37637351:
		tmp = (((math.sqrt((t_10 + 1.0)) - t_11) + (math.sqrt((t_8 + 1.0)) - t_9)) + (1.0 / (t_7 + t_6))) + t_13
	else:
		tmp = ((((1.0 / ((math.sqrt((1.0 + t_10)) + t_11) * t_9)) + (0.5 / t_8)) * t_9) + (t_6 - t_7)) + t_13
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmax(t_3, t)
	t_5 = fmin(t_2, t_4)
	t_6 = sqrt(Float64(t_5 + 1.0))
	t_7 = sqrt(t_5)
	t_8 = fmin(t_3, t)
	t_9 = sqrt(t_8)
	t_10 = fmin(fmin(x, y), z)
	t_11 = sqrt(t_10)
	t_12 = fmax(t_2, t_4)
	t_13 = Float64(sqrt(Float64(t_12 + 1.0)) - sqrt(t_12))
	tmp = 0.0
	if (t_8 <= 38884565.37637351)
		tmp = Float64(Float64(Float64(Float64(sqrt(Float64(t_10 + 1.0)) - t_11) + Float64(sqrt(Float64(t_8 + 1.0)) - t_9)) + Float64(1.0 / Float64(t_7 + t_6))) + t_13);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(1.0 / Float64(Float64(sqrt(Float64(1.0 + t_10)) + t_11) * t_9)) + Float64(0.5 / t_8)) * t_9) + Float64(t_6 - t_7)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = max(t_3, t);
	t_5 = min(t_2, t_4);
	t_6 = sqrt((t_5 + 1.0));
	t_7 = sqrt(t_5);
	t_8 = min(t_3, t);
	t_9 = sqrt(t_8);
	t_10 = min(min(x, y), z);
	t_11 = sqrt(t_10);
	t_12 = max(t_2, t_4);
	t_13 = sqrt((t_12 + 1.0)) - sqrt(t_12);
	tmp = 0.0;
	if (t_8 <= 38884565.37637351)
		tmp = (((sqrt((t_10 + 1.0)) - t_11) + (sqrt((t_8 + 1.0)) - t_9)) + (1.0 / (t_7 + t_6))) + t_13;
	else
		tmp = ((((1.0 / ((sqrt((1.0 + t_10)) + t_11) * t_9)) + (0.5 / t_8)) * t_9) + (t_6 - t_7)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Max[t$95$3, t], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$2, t$95$4], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$7 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$8 = N[Min[t$95$3, t], $MachinePrecision]}, Block[{t$95$9 = N[Sqrt[t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$12 = N[Max[t$95$2, t$95$4], $MachinePrecision]}, Block[{t$95$13 = N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$12], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$8, 38884565.37637351], N[(N[(N[(N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$11), $MachinePrecision] + N[(N[Sqrt[N[(t$95$8 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$9), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$7 + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision], N[(N[(N[(N[(N[(1.0 / N[(N[(N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision] + t$95$11), $MachinePrecision] * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(0.5 / t$95$8), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision] + N[(t$95$6 - t$95$7), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_12 = IF (t_3 > t) THEN t_3 ELSE t ENDIF IN
				LET t_4 = tmp_12 IN
					LET tmp_13 = IF (t_2 < t_4) THEN t_2 ELSE t_4 ENDIF IN
					LET t_5 = tmp_13 IN
						LET t_6 = (sqrt((t_5 + (1)))) IN
							LET t_7 = (sqrt(t_5)) IN
								LET tmp_14 = IF (t_3 < t) THEN t_3 ELSE t ENDIF IN
								LET t_8 = tmp_14 IN
									LET t_9 = (sqrt(t_8)) IN
										LET tmp_17 = IF (x < y) THEN x ELSE y ENDIF IN
										LET tmp_18 = IF (x < y) THEN x ELSE y ENDIF IN
										LET tmp_16 = IF (tmp_17 < z) THEN tmp_18 ELSE z ENDIF IN
										LET t_10 = tmp_16 IN
											LET t_11 = (sqrt(t_10)) IN
												LET tmp_19 = IF (t_2 > t_4) THEN t_2 ELSE t_4 ENDIF IN
												LET t_12 = tmp_19 IN
													LET t_13 = ((sqrt((t_12 + (1)))) - (sqrt(t_12))) IN
														LET tmp_20 = IF (t_8 <= (38884565376373507082462310791015625e-27)) THEN (((((sqrt((t_10 + (1)))) - t_11) + ((sqrt((t_8 + (1)))) - t_9)) + ((1) / (t_7 + t_6))) + t_13) ELSE ((((((1) / (((sqrt(((1) + t_10))) + t_11) * t_9)) + ((5e-1) / t_8)) * t_9) + (t_6 - t_7)) + t_13) ENDIF IN
	tmp_20
END code

Derivation

1. Split input into 2 regimes

2. if y < 38884565.376373507

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 38884565.376373507 < y

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\left(\frac{1}{2} \cdot \frac{1}{y \cdot \sqrt{\frac{1}{y}}} + \frac{1}{\sqrt{x} + \sqrt{1 + x}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 49.2%

      \[\leadsto \left(\mathsf{fma}\left(0.5, \frac{1}{y \cdot \sqrt{\frac{1}{y}}}, \frac{1}{\sqrt{x} + \sqrt{1 + x}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 49.2%

      \[\leadsto \left(\frac{\mathsf{fma}\left(\frac{1}{\sqrt{1 + x} + \sqrt{x}}, \frac{1}{\sqrt{y}}, \frac{0.5}{y}\right)}{\frac{1}{\sqrt{y}}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 49.1%

       \[\leadsto \left(\left(\frac{1}{\left(\sqrt{1 + x} + \sqrt{x}\right) \cdot \sqrt{y}} + \frac{0.5}{y}\right) \cdot \sqrt{y} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \sqrt{1 + t\_5}\\ t_8 := \mathsf{max}\left(t\_4, t\right)\\ t_9 := \mathsf{max}\left(t\_3, t\_8\right)\\ t_10 := \mathsf{min}\left(t\_2, t\_9\right)\\ t_11 := \mathsf{min}\left(t\_3, t\_8\right)\\ t_12 := \sqrt{t\_10}\\ t_13 := \sqrt{t\_11}\\ t_14 := \sqrt{t\_11 + 1} - t\_13\\ t_15 := \sqrt{t\_10 + 1} - t\_12\\ t_16 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + t\_14\right) + t\_15\\ t_17 := \mathsf{max}\left(t\_2, t\_9\right)\\ t_18 := \sqrt{t\_17}\\ \mathbf{if}\;t\_16 \leq 1:\\ \;\;\;\;\left(\frac{1}{t\_6 + t\_7} + t\_15\right) + \frac{0.5}{t\_18}\\ \mathbf{elif}\;t\_16 \leq 2.999995:\\ \;\;\;\;\left(t\_7 + \left(\sqrt{1 + t\_11} + \frac{1}{t\_12 + \sqrt{1 + t\_10}}\right)\right) - \left(t\_6 + t\_13\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(1 - t\_6\right) + t\_14\right) + \left(1 - t\_12\right)\right) + \frac{1}{t\_18 + \sqrt{t\_17 + 1}}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (sqrt (+ 1.0 t_5)))
       (t_8 (fmax t_4 t))
       (t_9 (fmax t_3 t_8))
       (t_10 (fmin t_2 t_9))
       (t_11 (fmin t_3 t_8))
       (t_12 (sqrt t_10))
       (t_13 (sqrt t_11))
       (t_14 (- (sqrt (+ t_11 1.0)) t_13))
       (t_15 (- (sqrt (+ t_10 1.0)) t_12))
       (t_16 (+ (+ (- (sqrt (+ t_5 1.0)) t_6) t_14) t_15))
       (t_17 (fmax t_2 t_9))
       (t_18 (sqrt t_17)))
  (if (<= t_16 1.0)
    (+ (+ (/ 1.0 (+ t_6 t_7)) t_15) (/ 0.5 t_18))
    (if (<= t_16 2.999995)
      (-
       (+
        t_7
        (+ (sqrt (+ 1.0 t_11)) (/ 1.0 (+ t_12 (sqrt (+ 1.0 t_10))))))
       (+ t_6 t_13))
      (+
       (+ (+ (- 1.0 t_6) t_14) (- 1.0 t_12))
       (/ 1.0 (+ t_18 (sqrt (+ t_17 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = sqrt((1.0 + t_5));
	double t_8 = fmax(t_4, t);
	double t_9 = fmax(t_3, t_8);
	double t_10 = fmin(t_2, t_9);
	double t_11 = fmin(t_3, t_8);
	double t_12 = sqrt(t_10);
	double t_13 = sqrt(t_11);
	double t_14 = sqrt((t_11 + 1.0)) - t_13;
	double t_15 = sqrt((t_10 + 1.0)) - t_12;
	double t_16 = ((sqrt((t_5 + 1.0)) - t_6) + t_14) + t_15;
	double t_17 = fmax(t_2, t_9);
	double t_18 = sqrt(t_17);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_18);
	} else if (t_16 <= 2.999995) {
		tmp = (t_7 + (sqrt((1.0 + t_11)) + (1.0 / (t_12 + sqrt((1.0 + t_10)))))) - (t_6 + t_13);
	} else {
		tmp = (((1.0 - t_6) + t_14) + (1.0 - t_12)) + (1.0 / (t_18 + sqrt((t_17 + 1.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_18
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = sqrt((1.0d0 + t_5))
    t_8 = fmax(t_4, t)
    t_9 = fmax(t_3, t_8)
    t_10 = fmin(t_2, t_9)
    t_11 = fmin(t_3, t_8)
    t_12 = sqrt(t_10)
    t_13 = sqrt(t_11)
    t_14 = sqrt((t_11 + 1.0d0)) - t_13
    t_15 = sqrt((t_10 + 1.0d0)) - t_12
    t_16 = ((sqrt((t_5 + 1.0d0)) - t_6) + t_14) + t_15
    t_17 = fmax(t_2, t_9)
    t_18 = sqrt(t_17)
    if (t_16 <= 1.0d0) then
        tmp = ((1.0d0 / (t_6 + t_7)) + t_15) + (0.5d0 / t_18)
    else if (t_16 <= 2.999995d0) then
        tmp = (t_7 + (sqrt((1.0d0 + t_11)) + (1.0d0 / (t_12 + sqrt((1.0d0 + t_10)))))) - (t_6 + t_13)
    else
        tmp = (((1.0d0 - t_6) + t_14) + (1.0d0 - t_12)) + (1.0d0 / (t_18 + sqrt((t_17 + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = Math.sqrt((1.0 + t_5));
	double t_8 = fmax(t_4, t);
	double t_9 = fmax(t_3, t_8);
	double t_10 = fmin(t_2, t_9);
	double t_11 = fmin(t_3, t_8);
	double t_12 = Math.sqrt(t_10);
	double t_13 = Math.sqrt(t_11);
	double t_14 = Math.sqrt((t_11 + 1.0)) - t_13;
	double t_15 = Math.sqrt((t_10 + 1.0)) - t_12;
	double t_16 = ((Math.sqrt((t_5 + 1.0)) - t_6) + t_14) + t_15;
	double t_17 = fmax(t_2, t_9);
	double t_18 = Math.sqrt(t_17);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_18);
	} else if (t_16 <= 2.999995) {
		tmp = (t_7 + (Math.sqrt((1.0 + t_11)) + (1.0 / (t_12 + Math.sqrt((1.0 + t_10)))))) - (t_6 + t_13);
	} else {
		tmp = (((1.0 - t_6) + t_14) + (1.0 - t_12)) + (1.0 / (t_18 + Math.sqrt((t_17 + 1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = math.sqrt((1.0 + t_5))
	t_8 = fmax(t_4, t)
	t_9 = fmax(t_3, t_8)
	t_10 = fmin(t_2, t_9)
	t_11 = fmin(t_3, t_8)
	t_12 = math.sqrt(t_10)
	t_13 = math.sqrt(t_11)
	t_14 = math.sqrt((t_11 + 1.0)) - t_13
	t_15 = math.sqrt((t_10 + 1.0)) - t_12
	t_16 = ((math.sqrt((t_5 + 1.0)) - t_6) + t_14) + t_15
	t_17 = fmax(t_2, t_9)
	t_18 = math.sqrt(t_17)
	tmp = 0
	if t_16 <= 1.0:
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_18)
	elif t_16 <= 2.999995:
		tmp = (t_7 + (math.sqrt((1.0 + t_11)) + (1.0 / (t_12 + math.sqrt((1.0 + t_10)))))) - (t_6 + t_13)
	else:
		tmp = (((1.0 - t_6) + t_14) + (1.0 - t_12)) + (1.0 / (t_18 + math.sqrt((t_17 + 1.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = sqrt(Float64(1.0 + t_5))
	t_8 = fmax(t_4, t)
	t_9 = fmax(t_3, t_8)
	t_10 = fmin(t_2, t_9)
	t_11 = fmin(t_3, t_8)
	t_12 = sqrt(t_10)
	t_13 = sqrt(t_11)
	t_14 = Float64(sqrt(Float64(t_11 + 1.0)) - t_13)
	t_15 = Float64(sqrt(Float64(t_10 + 1.0)) - t_12)
	t_16 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + t_14) + t_15)
	t_17 = fmax(t_2, t_9)
	t_18 = sqrt(t_17)
	tmp = 0.0
	if (t_16 <= 1.0)
		tmp = Float64(Float64(Float64(1.0 / Float64(t_6 + t_7)) + t_15) + Float64(0.5 / t_18));
	elseif (t_16 <= 2.999995)
		tmp = Float64(Float64(t_7 + Float64(sqrt(Float64(1.0 + t_11)) + Float64(1.0 / Float64(t_12 + sqrt(Float64(1.0 + t_10)))))) - Float64(t_6 + t_13));
	else
		tmp = Float64(Float64(Float64(Float64(1.0 - t_6) + t_14) + Float64(1.0 - t_12)) + Float64(1.0 / Float64(t_18 + sqrt(Float64(t_17 + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = sqrt((1.0 + t_5));
	t_8 = max(t_4, t);
	t_9 = max(t_3, t_8);
	t_10 = min(t_2, t_9);
	t_11 = min(t_3, t_8);
	t_12 = sqrt(t_10);
	t_13 = sqrt(t_11);
	t_14 = sqrt((t_11 + 1.0)) - t_13;
	t_15 = sqrt((t_10 + 1.0)) - t_12;
	t_16 = ((sqrt((t_5 + 1.0)) - t_6) + t_14) + t_15;
	t_17 = max(t_2, t_9);
	t_18 = sqrt(t_17);
	tmp = 0.0;
	if (t_16 <= 1.0)
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_18);
	elseif (t_16 <= 2.999995)
		tmp = (t_7 + (sqrt((1.0 + t_11)) + (1.0 / (t_12 + sqrt((1.0 + t_10)))))) - (t_6 + t_13);
	else
		tmp = (((1.0 - t_6) + t_14) + (1.0 - t_12)) + (1.0 / (t_18 + sqrt((t_17 + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$9 = N[Max[t$95$3, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$2, t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$3, t$95$8], $MachinePrecision]}, Block[{t$95$12 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$14 = N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]}, Block[{t$95$15 = N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$12), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + t$95$14), $MachinePrecision] + t$95$15), $MachinePrecision]}, Block[{t$95$17 = N[Max[t$95$2, t$95$9], $MachinePrecision]}, Block[{t$95$18 = N[Sqrt[t$95$17], $MachinePrecision]}, If[LessEqual[t$95$16, 1.0], N[(N[(N[(1.0 / N[(t$95$6 + t$95$7), $MachinePrecision]), $MachinePrecision] + t$95$15), $MachinePrecision] + N[(0.5 / t$95$18), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$16, 2.999995], N[(N[(t$95$7 + N[(N[Sqrt[N[(1.0 + t$95$11), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(t$95$12 + N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$13), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(1.0 - t$95$6), $MachinePrecision] + t$95$14), $MachinePrecision] + N[(1.0 - t$95$12), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$18 + N[Sqrt[N[(t$95$17 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET t_7 = (sqrt(((1) + t_5))) IN
								LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
								LET t_8 = tmp_17 IN
									LET tmp_18 = IF (t_3 > t_8) THEN t_3 ELSE t_8 ENDIF IN
									LET t_9 = tmp_18 IN
										LET tmp_19 = IF (t_2 < t_9) THEN t_2 ELSE t_9 ENDIF IN
										LET t_10 = tmp_19 IN
											LET tmp_20 = IF (t_3 < t_8) THEN t_3 ELSE t_8 ENDIF IN
											LET t_11 = tmp_20 IN
												LET t_12 = (sqrt(t_10)) IN
													LET t_13 = (sqrt(t_11)) IN
														LET t_14 = ((sqrt((t_11 + (1)))) - t_13) IN
															LET t_15 = ((sqrt((t_10 + (1)))) - t_12) IN
																LET t_16 = ((((sqrt((t_5 + (1)))) - t_6) + t_14) + t_15) IN
																	LET tmp_21 = IF (t_2 > t_9) THEN t_2 ELSE t_9 ENDIF IN
																	LET t_17 = tmp_21 IN
																		LET t_18 = (sqrt(t_17)) IN
																			LET tmp_23 = IF (t_16 <= (29999950000000001892885848064906895160675048828125e-49)) THEN ((t_7 + ((sqrt(((1) + t_11))) + ((1) / (t_12 + (sqrt(((1) + t_10))))))) - (t_6 + t_13)) ELSE (((((1) - t_6) + t_14) + ((1) - t_12)) + ((1) / (t_18 + (sqrt((t_17 + (1))))))) ENDIF IN
																			LET tmp_22 = IF (t_16 <= (1)) THEN ((((1) / (t_6 + t_7)) + t_15) + ((5e-1) / t_18)) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{t \cdot \sqrt{\frac{1}{t}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 28.6%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{t \cdot \sqrt{\frac{1}{t}}} \]

   10. Taylor expanded in t around 0

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{\sqrt{t}} \]
   11. Step-by-step derivation

   12. Applied rewrites 28.6%

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{\sqrt{t}} \]

   if 1 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.9999950000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.9999950000000002 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{1}{\sqrt{t} + \sqrt{t + 1}} \]

   4. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \frac{1}{\sqrt{t} + \sqrt{t + 1}} \]
   5. Step-by-step derivation

   6. Applied rewrites 49.4%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \frac{1}{\sqrt{t} + \sqrt{t + 1}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(1 - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \frac{1}{\sqrt{t} + \sqrt{t + 1}} \]
   8. Step-by-step derivation

   9. Applied rewrites 25.0%

      \[\leadsto \left(\left(\left(1 - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \frac{1}{\sqrt{t} + \sqrt{t + 1}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \sqrt{t\_2 + 1} - \sqrt{t\_2}\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{max}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{min}\left(t\_4, t\right)\\ t_8 := \sqrt{t\_7}\\ t_9 := \sqrt{t\_7 + 1} - t\_8\\ t_10 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ \mathbf{if}\;t\_9 \leq 0.2:\\ \;\;\;\;\left(\frac{1}{t\_8 + \sqrt{1 + t\_7}} + t\_3\right) + \frac{0.5}{t\_6}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t\_9 + \frac{1}{\sqrt{t\_10} + \sqrt{t\_10 + 1}}\right) + t\_3\right) + \left(\sqrt{t\_5 + 1} - t\_6\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (- (sqrt (+ t_2 1.0)) (sqrt t_2)))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmax t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmin t_4 t))
       (t_8 (sqrt t_7))
       (t_9 (- (sqrt (+ t_7 1.0)) t_8))
       (t_10 (fmin (fmax x y) t_1)))
  (if (<= t_9 0.2)
    (+ (+ (/ 1.0 (+ t_8 (sqrt (+ 1.0 t_7)))) t_3) (/ 0.5 t_6))
    (+
     (+ (+ t_9 (/ 1.0 (+ (sqrt t_10) (sqrt (+ t_10 1.0))))) t_3)
     (- (sqrt (+ t_5 1.0)) t_6)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = sqrt((t_2 + 1.0)) - sqrt(t_2);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmax(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmin(t_4, t);
	double t_8 = sqrt(t_7);
	double t_9 = sqrt((t_7 + 1.0)) - t_8;
	double t_10 = fmin(fmax(x, y), t_1);
	double tmp;
	if (t_9 <= 0.2) {
		tmp = ((1.0 / (t_8 + sqrt((1.0 + t_7)))) + t_3) + (0.5 / t_6);
	} else {
		tmp = ((t_9 + (1.0 / (sqrt(t_10) + sqrt((t_10 + 1.0))))) + t_3) + (sqrt((t_5 + 1.0)) - t_6);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = sqrt((t_2 + 1.0d0)) - sqrt(t_2)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmax(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmin(t_4, t)
    t_8 = sqrt(t_7)
    t_9 = sqrt((t_7 + 1.0d0)) - t_8
    t_10 = fmin(fmax(x, y), t_1)
    if (t_9 <= 0.2d0) then
        tmp = ((1.0d0 / (t_8 + sqrt((1.0d0 + t_7)))) + t_3) + (0.5d0 / t_6)
    else
        tmp = ((t_9 + (1.0d0 / (sqrt(t_10) + sqrt((t_10 + 1.0d0))))) + t_3) + (sqrt((t_5 + 1.0d0)) - t_6)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = Math.sqrt((t_2 + 1.0)) - Math.sqrt(t_2);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmax(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmin(t_4, t);
	double t_8 = Math.sqrt(t_7);
	double t_9 = Math.sqrt((t_7 + 1.0)) - t_8;
	double t_10 = fmin(fmax(x, y), t_1);
	double tmp;
	if (t_9 <= 0.2) {
		tmp = ((1.0 / (t_8 + Math.sqrt((1.0 + t_7)))) + t_3) + (0.5 / t_6);
	} else {
		tmp = ((t_9 + (1.0 / (Math.sqrt(t_10) + Math.sqrt((t_10 + 1.0))))) + t_3) + (Math.sqrt((t_5 + 1.0)) - t_6);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = math.sqrt((t_2 + 1.0)) - math.sqrt(t_2)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmax(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmin(t_4, t)
	t_8 = math.sqrt(t_7)
	t_9 = math.sqrt((t_7 + 1.0)) - t_8
	t_10 = fmin(fmax(x, y), t_1)
	tmp = 0
	if t_9 <= 0.2:
		tmp = ((1.0 / (t_8 + math.sqrt((1.0 + t_7)))) + t_3) + (0.5 / t_6)
	else:
		tmp = ((t_9 + (1.0 / (math.sqrt(t_10) + math.sqrt((t_10 + 1.0))))) + t_3) + (math.sqrt((t_5 + 1.0)) - t_6)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = Float64(sqrt(Float64(t_2 + 1.0)) - sqrt(t_2))
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmax(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmin(t_4, t)
	t_8 = sqrt(t_7)
	t_9 = Float64(sqrt(Float64(t_7 + 1.0)) - t_8)
	t_10 = fmin(fmax(x, y), t_1)
	tmp = 0.0
	if (t_9 <= 0.2)
		tmp = Float64(Float64(Float64(1.0 / Float64(t_8 + sqrt(Float64(1.0 + t_7)))) + t_3) + Float64(0.5 / t_6));
	else
		tmp = Float64(Float64(Float64(t_9 + Float64(1.0 / Float64(sqrt(t_10) + sqrt(Float64(t_10 + 1.0))))) + t_3) + Float64(sqrt(Float64(t_5 + 1.0)) - t_6));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = sqrt((t_2 + 1.0)) - sqrt(t_2);
	t_4 = min(min(x, y), z);
	t_5 = max(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = min(t_4, t);
	t_8 = sqrt(t_7);
	t_9 = sqrt((t_7 + 1.0)) - t_8;
	t_10 = min(max(x, y), t_1);
	tmp = 0.0;
	if (t_9 <= 0.2)
		tmp = ((1.0 / (t_8 + sqrt((1.0 + t_7)))) + t_3) + (0.5 / t_6);
	else
		tmp = ((t_9 + (1.0 / (sqrt(t_10) + sqrt((t_10 + 1.0))))) + t_3) + (sqrt((t_5 + 1.0)) - t_6);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[(N[Sqrt[N[(t$95$2 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$2], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Sqrt[t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[(N[Sqrt[N[(t$95$7 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$8), $MachinePrecision]}, Block[{t$95$10 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, If[LessEqual[t$95$9, 0.2], N[(N[(N[(1.0 / N[(t$95$8 + N[Sqrt[N[(1.0 + t$95$7), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(0.5 / t$95$6), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$9 + N[(1.0 / N[(N[Sqrt[t$95$10], $MachinePrecision] + N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET t_3 = ((sqrt((t_2 + (1)))) - (sqrt(t_2))) IN
				LET tmp_10 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_11 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_9 = IF (tmp_10 < z) THEN tmp_11 ELSE z ENDIF IN
				LET t_4 = tmp_9 IN
					LET tmp_12 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_12 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_13 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_13 IN
								LET t_8 = (sqrt(t_7)) IN
									LET t_9 = ((sqrt((t_7 + (1)))) - t_8) IN
										LET tmp_16 = IF (x > y) THEN x ELSE y ENDIF IN
										LET tmp_17 = IF (x > y) THEN x ELSE y ENDIF IN
										LET tmp_15 = IF (tmp_16 < t_1) THEN tmp_17 ELSE t_1 ENDIF IN
										LET t_10 = tmp_15 IN
											LET tmp_18 = IF (t_9 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((((1) / (t_8 + (sqrt(((1) + t_7))))) + t_3) + ((5e-1) / t_6)) ELSE (((t_9 + ((1) / ((sqrt(t_10)) + (sqrt((t_10 + (1))))))) + t_3) + ((sqrt((t_5 + (1)))) - t_6)) ENDIF IN
	tmp_18
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) < 0.20000000000000001

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{t \cdot \sqrt{\frac{1}{t}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 28.6%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{t \cdot \sqrt{\frac{1}{t}}} \]

   10. Taylor expanded in t around 0

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{\sqrt{t}} \]
   11. Step-by-step derivation

   12. Applied rewrites 28.6%

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{\sqrt{t}} \]

   if 0.20000000000000001 < (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.9%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{\sqrt{y} + \sqrt{y + 1}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 97.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \sqrt{1 + t\_5}\\ t_8 := \mathsf{max}\left(t\_4, t\right)\\ t_9 := \mathsf{min}\left(t\_3, t\_8\right)\\ t_10 := \mathsf{max}\left(t\_3, t\_8\right)\\ t_11 := \mathsf{min}\left(t\_2, t\_10\right)\\ t_12 := \sqrt{t\_11}\\ t_13 := \sqrt{t\_9}\\ t_14 := t\_6 + t\_13\\ t_15 := \sqrt{t\_11 + 1} - t\_12\\ t_16 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_9 + 1} - t\_13\right)\right) + t\_15\\ t_17 := \mathsf{max}\left(t\_2, t\_10\right)\\ t_18 := t\_17 + 1\\ t_19 := \sqrt{t\_17}\\ \mathbf{if}\;t\_16 \leq 1:\\ \;\;\;\;\left(\frac{1}{t\_6 + t\_7} + t\_15\right) + \frac{0.5}{t\_19}\\ \mathbf{elif}\;t\_16 \leq 2.999995:\\ \;\;\;\;\left(t\_7 + \left(\sqrt{1 + t\_9} + \frac{1}{t\_12 + \sqrt{1 + t\_11}}\right)\right) - t\_14\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - t\_14\right) + \left(1 - t\_12\right)\right) + \frac{t\_18 - t\_17}{t\_19 + \sqrt{t\_18}}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (sqrt (+ 1.0 t_5)))
       (t_8 (fmax t_4 t))
       (t_9 (fmin t_3 t_8))
       (t_10 (fmax t_3 t_8))
       (t_11 (fmin t_2 t_10))
       (t_12 (sqrt t_11))
       (t_13 (sqrt t_9))
       (t_14 (+ t_6 t_13))
       (t_15 (- (sqrt (+ t_11 1.0)) t_12))
       (t_16
        (+
         (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_9 1.0)) t_13))
         t_15))
       (t_17 (fmax t_2 t_10))
       (t_18 (+ t_17 1.0))
       (t_19 (sqrt t_17)))
  (if (<= t_16 1.0)
    (+ (+ (/ 1.0 (+ t_6 t_7)) t_15) (/ 0.5 t_19))
    (if (<= t_16 2.999995)
      (-
       (+
        t_7
        (+ (sqrt (+ 1.0 t_9)) (/ 1.0 (+ t_12 (sqrt (+ 1.0 t_11))))))
       t_14)
      (+
       (+ (- 2.0 t_14) (- 1.0 t_12))
       (/ (- t_18 t_17) (+ t_19 (sqrt t_18))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = sqrt((1.0 + t_5));
	double t_8 = fmax(t_4, t);
	double t_9 = fmin(t_3, t_8);
	double t_10 = fmax(t_3, t_8);
	double t_11 = fmin(t_2, t_10);
	double t_12 = sqrt(t_11);
	double t_13 = sqrt(t_9);
	double t_14 = t_6 + t_13;
	double t_15 = sqrt((t_11 + 1.0)) - t_12;
	double t_16 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_9 + 1.0)) - t_13)) + t_15;
	double t_17 = fmax(t_2, t_10);
	double t_18 = t_17 + 1.0;
	double t_19 = sqrt(t_17);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_19);
	} else if (t_16 <= 2.999995) {
		tmp = (t_7 + (sqrt((1.0 + t_9)) + (1.0 / (t_12 + sqrt((1.0 + t_11)))))) - t_14;
	} else {
		tmp = ((2.0 - t_14) + (1.0 - t_12)) + ((t_18 - t_17) / (t_19 + sqrt(t_18)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_18
    real(8) :: t_19
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = sqrt((1.0d0 + t_5))
    t_8 = fmax(t_4, t)
    t_9 = fmin(t_3, t_8)
    t_10 = fmax(t_3, t_8)
    t_11 = fmin(t_2, t_10)
    t_12 = sqrt(t_11)
    t_13 = sqrt(t_9)
    t_14 = t_6 + t_13
    t_15 = sqrt((t_11 + 1.0d0)) - t_12
    t_16 = ((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_9 + 1.0d0)) - t_13)) + t_15
    t_17 = fmax(t_2, t_10)
    t_18 = t_17 + 1.0d0
    t_19 = sqrt(t_17)
    if (t_16 <= 1.0d0) then
        tmp = ((1.0d0 / (t_6 + t_7)) + t_15) + (0.5d0 / t_19)
    else if (t_16 <= 2.999995d0) then
        tmp = (t_7 + (sqrt((1.0d0 + t_9)) + (1.0d0 / (t_12 + sqrt((1.0d0 + t_11)))))) - t_14
    else
        tmp = ((2.0d0 - t_14) + (1.0d0 - t_12)) + ((t_18 - t_17) / (t_19 + sqrt(t_18)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = Math.sqrt((1.0 + t_5));
	double t_8 = fmax(t_4, t);
	double t_9 = fmin(t_3, t_8);
	double t_10 = fmax(t_3, t_8);
	double t_11 = fmin(t_2, t_10);
	double t_12 = Math.sqrt(t_11);
	double t_13 = Math.sqrt(t_9);
	double t_14 = t_6 + t_13;
	double t_15 = Math.sqrt((t_11 + 1.0)) - t_12;
	double t_16 = ((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_9 + 1.0)) - t_13)) + t_15;
	double t_17 = fmax(t_2, t_10);
	double t_18 = t_17 + 1.0;
	double t_19 = Math.sqrt(t_17);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_19);
	} else if (t_16 <= 2.999995) {
		tmp = (t_7 + (Math.sqrt((1.0 + t_9)) + (1.0 / (t_12 + Math.sqrt((1.0 + t_11)))))) - t_14;
	} else {
		tmp = ((2.0 - t_14) + (1.0 - t_12)) + ((t_18 - t_17) / (t_19 + Math.sqrt(t_18)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = math.sqrt((1.0 + t_5))
	t_8 = fmax(t_4, t)
	t_9 = fmin(t_3, t_8)
	t_10 = fmax(t_3, t_8)
	t_11 = fmin(t_2, t_10)
	t_12 = math.sqrt(t_11)
	t_13 = math.sqrt(t_9)
	t_14 = t_6 + t_13
	t_15 = math.sqrt((t_11 + 1.0)) - t_12
	t_16 = ((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_9 + 1.0)) - t_13)) + t_15
	t_17 = fmax(t_2, t_10)
	t_18 = t_17 + 1.0
	t_19 = math.sqrt(t_17)
	tmp = 0
	if t_16 <= 1.0:
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_19)
	elif t_16 <= 2.999995:
		tmp = (t_7 + (math.sqrt((1.0 + t_9)) + (1.0 / (t_12 + math.sqrt((1.0 + t_11)))))) - t_14
	else:
		tmp = ((2.0 - t_14) + (1.0 - t_12)) + ((t_18 - t_17) / (t_19 + math.sqrt(t_18)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = sqrt(Float64(1.0 + t_5))
	t_8 = fmax(t_4, t)
	t_9 = fmin(t_3, t_8)
	t_10 = fmax(t_3, t_8)
	t_11 = fmin(t_2, t_10)
	t_12 = sqrt(t_11)
	t_13 = sqrt(t_9)
	t_14 = Float64(t_6 + t_13)
	t_15 = Float64(sqrt(Float64(t_11 + 1.0)) - t_12)
	t_16 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_9 + 1.0)) - t_13)) + t_15)
	t_17 = fmax(t_2, t_10)
	t_18 = Float64(t_17 + 1.0)
	t_19 = sqrt(t_17)
	tmp = 0.0
	if (t_16 <= 1.0)
		tmp = Float64(Float64(Float64(1.0 / Float64(t_6 + t_7)) + t_15) + Float64(0.5 / t_19));
	elseif (t_16 <= 2.999995)
		tmp = Float64(Float64(t_7 + Float64(sqrt(Float64(1.0 + t_9)) + Float64(1.0 / Float64(t_12 + sqrt(Float64(1.0 + t_11)))))) - t_14);
	else
		tmp = Float64(Float64(Float64(2.0 - t_14) + Float64(1.0 - t_12)) + Float64(Float64(t_18 - t_17) / Float64(t_19 + sqrt(t_18))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = sqrt((1.0 + t_5));
	t_8 = max(t_4, t);
	t_9 = min(t_3, t_8);
	t_10 = max(t_3, t_8);
	t_11 = min(t_2, t_10);
	t_12 = sqrt(t_11);
	t_13 = sqrt(t_9);
	t_14 = t_6 + t_13;
	t_15 = sqrt((t_11 + 1.0)) - t_12;
	t_16 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_9 + 1.0)) - t_13)) + t_15;
	t_17 = max(t_2, t_10);
	t_18 = t_17 + 1.0;
	t_19 = sqrt(t_17);
	tmp = 0.0;
	if (t_16 <= 1.0)
		tmp = ((1.0 / (t_6 + t_7)) + t_15) + (0.5 / t_19);
	elseif (t_16 <= 2.999995)
		tmp = (t_7 + (sqrt((1.0 + t_9)) + (1.0 / (t_12 + sqrt((1.0 + t_11)))))) - t_14;
	else
		tmp = ((2.0 - t_14) + (1.0 - t_12)) + ((t_18 - t_17) / (t_19 + sqrt(t_18)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$3, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Max[t$95$3, t$95$8], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$2, t$95$10], $MachinePrecision]}, Block[{t$95$12 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$14 = N[(t$95$6 + t$95$13), $MachinePrecision]}, Block[{t$95$15 = N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$12), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]), $MachinePrecision] + t$95$15), $MachinePrecision]}, Block[{t$95$17 = N[Max[t$95$2, t$95$10], $MachinePrecision]}, Block[{t$95$18 = N[(t$95$17 + 1.0), $MachinePrecision]}, Block[{t$95$19 = N[Sqrt[t$95$17], $MachinePrecision]}, If[LessEqual[t$95$16, 1.0], N[(N[(N[(1.0 / N[(t$95$6 + t$95$7), $MachinePrecision]), $MachinePrecision] + t$95$15), $MachinePrecision] + N[(0.5 / t$95$19), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$16, 2.999995], N[(N[(t$95$7 + N[(N[Sqrt[N[(1.0 + t$95$9), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(t$95$12 + N[Sqrt[N[(1.0 + t$95$11), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision], N[(N[(N[(2.0 - t$95$14), $MachinePrecision] + N[(1.0 - t$95$12), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$18 - t$95$17), $MachinePrecision] / N[(t$95$19 + N[Sqrt[t$95$18], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET t_7 = (sqrt(((1) + t_5))) IN
								LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
								LET t_8 = tmp_17 IN
									LET tmp_18 = IF (t_3 < t_8) THEN t_3 ELSE t_8 ENDIF IN
									LET t_9 = tmp_18 IN
										LET tmp_19 = IF (t_3 > t_8) THEN t_3 ELSE t_8 ENDIF IN
										LET t_10 = tmp_19 IN
											LET tmp_20 = IF (t_2 < t_10) THEN t_2 ELSE t_10 ENDIF IN
											LET t_11 = tmp_20 IN
												LET t_12 = (sqrt(t_11)) IN
													LET t_13 = (sqrt(t_9)) IN
														LET t_14 = (t_6 + t_13) IN
															LET t_15 = ((sqrt((t_11 + (1)))) - t_12) IN
																LET t_16 = ((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_9 + (1)))) - t_13)) + t_15) IN
																	LET tmp_21 = IF (t_2 > t_10) THEN t_2 ELSE t_10 ENDIF IN
																	LET t_17 = tmp_21 IN
																		LET t_18 = (t_17 + (1)) IN
																			LET t_19 = (sqrt(t_17)) IN
																				LET tmp_23 = IF (t_16 <= (29999950000000001892885848064906895160675048828125e-49)) THEN ((t_7 + ((sqrt(((1) + t_9))) + ((1) / (t_12 + (sqrt(((1) + t_11))))))) - t_14) ELSE ((((2) - t_14) + ((1) - t_12)) + ((t_18 - t_17) / (t_19 + (sqrt(t_18))))) ENDIF IN
																				LET tmp_22 = IF (t_16 <= (1)) THEN ((((1) / (t_6 + t_7)) + t_15) + ((5e-1) / t_19)) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{t \cdot \sqrt{\frac{1}{t}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 28.6%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{t \cdot \sqrt{\frac{1}{t}}} \]

   10. Taylor expanded in t around 0

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{\sqrt{t}} \]
   11. Step-by-step derivation

   12. Applied rewrites 28.6%

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{\sqrt{t}} \]

   if 1 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.9999950000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.9999950000000002 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \frac{\left(t + 1\right) - t}{\sqrt{t} + \sqrt{t + 1}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{min}\left(t\_1, t\right)\\ t_3 := \sqrt{t\_2}\\ t_4 := \sqrt{1 + t\_2}\\ t_5 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_6 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_5\right)\\ t_7 := \sqrt{t\_6 + 1} - \sqrt{t\_6}\\ t_8 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_5\right)\\ t_9 := \sqrt{t\_8}\\ t_10 := \left(\sqrt{t\_2 + 1} - t\_3\right) + \left(\sqrt{t\_8 + 1} - t\_9\right)\\ t_11 := \mathsf{max}\left(t\_1, t\right)\\ t_12 := \sqrt{t\_11}\\ t_13 := \sqrt{t\_11 + 1} - t\_12\\ \mathbf{if}\;t\_10 \leq 0.2:\\ \;\;\;\;\left(\frac{1}{t\_3 + t\_4} + t\_7\right) + \frac{0.5}{t\_12}\\ \mathbf{elif}\;t\_10 \leq 1.999998:\\ \;\;\;\;\left(\left(t\_4 + \frac{1}{t\_9 + \sqrt{1 + t\_8}}\right) - t\_3\right) + t\_13\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - \left(t\_3 + t\_9\right)\right) + t\_7\right) + t\_13\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fmin x y) z))
       (t_2 (fmin t_1 t))
       (t_3 (sqrt t_2))
       (t_4 (sqrt (+ 1.0 t_2)))
       (t_5 (fmax (fmin x y) z))
       (t_6 (fmax (fmax x y) t_5))
       (t_7 (- (sqrt (+ t_6 1.0)) (sqrt t_6)))
       (t_8 (fmin (fmax x y) t_5))
       (t_9 (sqrt t_8))
       (t_10
        (+ (- (sqrt (+ t_2 1.0)) t_3) (- (sqrt (+ t_8 1.0)) t_9)))
       (t_11 (fmax t_1 t))
       (t_12 (sqrt t_11))
       (t_13 (- (sqrt (+ t_11 1.0)) t_12)))
  (if (<= t_10 0.2)
    (+ (+ (/ 1.0 (+ t_3 t_4)) t_7) (/ 0.5 t_12))
    (if (<= t_10 1.999998)
      (+ (- (+ t_4 (/ 1.0 (+ t_9 (sqrt (+ 1.0 t_8))))) t_3) t_13)
      (+ (+ (- 2.0 (+ t_3 t_9)) t_7) t_13)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, y), z);
	double t_2 = fmin(t_1, t);
	double t_3 = sqrt(t_2);
	double t_4 = sqrt((1.0 + t_2));
	double t_5 = fmax(fmin(x, y), z);
	double t_6 = fmax(fmax(x, y), t_5);
	double t_7 = sqrt((t_6 + 1.0)) - sqrt(t_6);
	double t_8 = fmin(fmax(x, y), t_5);
	double t_9 = sqrt(t_8);
	double t_10 = (sqrt((t_2 + 1.0)) - t_3) + (sqrt((t_8 + 1.0)) - t_9);
	double t_11 = fmax(t_1, t);
	double t_12 = sqrt(t_11);
	double t_13 = sqrt((t_11 + 1.0)) - t_12;
	double tmp;
	if (t_10 <= 0.2) {
		tmp = ((1.0 / (t_3 + t_4)) + t_7) + (0.5 / t_12);
	} else if (t_10 <= 1.999998) {
		tmp = ((t_4 + (1.0 / (t_9 + sqrt((1.0 + t_8))))) - t_3) + t_13;
	} else {
		tmp = ((2.0 - (t_3 + t_9)) + t_7) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmin(fmin(x, y), z)
    t_2 = fmin(t_1, t)
    t_3 = sqrt(t_2)
    t_4 = sqrt((1.0d0 + t_2))
    t_5 = fmax(fmin(x, y), z)
    t_6 = fmax(fmax(x, y), t_5)
    t_7 = sqrt((t_6 + 1.0d0)) - sqrt(t_6)
    t_8 = fmin(fmax(x, y), t_5)
    t_9 = sqrt(t_8)
    t_10 = (sqrt((t_2 + 1.0d0)) - t_3) + (sqrt((t_8 + 1.0d0)) - t_9)
    t_11 = fmax(t_1, t)
    t_12 = sqrt(t_11)
    t_13 = sqrt((t_11 + 1.0d0)) - t_12
    if (t_10 <= 0.2d0) then
        tmp = ((1.0d0 / (t_3 + t_4)) + t_7) + (0.5d0 / t_12)
    else if (t_10 <= 1.999998d0) then
        tmp = ((t_4 + (1.0d0 / (t_9 + sqrt((1.0d0 + t_8))))) - t_3) + t_13
    else
        tmp = ((2.0d0 - (t_3 + t_9)) + t_7) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, y), z);
	double t_2 = fmin(t_1, t);
	double t_3 = Math.sqrt(t_2);
	double t_4 = Math.sqrt((1.0 + t_2));
	double t_5 = fmax(fmin(x, y), z);
	double t_6 = fmax(fmax(x, y), t_5);
	double t_7 = Math.sqrt((t_6 + 1.0)) - Math.sqrt(t_6);
	double t_8 = fmin(fmax(x, y), t_5);
	double t_9 = Math.sqrt(t_8);
	double t_10 = (Math.sqrt((t_2 + 1.0)) - t_3) + (Math.sqrt((t_8 + 1.0)) - t_9);
	double t_11 = fmax(t_1, t);
	double t_12 = Math.sqrt(t_11);
	double t_13 = Math.sqrt((t_11 + 1.0)) - t_12;
	double tmp;
	if (t_10 <= 0.2) {
		tmp = ((1.0 / (t_3 + t_4)) + t_7) + (0.5 / t_12);
	} else if (t_10 <= 1.999998) {
		tmp = ((t_4 + (1.0 / (t_9 + Math.sqrt((1.0 + t_8))))) - t_3) + t_13;
	} else {
		tmp = ((2.0 - (t_3 + t_9)) + t_7) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmin(fmin(x, y), z)
	t_2 = fmin(t_1, t)
	t_3 = math.sqrt(t_2)
	t_4 = math.sqrt((1.0 + t_2))
	t_5 = fmax(fmin(x, y), z)
	t_6 = fmax(fmax(x, y), t_5)
	t_7 = math.sqrt((t_6 + 1.0)) - math.sqrt(t_6)
	t_8 = fmin(fmax(x, y), t_5)
	t_9 = math.sqrt(t_8)
	t_10 = (math.sqrt((t_2 + 1.0)) - t_3) + (math.sqrt((t_8 + 1.0)) - t_9)
	t_11 = fmax(t_1, t)
	t_12 = math.sqrt(t_11)
	t_13 = math.sqrt((t_11 + 1.0)) - t_12
	tmp = 0
	if t_10 <= 0.2:
		tmp = ((1.0 / (t_3 + t_4)) + t_7) + (0.5 / t_12)
	elif t_10 <= 1.999998:
		tmp = ((t_4 + (1.0 / (t_9 + math.sqrt((1.0 + t_8))))) - t_3) + t_13
	else:
		tmp = ((2.0 - (t_3 + t_9)) + t_7) + t_13
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmin(fmin(x, y), z)
	t_2 = fmin(t_1, t)
	t_3 = sqrt(t_2)
	t_4 = sqrt(Float64(1.0 + t_2))
	t_5 = fmax(fmin(x, y), z)
	t_6 = fmax(fmax(x, y), t_5)
	t_7 = Float64(sqrt(Float64(t_6 + 1.0)) - sqrt(t_6))
	t_8 = fmin(fmax(x, y), t_5)
	t_9 = sqrt(t_8)
	t_10 = Float64(Float64(sqrt(Float64(t_2 + 1.0)) - t_3) + Float64(sqrt(Float64(t_8 + 1.0)) - t_9))
	t_11 = fmax(t_1, t)
	t_12 = sqrt(t_11)
	t_13 = Float64(sqrt(Float64(t_11 + 1.0)) - t_12)
	tmp = 0.0
	if (t_10 <= 0.2)
		tmp = Float64(Float64(Float64(1.0 / Float64(t_3 + t_4)) + t_7) + Float64(0.5 / t_12));
	elseif (t_10 <= 1.999998)
		tmp = Float64(Float64(Float64(t_4 + Float64(1.0 / Float64(t_9 + sqrt(Float64(1.0 + t_8))))) - t_3) + t_13);
	else
		tmp = Float64(Float64(Float64(2.0 - Float64(t_3 + t_9)) + t_7) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(min(x, y), z);
	t_2 = min(t_1, t);
	t_3 = sqrt(t_2);
	t_4 = sqrt((1.0 + t_2));
	t_5 = max(min(x, y), z);
	t_6 = max(max(x, y), t_5);
	t_7 = sqrt((t_6 + 1.0)) - sqrt(t_6);
	t_8 = min(max(x, y), t_5);
	t_9 = sqrt(t_8);
	t_10 = (sqrt((t_2 + 1.0)) - t_3) + (sqrt((t_8 + 1.0)) - t_9);
	t_11 = max(t_1, t);
	t_12 = sqrt(t_11);
	t_13 = sqrt((t_11 + 1.0)) - t_12;
	tmp = 0.0;
	if (t_10 <= 0.2)
		tmp = ((1.0 / (t_3 + t_4)) + t_7) + (0.5 / t_12);
	elseif (t_10 <= 1.999998)
		tmp = ((t_4 + (1.0 / (t_9 + sqrt((1.0 + t_8))))) - t_3) + t_13;
	else
		tmp = ((2.0 - (t_3 + t_9)) + t_7) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Min[t$95$1, t], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[N[(1.0 + t$95$2), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$5 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$6 = N[Max[N[Max[x, y], $MachinePrecision], t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[(N[Sqrt[N[(t$95$6 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$6], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[Min[N[Max[x, y], $MachinePrecision], t$95$5], $MachinePrecision]}, Block[{t$95$9 = N[Sqrt[t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[Sqrt[N[(t$95$2 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$3), $MachinePrecision] + N[(N[Sqrt[N[(t$95$8 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$9), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[Max[t$95$1, t], $MachinePrecision]}, Block[{t$95$12 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$13 = N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$12), $MachinePrecision]}, If[LessEqual[t$95$10, 0.2], N[(N[(N[(1.0 / N[(t$95$3 + t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] + N[(0.5 / t$95$12), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$10, 1.999998], N[(N[(N[(t$95$4 + N[(1.0 / N[(t$95$9 + N[Sqrt[N[(1.0 + t$95$8), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] + t$95$13), $MachinePrecision], N[(N[(N[(2.0 - N[(t$95$3 + t$95$9), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 < z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_4 = IF (t_1 < t) THEN t_1 ELSE t ENDIF IN
		LET t_2 = tmp_4 IN
			LET t_3 = (sqrt(t_2)) IN
				LET t_4 = (sqrt(((1) + t_2))) IN
					LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
					LET tmp_8 = IF (x < y) THEN x ELSE y ENDIF IN
					LET tmp_6 = IF (tmp_7 > z) THEN tmp_8 ELSE z ENDIF IN
					LET t_5 = tmp_6 IN
						LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
						LET tmp_12 = IF (x > y) THEN x ELSE y ENDIF IN
						LET tmp_10 = IF (tmp_11 > t_5) THEN tmp_12 ELSE t_5 ENDIF IN
						LET t_6 = tmp_10 IN
							LET t_7 = ((sqrt((t_6 + (1)))) - (sqrt(t_6))) IN
								LET tmp_15 = IF (x > y) THEN x ELSE y ENDIF IN
								LET tmp_16 = IF (x > y) THEN x ELSE y ENDIF IN
								LET tmp_14 = IF (tmp_15 < t_5) THEN tmp_16 ELSE t_5 ENDIF IN
								LET t_8 = tmp_14 IN
									LET t_9 = (sqrt(t_8)) IN
										LET t_10 = (((sqrt((t_2 + (1)))) - t_3) + ((sqrt((t_8 + (1)))) - t_9)) IN
											LET tmp_17 = IF (t_1 > t) THEN t_1 ELSE t ENDIF IN
											LET t_11 = tmp_17 IN
												LET t_12 = (sqrt(t_11)) IN
													LET t_13 = ((sqrt((t_11 + (1)))) - t_12) IN
														LET tmp_19 = IF (t_10 <= (19999979999999999424886709675774909555912017822265625e-52)) THEN (((t_4 + ((1) / (t_9 + (sqrt(((1) + t_8)))))) - t_3) + t_13) ELSE ((((2) - (t_3 + t_9)) + t_7) + t_13) ENDIF IN
														LET tmp_18 = IF (t_10 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((((1) / (t_3 + t_4)) + t_7) + ((5e-1) / t_12)) ELSE tmp_19 ENDIF IN
	tmp_18
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) < 0.20000000000000001

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{t \cdot \sqrt{\frac{1}{t}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 28.6%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{t \cdot \sqrt{\frac{1}{t}}} \]

   10. Taylor expanded in t around 0

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{\sqrt{t}} \]
   11. Step-by-step derivation

   12. Applied rewrites 28.6%

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{\sqrt{t}} \]

   if 0.20000000000000001 < (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) < 1.9999979999999999

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.9%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{\sqrt{y} + \sqrt{y + 1}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in z around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 40.0%

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 1.9999979999999999 < (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{min}\left(t\_1, t\right)\\ t_3 := \sqrt{t\_2}\\ t_4 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_4\right)\\ t_6 := \sqrt{t\_5 + 1} - \sqrt{t\_5}\\ t_7 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_4\right)\\ t_8 := \sqrt{t\_7}\\ t_9 := \left(\sqrt{t\_2 + 1} - t\_3\right) + \left(\sqrt{t\_7 + 1} - t\_8\right)\\ t_10 := \mathsf{max}\left(t\_1, t\right)\\ t_11 := \sqrt{t\_10}\\ t_12 := \sqrt{t\_10 + 1} - t\_11\\ \mathbf{if}\;t\_9 \leq 0.9995:\\ \;\;\;\;\left(\frac{1}{t\_3 + \sqrt{1 + t\_2}} + t\_6\right) + \frac{0.5}{t\_11}\\ \mathbf{elif}\;t\_9 \leq 1.999998:\\ \;\;\;\;\left(\left(1 + \frac{1}{t\_8 + \sqrt{1 + t\_7}}\right) - t\_3\right) + t\_12\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - \left(t\_3 + t\_8\right)\right) + t\_6\right) + t\_12\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fmin x y) z))
       (t_2 (fmin t_1 t))
       (t_3 (sqrt t_2))
       (t_4 (fmax (fmin x y) z))
       (t_5 (fmax (fmax x y) t_4))
       (t_6 (- (sqrt (+ t_5 1.0)) (sqrt t_5)))
       (t_7 (fmin (fmax x y) t_4))
       (t_8 (sqrt t_7))
       (t_9 (+ (- (sqrt (+ t_2 1.0)) t_3) (- (sqrt (+ t_7 1.0)) t_8)))
       (t_10 (fmax t_1 t))
       (t_11 (sqrt t_10))
       (t_12 (- (sqrt (+ t_10 1.0)) t_11)))
  (if (<= t_9 0.9995)
    (+ (+ (/ 1.0 (+ t_3 (sqrt (+ 1.0 t_2)))) t_6) (/ 0.5 t_11))
    (if (<= t_9 1.999998)
      (+ (- (+ 1.0 (/ 1.0 (+ t_8 (sqrt (+ 1.0 t_7))))) t_3) t_12)
      (+ (+ (- 2.0 (+ t_3 t_8)) t_6) t_12)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, y), z);
	double t_2 = fmin(t_1, t);
	double t_3 = sqrt(t_2);
	double t_4 = fmax(fmin(x, y), z);
	double t_5 = fmax(fmax(x, y), t_4);
	double t_6 = sqrt((t_5 + 1.0)) - sqrt(t_5);
	double t_7 = fmin(fmax(x, y), t_4);
	double t_8 = sqrt(t_7);
	double t_9 = (sqrt((t_2 + 1.0)) - t_3) + (sqrt((t_7 + 1.0)) - t_8);
	double t_10 = fmax(t_1, t);
	double t_11 = sqrt(t_10);
	double t_12 = sqrt((t_10 + 1.0)) - t_11;
	double tmp;
	if (t_9 <= 0.9995) {
		tmp = ((1.0 / (t_3 + sqrt((1.0 + t_2)))) + t_6) + (0.5 / t_11);
	} else if (t_9 <= 1.999998) {
		tmp = ((1.0 + (1.0 / (t_8 + sqrt((1.0 + t_7))))) - t_3) + t_12;
	} else {
		tmp = ((2.0 - (t_3 + t_8)) + t_6) + t_12;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmin(fmin(x, y), z)
    t_2 = fmin(t_1, t)
    t_3 = sqrt(t_2)
    t_4 = fmax(fmin(x, y), z)
    t_5 = fmax(fmax(x, y), t_4)
    t_6 = sqrt((t_5 + 1.0d0)) - sqrt(t_5)
    t_7 = fmin(fmax(x, y), t_4)
    t_8 = sqrt(t_7)
    t_9 = (sqrt((t_2 + 1.0d0)) - t_3) + (sqrt((t_7 + 1.0d0)) - t_8)
    t_10 = fmax(t_1, t)
    t_11 = sqrt(t_10)
    t_12 = sqrt((t_10 + 1.0d0)) - t_11
    if (t_9 <= 0.9995d0) then
        tmp = ((1.0d0 / (t_3 + sqrt((1.0d0 + t_2)))) + t_6) + (0.5d0 / t_11)
    else if (t_9 <= 1.999998d0) then
        tmp = ((1.0d0 + (1.0d0 / (t_8 + sqrt((1.0d0 + t_7))))) - t_3) + t_12
    else
        tmp = ((2.0d0 - (t_3 + t_8)) + t_6) + t_12
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, y), z);
	double t_2 = fmin(t_1, t);
	double t_3 = Math.sqrt(t_2);
	double t_4 = fmax(fmin(x, y), z);
	double t_5 = fmax(fmax(x, y), t_4);
	double t_6 = Math.sqrt((t_5 + 1.0)) - Math.sqrt(t_5);
	double t_7 = fmin(fmax(x, y), t_4);
	double t_8 = Math.sqrt(t_7);
	double t_9 = (Math.sqrt((t_2 + 1.0)) - t_3) + (Math.sqrt((t_7 + 1.0)) - t_8);
	double t_10 = fmax(t_1, t);
	double t_11 = Math.sqrt(t_10);
	double t_12 = Math.sqrt((t_10 + 1.0)) - t_11;
	double tmp;
	if (t_9 <= 0.9995) {
		tmp = ((1.0 / (t_3 + Math.sqrt((1.0 + t_2)))) + t_6) + (0.5 / t_11);
	} else if (t_9 <= 1.999998) {
		tmp = ((1.0 + (1.0 / (t_8 + Math.sqrt((1.0 + t_7))))) - t_3) + t_12;
	} else {
		tmp = ((2.0 - (t_3 + t_8)) + t_6) + t_12;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmin(fmin(x, y), z)
	t_2 = fmin(t_1, t)
	t_3 = math.sqrt(t_2)
	t_4 = fmax(fmin(x, y), z)
	t_5 = fmax(fmax(x, y), t_4)
	t_6 = math.sqrt((t_5 + 1.0)) - math.sqrt(t_5)
	t_7 = fmin(fmax(x, y), t_4)
	t_8 = math.sqrt(t_7)
	t_9 = (math.sqrt((t_2 + 1.0)) - t_3) + (math.sqrt((t_7 + 1.0)) - t_8)
	t_10 = fmax(t_1, t)
	t_11 = math.sqrt(t_10)
	t_12 = math.sqrt((t_10 + 1.0)) - t_11
	tmp = 0
	if t_9 <= 0.9995:
		tmp = ((1.0 / (t_3 + math.sqrt((1.0 + t_2)))) + t_6) + (0.5 / t_11)
	elif t_9 <= 1.999998:
		tmp = ((1.0 + (1.0 / (t_8 + math.sqrt((1.0 + t_7))))) - t_3) + t_12
	else:
		tmp = ((2.0 - (t_3 + t_8)) + t_6) + t_12
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmin(fmin(x, y), z)
	t_2 = fmin(t_1, t)
	t_3 = sqrt(t_2)
	t_4 = fmax(fmin(x, y), z)
	t_5 = fmax(fmax(x, y), t_4)
	t_6 = Float64(sqrt(Float64(t_5 + 1.0)) - sqrt(t_5))
	t_7 = fmin(fmax(x, y), t_4)
	t_8 = sqrt(t_7)
	t_9 = Float64(Float64(sqrt(Float64(t_2 + 1.0)) - t_3) + Float64(sqrt(Float64(t_7 + 1.0)) - t_8))
	t_10 = fmax(t_1, t)
	t_11 = sqrt(t_10)
	t_12 = Float64(sqrt(Float64(t_10 + 1.0)) - t_11)
	tmp = 0.0
	if (t_9 <= 0.9995)
		tmp = Float64(Float64(Float64(1.0 / Float64(t_3 + sqrt(Float64(1.0 + t_2)))) + t_6) + Float64(0.5 / t_11));
	elseif (t_9 <= 1.999998)
		tmp = Float64(Float64(Float64(1.0 + Float64(1.0 / Float64(t_8 + sqrt(Float64(1.0 + t_7))))) - t_3) + t_12);
	else
		tmp = Float64(Float64(Float64(2.0 - Float64(t_3 + t_8)) + t_6) + t_12);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(min(x, y), z);
	t_2 = min(t_1, t);
	t_3 = sqrt(t_2);
	t_4 = max(min(x, y), z);
	t_5 = max(max(x, y), t_4);
	t_6 = sqrt((t_5 + 1.0)) - sqrt(t_5);
	t_7 = min(max(x, y), t_4);
	t_8 = sqrt(t_7);
	t_9 = (sqrt((t_2 + 1.0)) - t_3) + (sqrt((t_7 + 1.0)) - t_8);
	t_10 = max(t_1, t);
	t_11 = sqrt(t_10);
	t_12 = sqrt((t_10 + 1.0)) - t_11;
	tmp = 0.0;
	if (t_9 <= 0.9995)
		tmp = ((1.0 / (t_3 + sqrt((1.0 + t_2)))) + t_6) + (0.5 / t_11);
	elseif (t_9 <= 1.999998)
		tmp = ((1.0 + (1.0 / (t_8 + sqrt((1.0 + t_7))))) - t_3) + t_12;
	else
		tmp = ((2.0 - (t_3 + t_8)) + t_6) + t_12;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Min[t$95$1, t], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Max[N[Max[x, y], $MachinePrecision], t$95$4], $MachinePrecision]}, Block[{t$95$6 = N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$5], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[Min[N[Max[x, y], $MachinePrecision], t$95$4], $MachinePrecision]}, Block[{t$95$8 = N[Sqrt[t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[(N[(N[Sqrt[N[(t$95$2 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$3), $MachinePrecision] + N[(N[Sqrt[N[(t$95$7 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$8), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[Max[t$95$1, t], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$12 = N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$11), $MachinePrecision]}, If[LessEqual[t$95$9, 0.9995], N[(N[(N[(1.0 / N[(t$95$3 + N[Sqrt[N[(1.0 + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + N[(0.5 / t$95$11), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$9, 1.999998], N[(N[(N[(1.0 + N[(1.0 / N[(t$95$8 + N[Sqrt[N[(1.0 + t$95$7), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] + t$95$12), $MachinePrecision], N[(N[(N[(2.0 - N[(t$95$3 + t$95$8), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + t$95$12), $MachinePrecision]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 < z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_4 = IF (t_1 < t) THEN t_1 ELSE t ENDIF IN
		LET t_2 = tmp_4 IN
			LET t_3 = (sqrt(t_2)) IN
				LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_8 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_6 = IF (tmp_7 > z) THEN tmp_8 ELSE z ENDIF IN
				LET t_4 = tmp_6 IN
					LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
					LET tmp_12 = IF (x > y) THEN x ELSE y ENDIF IN
					LET tmp_10 = IF (tmp_11 > t_4) THEN tmp_12 ELSE t_4 ENDIF IN
					LET t_5 = tmp_10 IN
						LET t_6 = ((sqrt((t_5 + (1)))) - (sqrt(t_5))) IN
							LET tmp_15 = IF (x > y) THEN x ELSE y ENDIF IN
							LET tmp_16 = IF (x > y) THEN x ELSE y ENDIF IN
							LET tmp_14 = IF (tmp_15 < t_4) THEN tmp_16 ELSE t_4 ENDIF IN
							LET t_7 = tmp_14 IN
								LET t_8 = (sqrt(t_7)) IN
									LET t_9 = (((sqrt((t_2 + (1)))) - t_3) + ((sqrt((t_7 + (1)))) - t_8)) IN
										LET tmp_17 = IF (t_1 > t) THEN t_1 ELSE t ENDIF IN
										LET t_10 = tmp_17 IN
											LET t_11 = (sqrt(t_10)) IN
												LET t_12 = ((sqrt((t_10 + (1)))) - t_11) IN
													LET tmp_19 = IF (t_9 <= (19999979999999999424886709675774909555912017822265625e-52)) THEN ((((1) + ((1) / (t_8 + (sqrt(((1) + t_7)))))) - t_3) + t_12) ELSE ((((2) - (t_3 + t_8)) + t_6) + t_12) ENDIF IN
													LET tmp_18 = IF (t_9 <= (9995000000000000550670620214077644050121307373046875e-52)) THEN ((((1) / (t_3 + (sqrt(((1) + t_2))))) + t_6) + ((5e-1) / t_11)) ELSE tmp_19 ENDIF IN
	tmp_18
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) < 0.99950000000000006

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{t \cdot \sqrt{\frac{1}{t}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 28.6%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{t \cdot \sqrt{\frac{1}{t}}} \]

   10. Taylor expanded in t around 0

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{\sqrt{t}} \]
   11. Step-by-step derivation

   12. Applied rewrites 28.6%

       \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{\sqrt{t}} \]

   if 0.99950000000000006 < (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) < 1.9999979999999999

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.9%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{\sqrt{y} + \sqrt{y + 1}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in z around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 40.0%

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.9%

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 1.9999979999999999 < (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 97.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(t\_1, t\right)\\ t_3 := \mathsf{min}\left(t\_1, t\right)\\ t_4 := \sqrt{t\_3}\\ t_5 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_6 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_5\right)\\ t_7 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_5\right)\\ t_8 := \mathsf{max}\left(t\_7, t\_2\right)\\ t_9 := \mathsf{min}\left(t\_6, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \sqrt{t\_9 + 1}\\ t_12 := \mathsf{min}\left(t\_7, t\_2\right)\\ t_13 := \mathsf{max}\left(t\_6, t\_8\right)\\ t_14 := \sqrt{t\_13 + 1}\\ t_15 := \sqrt{t\_13}\\ \mathbf{if}\;t\_12 \leq 2.0660407187798852 \cdot 10^{+30}:\\ \;\;\;\;\left(\left(\left(\sqrt{t\_3 + 1} - t\_4\right) + \left(\sqrt{t\_12 + 1} - \sqrt{t\_12}\right)\right) + \frac{1}{t\_10 + t\_11}\right) + \left(t\_14 - t\_15\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{1 + t\_3} + t\_4} + \left(\left(t\_11 - t\_10\right) - \left(t\_15 - t\_14\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fmin x y) z))
       (t_2 (fmax t_1 t))
       (t_3 (fmin t_1 t))
       (t_4 (sqrt t_3))
       (t_5 (fmax (fmin x y) z))
       (t_6 (fmax (fmax x y) t_5))
       (t_7 (fmin (fmax x y) t_5))
       (t_8 (fmax t_7 t_2))
       (t_9 (fmin t_6 t_8))
       (t_10 (sqrt t_9))
       (t_11 (sqrt (+ t_9 1.0)))
       (t_12 (fmin t_7 t_2))
       (t_13 (fmax t_6 t_8))
       (t_14 (sqrt (+ t_13 1.0)))
       (t_15 (sqrt t_13)))
  (if (<= t_12 2.0660407187798852e+30)
    (+
     (+
      (+
       (- (sqrt (+ t_3 1.0)) t_4)
       (- (sqrt (+ t_12 1.0)) (sqrt t_12)))
      (/ 1.0 (+ t_10 t_11)))
     (- t_14 t_15))
    (+
     (/ 1.0 (+ (sqrt (+ 1.0 t_3)) t_4))
     (- (- t_11 t_10) (- t_15 t_14))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, y), z);
	double t_2 = fmax(t_1, t);
	double t_3 = fmin(t_1, t);
	double t_4 = sqrt(t_3);
	double t_5 = fmax(fmin(x, y), z);
	double t_6 = fmax(fmax(x, y), t_5);
	double t_7 = fmin(fmax(x, y), t_5);
	double t_8 = fmax(t_7, t_2);
	double t_9 = fmin(t_6, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = sqrt((t_9 + 1.0));
	double t_12 = fmin(t_7, t_2);
	double t_13 = fmax(t_6, t_8);
	double t_14 = sqrt((t_13 + 1.0));
	double t_15 = sqrt(t_13);
	double tmp;
	if (t_12 <= 2.0660407187798852e+30) {
		tmp = (((sqrt((t_3 + 1.0)) - t_4) + (sqrt((t_12 + 1.0)) - sqrt(t_12))) + (1.0 / (t_10 + t_11))) + (t_14 - t_15);
	} else {
		tmp = (1.0 / (sqrt((1.0 + t_3)) + t_4)) + ((t_11 - t_10) - (t_15 - t_14));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmin(fmin(x, y), z)
    t_2 = fmax(t_1, t)
    t_3 = fmin(t_1, t)
    t_4 = sqrt(t_3)
    t_5 = fmax(fmin(x, y), z)
    t_6 = fmax(fmax(x, y), t_5)
    t_7 = fmin(fmax(x, y), t_5)
    t_8 = fmax(t_7, t_2)
    t_9 = fmin(t_6, t_8)
    t_10 = sqrt(t_9)
    t_11 = sqrt((t_9 + 1.0d0))
    t_12 = fmin(t_7, t_2)
    t_13 = fmax(t_6, t_8)
    t_14 = sqrt((t_13 + 1.0d0))
    t_15 = sqrt(t_13)
    if (t_12 <= 2.0660407187798852d+30) then
        tmp = (((sqrt((t_3 + 1.0d0)) - t_4) + (sqrt((t_12 + 1.0d0)) - sqrt(t_12))) + (1.0d0 / (t_10 + t_11))) + (t_14 - t_15)
    else
        tmp = (1.0d0 / (sqrt((1.0d0 + t_3)) + t_4)) + ((t_11 - t_10) - (t_15 - t_14))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, y), z);
	double t_2 = fmax(t_1, t);
	double t_3 = fmin(t_1, t);
	double t_4 = Math.sqrt(t_3);
	double t_5 = fmax(fmin(x, y), z);
	double t_6 = fmax(fmax(x, y), t_5);
	double t_7 = fmin(fmax(x, y), t_5);
	double t_8 = fmax(t_7, t_2);
	double t_9 = fmin(t_6, t_8);
	double t_10 = Math.sqrt(t_9);
	double t_11 = Math.sqrt((t_9 + 1.0));
	double t_12 = fmin(t_7, t_2);
	double t_13 = fmax(t_6, t_8);
	double t_14 = Math.sqrt((t_13 + 1.0));
	double t_15 = Math.sqrt(t_13);
	double tmp;
	if (t_12 <= 2.0660407187798852e+30) {
		tmp = (((Math.sqrt((t_3 + 1.0)) - t_4) + (Math.sqrt((t_12 + 1.0)) - Math.sqrt(t_12))) + (1.0 / (t_10 + t_11))) + (t_14 - t_15);
	} else {
		tmp = (1.0 / (Math.sqrt((1.0 + t_3)) + t_4)) + ((t_11 - t_10) - (t_15 - t_14));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmin(fmin(x, y), z)
	t_2 = fmax(t_1, t)
	t_3 = fmin(t_1, t)
	t_4 = math.sqrt(t_3)
	t_5 = fmax(fmin(x, y), z)
	t_6 = fmax(fmax(x, y), t_5)
	t_7 = fmin(fmax(x, y), t_5)
	t_8 = fmax(t_7, t_2)
	t_9 = fmin(t_6, t_8)
	t_10 = math.sqrt(t_9)
	t_11 = math.sqrt((t_9 + 1.0))
	t_12 = fmin(t_7, t_2)
	t_13 = fmax(t_6, t_8)
	t_14 = math.sqrt((t_13 + 1.0))
	t_15 = math.sqrt(t_13)
	tmp = 0
	if t_12 <= 2.0660407187798852e+30:
		tmp = (((math.sqrt((t_3 + 1.0)) - t_4) + (math.sqrt((t_12 + 1.0)) - math.sqrt(t_12))) + (1.0 / (t_10 + t_11))) + (t_14 - t_15)
	else:
		tmp = (1.0 / (math.sqrt((1.0 + t_3)) + t_4)) + ((t_11 - t_10) - (t_15 - t_14))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmin(fmin(x, y), z)
	t_2 = fmax(t_1, t)
	t_3 = fmin(t_1, t)
	t_4 = sqrt(t_3)
	t_5 = fmax(fmin(x, y), z)
	t_6 = fmax(fmax(x, y), t_5)
	t_7 = fmin(fmax(x, y), t_5)
	t_8 = fmax(t_7, t_2)
	t_9 = fmin(t_6, t_8)
	t_10 = sqrt(t_9)
	t_11 = sqrt(Float64(t_9 + 1.0))
	t_12 = fmin(t_7, t_2)
	t_13 = fmax(t_6, t_8)
	t_14 = sqrt(Float64(t_13 + 1.0))
	t_15 = sqrt(t_13)
	tmp = 0.0
	if (t_12 <= 2.0660407187798852e+30)
		tmp = Float64(Float64(Float64(Float64(sqrt(Float64(t_3 + 1.0)) - t_4) + Float64(sqrt(Float64(t_12 + 1.0)) - sqrt(t_12))) + Float64(1.0 / Float64(t_10 + t_11))) + Float64(t_14 - t_15));
	else
		tmp = Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + t_3)) + t_4)) + Float64(Float64(t_11 - t_10) - Float64(t_15 - t_14)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(min(x, y), z);
	t_2 = max(t_1, t);
	t_3 = min(t_1, t);
	t_4 = sqrt(t_3);
	t_5 = max(min(x, y), z);
	t_6 = max(max(x, y), t_5);
	t_7 = min(max(x, y), t_5);
	t_8 = max(t_7, t_2);
	t_9 = min(t_6, t_8);
	t_10 = sqrt(t_9);
	t_11 = sqrt((t_9 + 1.0));
	t_12 = min(t_7, t_2);
	t_13 = max(t_6, t_8);
	t_14 = sqrt((t_13 + 1.0));
	t_15 = sqrt(t_13);
	tmp = 0.0;
	if (t_12 <= 2.0660407187798852e+30)
		tmp = (((sqrt((t_3 + 1.0)) - t_4) + (sqrt((t_12 + 1.0)) - sqrt(t_12))) + (1.0 / (t_10 + t_11))) + (t_14 - t_15);
	else
		tmp = (1.0 / (sqrt((1.0 + t_3)) + t_4)) + ((t_11 - t_10) - (t_15 - t_14));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[t$95$1, t], $MachinePrecision]}, Block[{t$95$3 = N[Min[t$95$1, t], $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[t$95$3], $MachinePrecision]}, Block[{t$95$5 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$6 = N[Max[N[Max[x, y], $MachinePrecision], t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Min[N[Max[x, y], $MachinePrecision], t$95$5], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$7, t$95$2], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$6, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$12 = N[Min[t$95$7, t$95$2], $MachinePrecision]}, Block[{t$95$13 = N[Max[t$95$6, t$95$8], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[N[(t$95$13 + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$15 = N[Sqrt[t$95$13], $MachinePrecision]}, If[LessEqual[t$95$12, 2.0660407187798852e+30], N[(N[(N[(N[(N[Sqrt[N[(t$95$3 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$4), $MachinePrecision] + N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$12], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$10 + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$14 - t$95$15), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + t$95$3), $MachinePrecision]], $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$11 - t$95$10), $MachinePrecision] - N[(t$95$15 - t$95$14), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 < z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_4 = IF (t_1 > t) THEN t_1 ELSE t ENDIF IN
		LET t_2 = tmp_4 IN
			LET tmp_5 = IF (t_1 < t) THEN t_1 ELSE t ENDIF IN
			LET t_3 = tmp_5 IN
				LET t_4 = (sqrt(t_3)) IN
					LET tmp_8 = IF (x < y) THEN x ELSE y ENDIF IN
					LET tmp_9 = IF (x < y) THEN x ELSE y ENDIF IN
					LET tmp_7 = IF (tmp_8 > z) THEN tmp_9 ELSE z ENDIF IN
					LET t_5 = tmp_7 IN
						LET tmp_12 = IF (x > y) THEN x ELSE y ENDIF IN
						LET tmp_13 = IF (x > y) THEN x ELSE y ENDIF IN
						LET tmp_11 = IF (tmp_12 > t_5) THEN tmp_13 ELSE t_5 ENDIF IN
						LET t_6 = tmp_11 IN
							LET tmp_16 = IF (x > y) THEN x ELSE y ENDIF IN
							LET tmp_17 = IF (x > y) THEN x ELSE y ENDIF IN
							LET tmp_15 = IF (tmp_16 < t_5) THEN tmp_17 ELSE t_5 ENDIF IN
							LET t_7 = tmp_15 IN
								LET tmp_18 = IF (t_7 > t_2) THEN t_7 ELSE t_2 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_6 < t_8) THEN t_6 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET t_11 = (sqrt((t_9 + (1)))) IN
												LET tmp_20 = IF (t_7 < t_2) THEN t_7 ELSE t_2 ENDIF IN
												LET t_12 = tmp_20 IN
													LET tmp_21 = IF (t_6 > t_8) THEN t_6 ELSE t_8 ENDIF IN
													LET t_13 = tmp_21 IN
														LET t_14 = (sqrt((t_13 + (1)))) IN
															LET t_15 = (sqrt(t_13)) IN
																LET tmp_22 = IF (t_12 <= (2066040718779885161499959754752)) THEN (((((sqrt((t_3 + (1)))) - t_4) + ((sqrt((t_12 + (1)))) - (sqrt(t_12)))) + ((1) / (t_10 + t_11))) + (t_14 - t_15)) ELSE (((1) / ((sqrt(((1) + t_3))) + t_4)) + ((t_11 - t_10) - (t_15 - t_14))) ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 2 regimes

2. if y < 2.0660407187798852e30

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 2.0660407187798852e30 < y

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Applied rewrites 52.4%

      \[\leadsto \frac{1}{\sqrt{1 + x} + \sqrt{x}} + \left(\left(\sqrt{z + 1} - \sqrt{z}\right) - \left(\sqrt{t} - \sqrt{t + 1}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_11 := \sqrt{t\_9}\\ t_12 := \frac{1}{t\_11 + \sqrt{1 + t\_9}}\\ t_13 := \sqrt{t\_10}\\ t_14 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_10 + 1} - t\_13\right)\right) + \left(\sqrt{t\_9 + 1} - t\_11\right)\\ t_15 := t\_6 + t\_13\\ t_16 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_17 := \sqrt{t\_16 + 1} - \sqrt{t\_16}\\ \mathbf{if}\;t\_14 \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{1}{t\_5 \cdot \sqrt{\frac{1}{t\_5}}}, t\_12\right)\\ \mathbf{elif}\;t\_14 \leq 1.999998:\\ \;\;\;\;\left(\left(1 + \frac{1}{t\_13 + \sqrt{1 + t\_10}}\right) - t\_6\right) + t\_17\\ \mathbf{elif}\;t\_14 \leq 2.999995:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \left(1 + t\_12\right)\right) - t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - t\_15\right) + \left(1 - t\_11\right)\right) + t\_17\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (fmin t_3 t_7))
       (t_11 (sqrt t_9))
       (t_12 (/ 1.0 (+ t_11 (sqrt (+ 1.0 t_9)))))
       (t_13 (sqrt t_10))
       (t_14
        (+
         (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_10 1.0)) t_13))
         (- (sqrt (+ t_9 1.0)) t_11)))
       (t_15 (+ t_6 t_13))
       (t_16 (fmax t_2 t_8))
       (t_17 (- (sqrt (+ t_16 1.0)) (sqrt t_16))))
  (if (<= t_14 0.2)
    (fma 0.5 (/ 1.0 (* t_5 (sqrt (/ 1.0 t_5)))) t_12)
    (if (<= t_14 1.999998)
      (+ (- (+ 1.0 (/ 1.0 (+ t_13 (sqrt (+ 1.0 t_10))))) t_6) t_17)
      (if (<= t_14 2.999995)
        (- (+ (sqrt (+ 1.0 t_5)) (+ 1.0 t_12)) t_15)
        (+ (+ (- 2.0 t_15) (- 1.0 t_11)) t_17))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = sqrt(t_9);
	double t_12 = 1.0 / (t_11 + sqrt((1.0 + t_9)));
	double t_13 = sqrt(t_10);
	double t_14 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_13)) + (sqrt((t_9 + 1.0)) - t_11);
	double t_15 = t_6 + t_13;
	double t_16 = fmax(t_2, t_8);
	double t_17 = sqrt((t_16 + 1.0)) - sqrt(t_16);
	double tmp;
	if (t_14 <= 0.2) {
		tmp = fma(0.5, (1.0 / (t_5 * sqrt((1.0 / t_5)))), t_12);
	} else if (t_14 <= 1.999998) {
		tmp = ((1.0 + (1.0 / (t_13 + sqrt((1.0 + t_10))))) - t_6) + t_17;
	} else if (t_14 <= 2.999995) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 + t_12)) - t_15;
	} else {
		tmp = ((2.0 - t_15) + (1.0 - t_11)) + t_17;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = sqrt(t_9)
	t_12 = Float64(1.0 / Float64(t_11 + sqrt(Float64(1.0 + t_9))))
	t_13 = sqrt(t_10)
	t_14 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_10 + 1.0)) - t_13)) + Float64(sqrt(Float64(t_9 + 1.0)) - t_11))
	t_15 = Float64(t_6 + t_13)
	t_16 = fmax(t_2, t_8)
	t_17 = Float64(sqrt(Float64(t_16 + 1.0)) - sqrt(t_16))
	tmp = 0.0
	if (t_14 <= 0.2)
		tmp = fma(0.5, Float64(1.0 / Float64(t_5 * sqrt(Float64(1.0 / t_5)))), t_12);
	elseif (t_14 <= 1.999998)
		tmp = Float64(Float64(Float64(1.0 + Float64(1.0 / Float64(t_13 + sqrt(Float64(1.0 + t_10))))) - t_6) + t_17);
	elseif (t_14 <= 2.999995)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 + t_12)) - t_15);
	else
		tmp = Float64(Float64(Float64(2.0 - t_15) + Float64(1.0 - t_11)) + t_17);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$12 = N[(1.0 / N[(t$95$11 + N[Sqrt[N[(1.0 + t$95$9), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$11), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$15 = N[(t$95$6 + t$95$13), $MachinePrecision]}, Block[{t$95$16 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$17 = N[(N[Sqrt[N[(t$95$16 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$16], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$14, 0.2], N[(0.5 * N[(1.0 / N[(t$95$5 * N[Sqrt[N[(1.0 / t$95$5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$12), $MachinePrecision], If[LessEqual[t$95$14, 1.999998], N[(N[(N[(1.0 + N[(1.0 / N[(t$95$13 + N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] + t$95$17), $MachinePrecision], If[LessEqual[t$95$14, 2.999995], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 + t$95$12), $MachinePrecision]), $MachinePrecision] - t$95$15), $MachinePrecision], N[(N[(N[(2.0 - t$95$15), $MachinePrecision] + N[(1.0 - t$95$11), $MachinePrecision]), $MachinePrecision] + t$95$17), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
										LET t_10 = tmp_20 IN
											LET t_11 = (sqrt(t_9)) IN
												LET t_12 = ((1) / (t_11 + (sqrt(((1) + t_9))))) IN
													LET t_13 = (sqrt(t_10)) IN
														LET t_14 = ((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_10 + (1)))) - t_13)) + ((sqrt((t_9 + (1)))) - t_11)) IN
															LET t_15 = (t_6 + t_13) IN
																LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
																LET t_16 = tmp_21 IN
																	LET t_17 = ((sqrt((t_16 + (1)))) - (sqrt(t_16))) IN
																		LET tmp_24 = IF (t_14 <= (29999950000000001892885848064906895160675048828125e-49)) THEN (((sqrt(((1) + t_5))) + ((1) + t_12)) - t_15) ELSE ((((2) - t_15) + ((1) - t_11)) + t_17) ENDIF IN
																		LET tmp_23 = IF (t_14 <= (19999979999999999424886709675774909555912017822265625e-52)) THEN ((((1) + ((1) / (t_13 + (sqrt(((1) + t_10)))))) - t_6) + t_17) ELSE tmp_24 ENDIF IN
																		LET tmp_22 = IF (t_14 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN (((5e-1) * ((1) / (t_5 * (sqrt(((1) / t_5)))))) + t_12) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 0.20000000000000001

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{1}{2} \cdot \frac{1}{x \cdot \sqrt{\frac{1}{x}}} + \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

       \[\leadsto \mathsf{fma}\left(0.5, \frac{1}{x \cdot \sqrt{\frac{1}{x}}}, \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) \]

   if 0.20000000000000001 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1.9999979999999999

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.9%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{\sqrt{y} + \sqrt{y + 1}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in z around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 40.0%

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.9%

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 1.9999979999999999 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.9999950000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around 0

      \[\leadsto \left(\sqrt{1 + x} + \left(1 + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 17.0%

      \[\leadsto \left(\sqrt{1 + x} + \left(1 + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.9999950000000002 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 96.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \sqrt{t\_9 + 1} - t\_10\\ t_12 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_13 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_14 := \sqrt{t\_13}\\ t_15 := \sqrt{t\_13 + 1} - t\_14\\ t_16 := \sqrt{t\_12}\\ t_17 := \left(\left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_12 + 1} - t\_16\right)\right) + t\_11\right) + t\_15\\ t_18 := 2 - \left(t\_6 + t\_16\right)\\ \mathbf{if}\;t\_17 \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{1}{t\_5 \cdot \sqrt{\frac{1}{t\_5}}}, \frac{1}{t\_10 + \sqrt{1 + t\_9}}\right)\\ \mathbf{elif}\;t\_17 \leq 1.999998:\\ \;\;\;\;\left(\left(1 + \frac{1}{t\_16 + \sqrt{1 + t\_12}}\right) - t\_6\right) + t\_15\\ \mathbf{elif}\;t\_17 \leq 3.0001:\\ \;\;\;\;\left(t\_18 + t\_11\right) + \frac{0.5}{t\_14}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_18 + \left(1 - t\_10\right)\right) + t\_15\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (sqrt t_9))
       (t_11 (- (sqrt (+ t_9 1.0)) t_10))
       (t_12 (fmin t_3 t_7))
       (t_13 (fmax t_2 t_8))
       (t_14 (sqrt t_13))
       (t_15 (- (sqrt (+ t_13 1.0)) t_14))
       (t_16 (sqrt t_12))
       (t_17
        (+
         (+
          (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_12 1.0)) t_16))
          t_11)
         t_15))
       (t_18 (- 2.0 (+ t_6 t_16))))
  (if (<= t_17 0.2)
    (fma
     0.5
     (/ 1.0 (* t_5 (sqrt (/ 1.0 t_5))))
     (/ 1.0 (+ t_10 (sqrt (+ 1.0 t_9)))))
    (if (<= t_17 1.999998)
      (+ (- (+ 1.0 (/ 1.0 (+ t_16 (sqrt (+ 1.0 t_12))))) t_6) t_15)
      (if (<= t_17 3.0001)
        (+ (+ t_18 t_11) (/ 0.5 t_14))
        (+ (+ t_18 (- 1.0 t_10)) t_15))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = sqrt((t_9 + 1.0)) - t_10;
	double t_12 = fmin(t_3, t_7);
	double t_13 = fmax(t_2, t_8);
	double t_14 = sqrt(t_13);
	double t_15 = sqrt((t_13 + 1.0)) - t_14;
	double t_16 = sqrt(t_12);
	double t_17 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_12 + 1.0)) - t_16)) + t_11) + t_15;
	double t_18 = 2.0 - (t_6 + t_16);
	double tmp;
	if (t_17 <= 0.2) {
		tmp = fma(0.5, (1.0 / (t_5 * sqrt((1.0 / t_5)))), (1.0 / (t_10 + sqrt((1.0 + t_9)))));
	} else if (t_17 <= 1.999998) {
		tmp = ((1.0 + (1.0 / (t_16 + sqrt((1.0 + t_12))))) - t_6) + t_15;
	} else if (t_17 <= 3.0001) {
		tmp = (t_18 + t_11) + (0.5 / t_14);
	} else {
		tmp = (t_18 + (1.0 - t_10)) + t_15;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = sqrt(t_9)
	t_11 = Float64(sqrt(Float64(t_9 + 1.0)) - t_10)
	t_12 = fmin(t_3, t_7)
	t_13 = fmax(t_2, t_8)
	t_14 = sqrt(t_13)
	t_15 = Float64(sqrt(Float64(t_13 + 1.0)) - t_14)
	t_16 = sqrt(t_12)
	t_17 = Float64(Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_12 + 1.0)) - t_16)) + t_11) + t_15)
	t_18 = Float64(2.0 - Float64(t_6 + t_16))
	tmp = 0.0
	if (t_17 <= 0.2)
		tmp = fma(0.5, Float64(1.0 / Float64(t_5 * sqrt(Float64(1.0 / t_5)))), Float64(1.0 / Float64(t_10 + sqrt(Float64(1.0 + t_9)))));
	elseif (t_17 <= 1.999998)
		tmp = Float64(Float64(Float64(1.0 + Float64(1.0 / Float64(t_16 + sqrt(Float64(1.0 + t_12))))) - t_6) + t_15);
	elseif (t_17 <= 3.0001)
		tmp = Float64(Float64(t_18 + t_11) + Float64(0.5 / t_14));
	else
		tmp = Float64(Float64(t_18 + Float64(1.0 - t_10)) + t_15);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]}, Block[{t$95$12 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$13 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$13], $MachinePrecision]}, Block[{t$95$15 = N[(N[Sqrt[N[(t$95$13 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$14), $MachinePrecision]}, Block[{t$95$16 = N[Sqrt[t$95$12], $MachinePrecision]}, Block[{t$95$17 = N[(N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$16), $MachinePrecision]), $MachinePrecision] + t$95$11), $MachinePrecision] + t$95$15), $MachinePrecision]}, Block[{t$95$18 = N[(2.0 - N[(t$95$6 + t$95$16), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$17, 0.2], N[(0.5 * N[(1.0 / N[(t$95$5 * N[Sqrt[N[(1.0 / t$95$5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$10 + N[Sqrt[N[(1.0 + t$95$9), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$17, 1.999998], N[(N[(N[(1.0 + N[(1.0 / N[(t$95$16 + N[Sqrt[N[(1.0 + t$95$12), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] + t$95$15), $MachinePrecision], If[LessEqual[t$95$17, 3.0001], N[(N[(t$95$18 + t$95$11), $MachinePrecision] + N[(0.5 / t$95$14), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$18 + N[(1.0 - t$95$10), $MachinePrecision]), $MachinePrecision] + t$95$15), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET t_11 = ((sqrt((t_9 + (1)))) - t_10) IN
												LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
												LET t_12 = tmp_20 IN
													LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
													LET t_13 = tmp_21 IN
														LET t_14 = (sqrt(t_13)) IN
															LET t_15 = ((sqrt((t_13 + (1)))) - t_14) IN
																LET t_16 = (sqrt(t_12)) IN
																	LET t_17 = (((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_12 + (1)))) - t_16)) + t_11) + t_15) IN
																		LET t_18 = ((2) - (t_6 + t_16)) IN
																			LET tmp_24 = IF (t_17 <= (3000100000000000211031192520749755203723907470703125e-51)) THEN ((t_18 + t_11) + ((5e-1) / t_14)) ELSE ((t_18 + ((1) - t_10)) + t_15) ENDIF IN
																			LET tmp_23 = IF (t_17 <= (19999979999999999424886709675774909555912017822265625e-52)) THEN ((((1) + ((1) / (t_16 + (sqrt(((1) + t_12)))))) - t_6) + t_15) ELSE tmp_24 ENDIF IN
																			LET tmp_22 = IF (t_17 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN (((5e-1) * ((1) / (t_5 * (sqrt(((1) / t_5)))))) + ((1) / (t_10 + (sqrt(((1) + t_9)))))) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 0.20000000000000001

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{1}{2} \cdot \frac{1}{x \cdot \sqrt{\frac{1}{x}}} + \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

       \[\leadsto \mathsf{fma}\left(0.5, \frac{1}{x \cdot \sqrt{\frac{1}{x}}}, \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) \]

   if 0.20000000000000001 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1.9999979999999999

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.9%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{\sqrt{y} + \sqrt{y + 1}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in z around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 40.0%

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.9%

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 1.9999979999999999 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 3.0001000000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{t \cdot \sqrt{\frac{1}{t}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 14.1%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{t \cdot \sqrt{\frac{1}{t}}} \]

   11. Taylor expanded in t around 0

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{\frac{1}{2}}{\sqrt{t}} \]
   12. Step-by-step derivation

   13. Applied rewrites 14.1%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \frac{0.5}{\sqrt{t}} \]

   if 3.0001000000000002 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \sqrt{t\_1 + 1} - \sqrt{t\_1}\\ t_3 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_4 := \mathsf{min}\left(t\_3, t\right)\\ t_5 := \mathsf{max}\left(t\_3, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \sqrt{t\_4}\\ t_8 := \sqrt{t\_5 + 1}\\ \mathbf{if}\;\mathsf{max}\left(x, y\right) \leq 4062571952146190:\\ \;\;\;\;\left(\left(\left(1 - t\_7\right) + \left(\sqrt{\mathsf{max}\left(x, y\right) + 1} - \sqrt{\mathsf{max}\left(x, y\right)}\right)\right) + t\_2\right) + \left(t\_8 - t\_6\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{1 + t\_4} + t\_7} + \left(t\_2 - \left(t\_6 - t\_8\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (- (sqrt (+ t_1 1.0)) (sqrt t_1)))
       (t_3 (fmin (fmin x y) z))
       (t_4 (fmin t_3 t))
       (t_5 (fmax t_3 t))
       (t_6 (sqrt t_5))
       (t_7 (sqrt t_4))
       (t_8 (sqrt (+ t_5 1.0))))
  (if (<= (fmax x y) 4062571952146190.0)
    (+
     (+
      (+ (- 1.0 t_7) (- (sqrt (+ (fmax x y) 1.0)) (sqrt (fmax x y))))
      t_2)
     (- t_8 t_6))
    (+ (/ 1.0 (+ (sqrt (+ 1.0 t_4)) t_7)) (- t_2 (- t_6 t_8))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = sqrt((t_1 + 1.0)) - sqrt(t_1);
	double t_3 = fmin(fmin(x, y), z);
	double t_4 = fmin(t_3, t);
	double t_5 = fmax(t_3, t);
	double t_6 = sqrt(t_5);
	double t_7 = sqrt(t_4);
	double t_8 = sqrt((t_5 + 1.0));
	double tmp;
	if (fmax(x, y) <= 4062571952146190.0) {
		tmp = (((1.0 - t_7) + (sqrt((fmax(x, y) + 1.0)) - sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6);
	} else {
		tmp = (1.0 / (sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = sqrt((t_1 + 1.0d0)) - sqrt(t_1)
    t_3 = fmin(fmin(x, y), z)
    t_4 = fmin(t_3, t)
    t_5 = fmax(t_3, t)
    t_6 = sqrt(t_5)
    t_7 = sqrt(t_4)
    t_8 = sqrt((t_5 + 1.0d0))
    if (fmax(x, y) <= 4062571952146190.0d0) then
        tmp = (((1.0d0 - t_7) + (sqrt((fmax(x, y) + 1.0d0)) - sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6)
    else
        tmp = (1.0d0 / (sqrt((1.0d0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = Math.sqrt((t_1 + 1.0)) - Math.sqrt(t_1);
	double t_3 = fmin(fmin(x, y), z);
	double t_4 = fmin(t_3, t);
	double t_5 = fmax(t_3, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = Math.sqrt(t_4);
	double t_8 = Math.sqrt((t_5 + 1.0));
	double tmp;
	if (fmax(x, y) <= 4062571952146190.0) {
		tmp = (((1.0 - t_7) + (Math.sqrt((fmax(x, y) + 1.0)) - Math.sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6);
	} else {
		tmp = (1.0 / (Math.sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = math.sqrt((t_1 + 1.0)) - math.sqrt(t_1)
	t_3 = fmin(fmin(x, y), z)
	t_4 = fmin(t_3, t)
	t_5 = fmax(t_3, t)
	t_6 = math.sqrt(t_5)
	t_7 = math.sqrt(t_4)
	t_8 = math.sqrt((t_5 + 1.0))
	tmp = 0
	if fmax(x, y) <= 4062571952146190.0:
		tmp = (((1.0 - t_7) + (math.sqrt((fmax(x, y) + 1.0)) - math.sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6)
	else:
		tmp = (1.0 / (math.sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = Float64(sqrt(Float64(t_1 + 1.0)) - sqrt(t_1))
	t_3 = fmin(fmin(x, y), z)
	t_4 = fmin(t_3, t)
	t_5 = fmax(t_3, t)
	t_6 = sqrt(t_5)
	t_7 = sqrt(t_4)
	t_8 = sqrt(Float64(t_5 + 1.0))
	tmp = 0.0
	if (fmax(x, y) <= 4062571952146190.0)
		tmp = Float64(Float64(Float64(Float64(1.0 - t_7) + Float64(sqrt(Float64(fmax(x, y) + 1.0)) - sqrt(fmax(x, y)))) + t_2) + Float64(t_8 - t_6));
	else
		tmp = Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + t_4)) + t_7)) + Float64(t_2 - Float64(t_6 - t_8)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = sqrt((t_1 + 1.0)) - sqrt(t_1);
	t_3 = min(min(x, y), z);
	t_4 = min(t_3, t);
	t_5 = max(t_3, t);
	t_6 = sqrt(t_5);
	t_7 = sqrt(t_4);
	t_8 = sqrt((t_5 + 1.0));
	tmp = 0.0;
	if (max(x, y) <= 4062571952146190.0)
		tmp = (((1.0 - t_7) + (sqrt((max(x, y) + 1.0)) - sqrt(max(x, y)))) + t_2) + (t_8 - t_6);
	else
		tmp = (1.0 / (sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[N[(t$95$1 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$4 = N[Min[t$95$3, t], $MachinePrecision]}, Block[{t$95$5 = N[Max[t$95$3, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Sqrt[t$95$4], $MachinePrecision]}, Block[{t$95$8 = N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[x, y], $MachinePrecision], 4062571952146190.0], N[(N[(N[(N[(1.0 - t$95$7), $MachinePrecision] + N[(N[Sqrt[N[(N[Max[x, y], $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[N[Max[x, y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(t$95$8 - t$95$6), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + t$95$4), $MachinePrecision]], $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 - N[(t$95$6 - t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET t_2 = ((sqrt((t_1 + (1)))) - (sqrt(t_1))) IN
			LET tmp_6 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_5 = IF (tmp_6 < z) THEN tmp_7 ELSE z ENDIF IN
			LET t_3 = tmp_5 IN
				LET tmp_8 = IF (t_3 < t) THEN t_3 ELSE t ENDIF IN
				LET t_4 = tmp_8 IN
					LET tmp_9 = IF (t_3 > t) THEN t_3 ELSE t ENDIF IN
					LET t_5 = tmp_9 IN
						LET t_6 = (sqrt(t_5)) IN
							LET t_7 = (sqrt(t_4)) IN
								LET t_8 = (sqrt((t_5 + (1)))) IN
									LET tmp_13 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_14 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_15 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_12 = IF (tmp_13 <= (4062571952146190)) THEN (((((1) - t_7) + ((sqrt((tmp_14 + (1)))) - (sqrt(tmp_15)))) + t_2) + (t_8 - t_6)) ELSE (((1) / ((sqrt(((1) + t_4))) + t_7)) + (t_2 - (t_6 - t_8))) ENDIF IN
	tmp_12
END code

Derivation

1. Split input into 2 regimes

2. if y < 4062571952146190

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(1 - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 48.4%

      \[\leadsto \left(\left(\left(1 - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 4062571952146190 < y

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Applied rewrites 52.4%

      \[\leadsto \frac{1}{\sqrt{1 + x} + \sqrt{x}} + \left(\left(\sqrt{z + 1} - \sqrt{z}\right) - \left(\sqrt{t} - \sqrt{t + 1}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 96.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(x, z\right), t\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(x, z\right), t\right)\\ \left(\left(\frac{1}{\sqrt{t\_1} + \sqrt{1 + t\_1}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{\mathsf{max}\left(x, z\right) + 1} - \sqrt{\mathsf{max}\left(x, z\right)}\right)\right) + \left(\sqrt{t\_2 + 1} - \sqrt{t\_2}\right) \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fmin x z) t)) (t_2 (fmax (fmin x z) t)))
  (+
   (+
    (+
     (/ 1.0 (+ (sqrt t_1) (sqrt (+ 1.0 t_1))))
     (- (sqrt (+ y 1.0)) (sqrt y)))
    (- (sqrt (+ (fmax x z) 1.0)) (sqrt (fmax x z))))
   (- (sqrt (+ t_2 1.0)) (sqrt t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, z), t);
	double t_2 = fmax(fmin(x, z), t);
	return (((1.0 / (sqrt(t_1) + sqrt((1.0 + t_1)))) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((fmax(x, z) + 1.0)) - sqrt(fmax(x, z)))) + (sqrt((t_2 + 1.0)) - sqrt(t_2));
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    t_1 = fmin(fmin(x, z), t)
    t_2 = fmax(fmin(x, z), t)
    code = (((1.0d0 / (sqrt(t_1) + sqrt((1.0d0 + t_1)))) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((fmax(x, z) + 1.0d0)) - sqrt(fmax(x, z)))) + (sqrt((t_2 + 1.0d0)) - sqrt(t_2))
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(fmin(x, z), t);
	double t_2 = fmax(fmin(x, z), t);
	return (((1.0 / (Math.sqrt(t_1) + Math.sqrt((1.0 + t_1)))) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + (Math.sqrt((fmax(x, z) + 1.0)) - Math.sqrt(fmax(x, z)))) + (Math.sqrt((t_2 + 1.0)) - Math.sqrt(t_2));
}

Python

def code(x, y, z, t):
	t_1 = fmin(fmin(x, z), t)
	t_2 = fmax(fmin(x, z), t)
	return (((1.0 / (math.sqrt(t_1) + math.sqrt((1.0 + t_1)))) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + (math.sqrt((fmax(x, z) + 1.0)) - math.sqrt(fmax(x, z)))) + (math.sqrt((t_2 + 1.0)) - math.sqrt(t_2))

Julia

function code(x, y, z, t)
	t_1 = fmin(fmin(x, z), t)
	t_2 = fmax(fmin(x, z), t)
	return Float64(Float64(Float64(Float64(1.0 / Float64(sqrt(t_1) + sqrt(Float64(1.0 + t_1)))) + Float64(sqrt(Float64(y + 1.0)) - sqrt(y))) + Float64(sqrt(Float64(fmax(x, z) + 1.0)) - sqrt(fmax(x, z)))) + Float64(sqrt(Float64(t_2 + 1.0)) - sqrt(t_2)))
end

MATLAB

function tmp = code(x, y, z, t)
	t_1 = min(min(x, z), t);
	t_2 = max(min(x, z), t);
	tmp = (((1.0 / (sqrt(t_1) + sqrt((1.0 + t_1)))) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((max(x, z) + 1.0)) - sqrt(max(x, z)))) + (sqrt((t_2 + 1.0)) - sqrt(t_2));
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Min[x, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[x, z], $MachinePrecision], t], $MachinePrecision]}, N[(N[(N[(N[(1.0 / N[(N[Sqrt[t$95$1], $MachinePrecision] + N[Sqrt[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(N[Max[x, z], $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[N[Max[x, z], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$2 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < z) THEN x ELSE z ENDIF IN
	LET tmp_3 = IF (x < z) THEN x ELSE z ENDIF IN
	LET tmp_1 = IF (tmp_2 < t) THEN tmp_3 ELSE t ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x < z) THEN x ELSE z ENDIF IN
		LET tmp_7 = IF (x < z) THEN x ELSE z ENDIF IN
		LET tmp_5 = IF (tmp_6 > t) THEN tmp_7 ELSE t ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_8 = IF (x > z) THEN x ELSE z ENDIF IN
			LET tmp_9 = IF (x > z) THEN x ELSE z ENDIF IN
	((((1) / ((sqrt(t_1)) + (sqrt(((1) + t_1))))) + ((sqrt((y + (1)))) - (sqrt(y)))) + ((sqrt((tmp_8 + (1)))) - (sqrt(tmp_9)))) + ((sqrt((t_2 + (1)))) - (sqrt(t_2)))
END code

Derivation

1. Initial program 92.0%

   \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
2. Step-by-step derivation

3. Applied rewrites 94.0%

   \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
4. Add Preprocessing

Alternative 13: 96.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \sqrt{t\_1 + 1} - \sqrt{t\_1}\\ t_3 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_4 := \mathsf{min}\left(t\_3, t\right)\\ t_5 := \mathsf{max}\left(t\_3, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \sqrt{t\_4}\\ t_8 := \sqrt{t\_5 + 1}\\ \mathbf{if}\;\mathsf{max}\left(x, y\right) \leq 1.2000225462603408 \cdot 10^{+30}:\\ \;\;\;\;\left(\left(\left(\sqrt{t\_4 + 1} - t\_7\right) + \left(\sqrt{\mathsf{max}\left(x, y\right) + 1} - \sqrt{\mathsf{max}\left(x, y\right)}\right)\right) + t\_2\right) + \left(t\_8 - t\_6\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{1 + t\_4} + t\_7} + \left(t\_2 - \left(t\_6 - t\_8\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (- (sqrt (+ t_1 1.0)) (sqrt t_1)))
       (t_3 (fmin (fmin x y) z))
       (t_4 (fmin t_3 t))
       (t_5 (fmax t_3 t))
       (t_6 (sqrt t_5))
       (t_7 (sqrt t_4))
       (t_8 (sqrt (+ t_5 1.0))))
  (if (<= (fmax x y) 1.2000225462603408e+30)
    (+
     (+
      (+
       (- (sqrt (+ t_4 1.0)) t_7)
       (- (sqrt (+ (fmax x y) 1.0)) (sqrt (fmax x y))))
      t_2)
     (- t_8 t_6))
    (+ (/ 1.0 (+ (sqrt (+ 1.0 t_4)) t_7)) (- t_2 (- t_6 t_8))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = sqrt((t_1 + 1.0)) - sqrt(t_1);
	double t_3 = fmin(fmin(x, y), z);
	double t_4 = fmin(t_3, t);
	double t_5 = fmax(t_3, t);
	double t_6 = sqrt(t_5);
	double t_7 = sqrt(t_4);
	double t_8 = sqrt((t_5 + 1.0));
	double tmp;
	if (fmax(x, y) <= 1.2000225462603408e+30) {
		tmp = (((sqrt((t_4 + 1.0)) - t_7) + (sqrt((fmax(x, y) + 1.0)) - sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6);
	} else {
		tmp = (1.0 / (sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = sqrt((t_1 + 1.0d0)) - sqrt(t_1)
    t_3 = fmin(fmin(x, y), z)
    t_4 = fmin(t_3, t)
    t_5 = fmax(t_3, t)
    t_6 = sqrt(t_5)
    t_7 = sqrt(t_4)
    t_8 = sqrt((t_5 + 1.0d0))
    if (fmax(x, y) <= 1.2000225462603408d+30) then
        tmp = (((sqrt((t_4 + 1.0d0)) - t_7) + (sqrt((fmax(x, y) + 1.0d0)) - sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6)
    else
        tmp = (1.0d0 / (sqrt((1.0d0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = Math.sqrt((t_1 + 1.0)) - Math.sqrt(t_1);
	double t_3 = fmin(fmin(x, y), z);
	double t_4 = fmin(t_3, t);
	double t_5 = fmax(t_3, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = Math.sqrt(t_4);
	double t_8 = Math.sqrt((t_5 + 1.0));
	double tmp;
	if (fmax(x, y) <= 1.2000225462603408e+30) {
		tmp = (((Math.sqrt((t_4 + 1.0)) - t_7) + (Math.sqrt((fmax(x, y) + 1.0)) - Math.sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6);
	} else {
		tmp = (1.0 / (Math.sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = math.sqrt((t_1 + 1.0)) - math.sqrt(t_1)
	t_3 = fmin(fmin(x, y), z)
	t_4 = fmin(t_3, t)
	t_5 = fmax(t_3, t)
	t_6 = math.sqrt(t_5)
	t_7 = math.sqrt(t_4)
	t_8 = math.sqrt((t_5 + 1.0))
	tmp = 0
	if fmax(x, y) <= 1.2000225462603408e+30:
		tmp = (((math.sqrt((t_4 + 1.0)) - t_7) + (math.sqrt((fmax(x, y) + 1.0)) - math.sqrt(fmax(x, y)))) + t_2) + (t_8 - t_6)
	else:
		tmp = (1.0 / (math.sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = Float64(sqrt(Float64(t_1 + 1.0)) - sqrt(t_1))
	t_3 = fmin(fmin(x, y), z)
	t_4 = fmin(t_3, t)
	t_5 = fmax(t_3, t)
	t_6 = sqrt(t_5)
	t_7 = sqrt(t_4)
	t_8 = sqrt(Float64(t_5 + 1.0))
	tmp = 0.0
	if (fmax(x, y) <= 1.2000225462603408e+30)
		tmp = Float64(Float64(Float64(Float64(sqrt(Float64(t_4 + 1.0)) - t_7) + Float64(sqrt(Float64(fmax(x, y) + 1.0)) - sqrt(fmax(x, y)))) + t_2) + Float64(t_8 - t_6));
	else
		tmp = Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + t_4)) + t_7)) + Float64(t_2 - Float64(t_6 - t_8)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = sqrt((t_1 + 1.0)) - sqrt(t_1);
	t_3 = min(min(x, y), z);
	t_4 = min(t_3, t);
	t_5 = max(t_3, t);
	t_6 = sqrt(t_5);
	t_7 = sqrt(t_4);
	t_8 = sqrt((t_5 + 1.0));
	tmp = 0.0;
	if (max(x, y) <= 1.2000225462603408e+30)
		tmp = (((sqrt((t_4 + 1.0)) - t_7) + (sqrt((max(x, y) + 1.0)) - sqrt(max(x, y)))) + t_2) + (t_8 - t_6);
	else
		tmp = (1.0 / (sqrt((1.0 + t_4)) + t_7)) + (t_2 - (t_6 - t_8));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[N[(t$95$1 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$4 = N[Min[t$95$3, t], $MachinePrecision]}, Block[{t$95$5 = N[Max[t$95$3, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Sqrt[t$95$4], $MachinePrecision]}, Block[{t$95$8 = N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Max[x, y], $MachinePrecision], 1.2000225462603408e+30], N[(N[(N[(N[(N[Sqrt[N[(t$95$4 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$7), $MachinePrecision] + N[(N[Sqrt[N[(N[Max[x, y], $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[N[Max[x, y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(t$95$8 - t$95$6), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + t$95$4), $MachinePrecision]], $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 - N[(t$95$6 - t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET t_2 = ((sqrt((t_1 + (1)))) - (sqrt(t_1))) IN
			LET tmp_6 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_5 = IF (tmp_6 < z) THEN tmp_7 ELSE z ENDIF IN
			LET t_3 = tmp_5 IN
				LET tmp_8 = IF (t_3 < t) THEN t_3 ELSE t ENDIF IN
				LET t_4 = tmp_8 IN
					LET tmp_9 = IF (t_3 > t) THEN t_3 ELSE t ENDIF IN
					LET t_5 = tmp_9 IN
						LET t_6 = (sqrt(t_5)) IN
							LET t_7 = (sqrt(t_4)) IN
								LET t_8 = (sqrt((t_5 + (1)))) IN
									LET tmp_13 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_14 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_15 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_12 = IF (tmp_13 <= (1200022546260340751408815931392)) THEN (((((sqrt((t_4 + (1)))) - t_7) + ((sqrt((tmp_14 + (1)))) - (sqrt(tmp_15)))) + t_2) + (t_8 - t_6)) ELSE (((1) / ((sqrt(((1) + t_4))) + t_7)) + (t_2 - (t_6 - t_8))) ENDIF IN
	tmp_12
END code

Derivation

1. Split input into 2 regimes

2. if y < 1.2000225462603408e30

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 1.2000225462603408e30 < y

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 94.0%

      \[\leadsto \left(\left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in y around inf

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 52.4%

      \[\leadsto \left(\frac{1}{\sqrt{x} + \sqrt{1 + x}} + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Applied rewrites 52.4%

      \[\leadsto \frac{1}{\sqrt{1 + x} + \sqrt{x}} + \left(\left(\sqrt{z + 1} - \sqrt{z}\right) - \left(\sqrt{t} - \sqrt{t + 1}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 95.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_11 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_12 := \sqrt{t\_9}\\ t_13 := \sqrt{t\_9 + 1} - t\_12\\ t_14 := \sqrt{t\_10}\\ t_15 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_10 + 1} - t\_14\right)\right) + t\_13\\ \mathbf{if}\;t\_15 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{1}{t\_5 \cdot \sqrt{\frac{1}{t\_5}}}, \frac{1}{t\_12 + \sqrt{1 + t\_9}}\right)\\ \mathbf{elif}\;t\_15 \leq 1:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \frac{1}{1 + t\_12}\right) - t\_6\\ \mathbf{elif}\;t\_15 \leq 2.999995:\\ \;\;\;\;\left(\left(1 + \sqrt{1 + t\_10}\right) - t\_6\right) - \left(t\_14 - t\_13\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - \left(t\_6 + t\_14\right)\right) + \left(1 - t\_12\right)\right) + \left(\sqrt{t\_11 + 1} - \sqrt{t\_11}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (fmin t_3 t_7))
       (t_11 (fmax t_2 t_8))
       (t_12 (sqrt t_9))
       (t_13 (- (sqrt (+ t_9 1.0)) t_12))
       (t_14 (sqrt t_10))
       (t_15
        (+
         (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_10 1.0)) t_14))
         t_13)))
  (if (<= t_15 0.0)
    (fma
     0.5
     (/ 1.0 (* t_5 (sqrt (/ 1.0 t_5))))
     (/ 1.0 (+ t_12 (sqrt (+ 1.0 t_9)))))
    (if (<= t_15 1.0)
      (- (+ (sqrt (+ 1.0 t_5)) (/ 1.0 (+ 1.0 t_12))) t_6)
      (if (<= t_15 2.999995)
        (- (- (+ 1.0 (sqrt (+ 1.0 t_10))) t_6) (- t_14 t_13))
        (+
         (+ (- 2.0 (+ t_6 t_14)) (- 1.0 t_12))
         (- (sqrt (+ t_11 1.0)) (sqrt t_11))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = fmax(t_2, t_8);
	double t_12 = sqrt(t_9);
	double t_13 = sqrt((t_9 + 1.0)) - t_12;
	double t_14 = sqrt(t_10);
	double t_15 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_14)) + t_13;
	double tmp;
	if (t_15 <= 0.0) {
		tmp = fma(0.5, (1.0 / (t_5 * sqrt((1.0 / t_5)))), (1.0 / (t_12 + sqrt((1.0 + t_9)))));
	} else if (t_15 <= 1.0) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_12))) - t_6;
	} else if (t_15 <= 2.999995) {
		tmp = ((1.0 + sqrt((1.0 + t_10))) - t_6) - (t_14 - t_13);
	} else {
		tmp = ((2.0 - (t_6 + t_14)) + (1.0 - t_12)) + (sqrt((t_11 + 1.0)) - sqrt(t_11));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = fmax(t_2, t_8)
	t_12 = sqrt(t_9)
	t_13 = Float64(sqrt(Float64(t_9 + 1.0)) - t_12)
	t_14 = sqrt(t_10)
	t_15 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_10 + 1.0)) - t_14)) + t_13)
	tmp = 0.0
	if (t_15 <= 0.0)
		tmp = fma(0.5, Float64(1.0 / Float64(t_5 * sqrt(Float64(1.0 / t_5)))), Float64(1.0 / Float64(t_12 + sqrt(Float64(1.0 + t_9)))));
	elseif (t_15 <= 1.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 / Float64(1.0 + t_12))) - t_6);
	elseif (t_15 <= 2.999995)
		tmp = Float64(Float64(Float64(1.0 + sqrt(Float64(1.0 + t_10))) - t_6) - Float64(t_14 - t_13));
	else
		tmp = Float64(Float64(Float64(2.0 - Float64(t_6 + t_14)) + Float64(1.0 - t_12)) + Float64(sqrt(Float64(t_11 + 1.0)) - sqrt(t_11)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$11 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$12 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$13 = N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]}, If[LessEqual[t$95$15, 0.0], N[(0.5 * N[(1.0 / N[(t$95$5 * N[Sqrt[N[(1.0 / t$95$5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$12 + N[Sqrt[N[(1.0 + t$95$9), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$15, 1.0], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision], If[LessEqual[t$95$15, 2.999995], N[(N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] - N[(t$95$14 - t$95$13), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 - N[(t$95$6 + t$95$14), $MachinePrecision]), $MachinePrecision] + N[(1.0 - t$95$12), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$11], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
										LET t_10 = tmp_20 IN
											LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
											LET t_11 = tmp_21 IN
												LET t_12 = (sqrt(t_9)) IN
													LET t_13 = ((sqrt((t_9 + (1)))) - t_12) IN
														LET t_14 = (sqrt(t_10)) IN
															LET t_15 = ((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_10 + (1)))) - t_14)) + t_13) IN
																LET tmp_24 = IF (t_15 <= (29999950000000001892885848064906895160675048828125e-49)) THEN ((((1) + (sqrt(((1) + t_10)))) - t_6) - (t_14 - t_13)) ELSE ((((2) - (t_6 + t_14)) + ((1) - t_12)) + ((sqrt((t_11 + (1)))) - (sqrt(t_11)))) ENDIF IN
																LET tmp_23 = IF (t_15 <= (1)) THEN (((sqrt(((1) + t_5))) + ((1) / ((1) + t_12))) - t_6) ELSE tmp_24 ENDIF IN
																LET tmp_22 = IF (t_15 <= (0)) THEN (((5e-1) * ((1) / (t_5 * (sqrt(((1) / t_5)))))) + ((1) / (t_12 + (sqrt(((1) + t_9)))))) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 0.0

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{1}{2} \cdot \frac{1}{x \cdot \sqrt{\frac{1}{x}}} + \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

       \[\leadsto \mathsf{fma}\left(0.5, \frac{1}{x \cdot \sqrt{\frac{1}{x}}}, \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) \]

   if 0.0 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in z around 0

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]
   11. Step-by-step derivation

   12. Applied rewrites 21.3%

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]

   if 1 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.9999950000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 54.5%

      \[\leadsto \left(\left(\sqrt{t + 1} - \sqrt{t}\right) + \left(\sqrt{y + 1} - \left(\sqrt{x} - \sqrt{1 + x}\right)\right)\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 20.8%

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 16.9%

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   if 2.9999950000000002 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 95.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_3 := \mathsf{min}\left(t\_2, t\right)\\ t_4 := \sqrt{t\_3}\\ t_5 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_2, t\right)\\ t_8 := \sqrt{t\_7 + 1} - \sqrt{t\_7}\\ t_9 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \left(\sqrt{t\_3 + 1} - t\_4\right) + \left(\sqrt{t\_9 + 1} - t\_10\right)\\ \mathbf{if}\;t\_11 \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{1}{t\_3 \cdot \sqrt{\frac{1}{t\_3}}}, \frac{1}{t\_6 + \sqrt{1 + t\_5}}\right)\\ \mathbf{elif}\;t\_11 \leq 1.999998:\\ \;\;\;\;\left(\left(1 + \frac{1}{t\_10 + \sqrt{1 + t\_9}}\right) - t\_4\right) + t\_8\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - \left(t\_4 + t\_10\right)\right) + \left(\sqrt{t\_5 + 1} - t\_6\right)\right) + t\_8\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmin (fmin x y) z))
       (t_3 (fmin t_2 t))
       (t_4 (sqrt t_3))
       (t_5 (fmax (fmax x y) t_1))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_2 t))
       (t_8 (- (sqrt (+ t_7 1.0)) (sqrt t_7)))
       (t_9 (fmin (fmax x y) t_1))
       (t_10 (sqrt t_9))
       (t_11
        (+ (- (sqrt (+ t_3 1.0)) t_4) (- (sqrt (+ t_9 1.0)) t_10))))
  (if (<= t_11 0.2)
    (fma
     0.5
     (/ 1.0 (* t_3 (sqrt (/ 1.0 t_3))))
     (/ 1.0 (+ t_6 (sqrt (+ 1.0 t_5)))))
    (if (<= t_11 1.999998)
      (+ (- (+ 1.0 (/ 1.0 (+ t_10 (sqrt (+ 1.0 t_9))))) t_4) t_8)
      (+ (+ (- 2.0 (+ t_4 t_10)) (- (sqrt (+ t_5 1.0)) t_6)) t_8)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmin(fmin(x, y), z);
	double t_3 = fmin(t_2, t);
	double t_4 = sqrt(t_3);
	double t_5 = fmax(fmax(x, y), t_1);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_2, t);
	double t_8 = sqrt((t_7 + 1.0)) - sqrt(t_7);
	double t_9 = fmin(fmax(x, y), t_1);
	double t_10 = sqrt(t_9);
	double t_11 = (sqrt((t_3 + 1.0)) - t_4) + (sqrt((t_9 + 1.0)) - t_10);
	double tmp;
	if (t_11 <= 0.2) {
		tmp = fma(0.5, (1.0 / (t_3 * sqrt((1.0 / t_3)))), (1.0 / (t_6 + sqrt((1.0 + t_5)))));
	} else if (t_11 <= 1.999998) {
		tmp = ((1.0 + (1.0 / (t_10 + sqrt((1.0 + t_9))))) - t_4) + t_8;
	} else {
		tmp = ((2.0 - (t_4 + t_10)) + (sqrt((t_5 + 1.0)) - t_6)) + t_8;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmin(fmin(x, y), z)
	t_3 = fmin(t_2, t)
	t_4 = sqrt(t_3)
	t_5 = fmax(fmax(x, y), t_1)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_2, t)
	t_8 = Float64(sqrt(Float64(t_7 + 1.0)) - sqrt(t_7))
	t_9 = fmin(fmax(x, y), t_1)
	t_10 = sqrt(t_9)
	t_11 = Float64(Float64(sqrt(Float64(t_3 + 1.0)) - t_4) + Float64(sqrt(Float64(t_9 + 1.0)) - t_10))
	tmp = 0.0
	if (t_11 <= 0.2)
		tmp = fma(0.5, Float64(1.0 / Float64(t_3 * sqrt(Float64(1.0 / t_3)))), Float64(1.0 / Float64(t_6 + sqrt(Float64(1.0 + t_5)))));
	elseif (t_11 <= 1.999998)
		tmp = Float64(Float64(Float64(1.0 + Float64(1.0 / Float64(t_10 + sqrt(Float64(1.0 + t_9))))) - t_4) + t_8);
	else
		tmp = Float64(Float64(Float64(2.0 - Float64(t_4 + t_10)) + Float64(sqrt(Float64(t_5 + 1.0)) - t_6)) + t_8);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$3 = N[Min[t$95$2, t], $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[t$95$3], $MachinePrecision]}, Block[{t$95$5 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$2, t], $MachinePrecision]}, Block[{t$95$8 = N[(N[Sqrt[N[(t$95$7 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$7], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[(N[(N[Sqrt[N[(t$95$3 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$4), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$11, 0.2], N[(0.5 * N[(1.0 / N[(t$95$3 * N[Sqrt[N[(1.0 / t$95$3), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$6 + N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$11, 1.999998], N[(N[(N[(1.0 + N[(1.0 / N[(t$95$10 + N[Sqrt[N[(1.0 + t$95$9), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision] + t$95$8), $MachinePrecision], N[(N[(N[(2.0 - N[(t$95$4 + t$95$10), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 < z) THEN tmp_7 ELSE z ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_8 = IF (t_2 < t) THEN t_2 ELSE t ENDIF IN
			LET t_3 = tmp_8 IN
				LET t_4 = (sqrt(t_3)) IN
					LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
					LET tmp_12 = IF (x > y) THEN x ELSE y ENDIF IN
					LET tmp_10 = IF (tmp_11 > t_1) THEN tmp_12 ELSE t_1 ENDIF IN
					LET t_5 = tmp_10 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_13 = IF (t_2 > t) THEN t_2 ELSE t ENDIF IN
							LET t_7 = tmp_13 IN
								LET t_8 = ((sqrt((t_7 + (1)))) - (sqrt(t_7))) IN
									LET tmp_16 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_17 = IF (x > y) THEN x ELSE y ENDIF IN
									LET tmp_15 = IF (tmp_16 < t_1) THEN tmp_17 ELSE t_1 ENDIF IN
									LET t_9 = tmp_15 IN
										LET t_10 = (sqrt(t_9)) IN
											LET t_11 = (((sqrt((t_3 + (1)))) - t_4) + ((sqrt((t_9 + (1)))) - t_10)) IN
												LET tmp_19 = IF (t_11 <= (19999979999999999424886709675774909555912017822265625e-52)) THEN ((((1) + ((1) / (t_10 + (sqrt(((1) + t_9)))))) - t_4) + t_8) ELSE ((((2) - (t_4 + t_10)) + ((sqrt((t_5 + (1)))) - t_6)) + t_8) ENDIF IN
												LET tmp_18 = IF (t_11 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN (((5e-1) * ((1) / (t_3 * (sqrt(((1) / t_3)))))) + ((1) / (t_6 + (sqrt(((1) + t_5)))))) ELSE tmp_19 ENDIF IN
	tmp_18
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) < 0.20000000000000001

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{1}{2} \cdot \frac{1}{x \cdot \sqrt{\frac{1}{x}}} + \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]
   11. Step-by-step derivation

   12. Applied rewrites 17.0%

       \[\leadsto \mathsf{fma}\left(0.5, \frac{1}{x \cdot \sqrt{\frac{1}{x}}}, \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) \]

   if 0.20000000000000001 < (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) < 1.9999979999999999

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.9%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{\sqrt{y} + \sqrt{y + 1}}\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in z around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 40.0%

      \[\leadsto \left(\left(\sqrt{1 + x} + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 28.9%

      \[\leadsto \left(\left(1 + \frac{1}{\sqrt{y} + \sqrt{1 + y}}\right) - \sqrt{x}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 1.9999979999999999 < (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_11 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_12 := \sqrt{t\_9}\\ t_13 := \sqrt{t\_9 + 1} - t\_12\\ t_14 := \sqrt{t\_11 + 1} - \sqrt{t\_11}\\ t_15 := \sqrt{t\_10}\\ t_16 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_10 + 1} - t\_15\right)\right) + t\_13\\ \mathbf{if}\;t\_16 \leq 1:\\ \;\;\;\;\left(\left(\sqrt{1 + t\_5} - t\_6\right) + \frac{0.5}{t\_12}\right) + t\_14\\ \mathbf{elif}\;t\_16 \leq 2.999995:\\ \;\;\;\;\left(\left(1 + \sqrt{1 + t\_10}\right) - t\_6\right) - \left(t\_15 - t\_13\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - \left(t\_6 + t\_15\right)\right) + \left(1 - t\_12\right)\right) + t\_14\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (fmin t_3 t_7))
       (t_11 (fmax t_2 t_8))
       (t_12 (sqrt t_9))
       (t_13 (- (sqrt (+ t_9 1.0)) t_12))
       (t_14 (- (sqrt (+ t_11 1.0)) (sqrt t_11)))
       (t_15 (sqrt t_10))
       (t_16
        (+
         (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_10 1.0)) t_15))
         t_13)))
  (if (<= t_16 1.0)
    (+ (+ (- (sqrt (+ 1.0 t_5)) t_6) (/ 0.5 t_12)) t_14)
    (if (<= t_16 2.999995)
      (- (- (+ 1.0 (sqrt (+ 1.0 t_10))) t_6) (- t_15 t_13))
      (+ (+ (- 2.0 (+ t_6 t_15)) (- 1.0 t_12)) t_14)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = fmax(t_2, t_8);
	double t_12 = sqrt(t_9);
	double t_13 = sqrt((t_9 + 1.0)) - t_12;
	double t_14 = sqrt((t_11 + 1.0)) - sqrt(t_11);
	double t_15 = sqrt(t_10);
	double t_16 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_15)) + t_13;
	double tmp;
	if (t_16 <= 1.0) {
		tmp = ((sqrt((1.0 + t_5)) - t_6) + (0.5 / t_12)) + t_14;
	} else if (t_16 <= 2.999995) {
		tmp = ((1.0 + sqrt((1.0 + t_10))) - t_6) - (t_15 - t_13);
	} else {
		tmp = ((2.0 - (t_6 + t_15)) + (1.0 - t_12)) + t_14;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = fmin(t_3, t_7)
    t_11 = fmax(t_2, t_8)
    t_12 = sqrt(t_9)
    t_13 = sqrt((t_9 + 1.0d0)) - t_12
    t_14 = sqrt((t_11 + 1.0d0)) - sqrt(t_11)
    t_15 = sqrt(t_10)
    t_16 = ((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_10 + 1.0d0)) - t_15)) + t_13
    if (t_16 <= 1.0d0) then
        tmp = ((sqrt((1.0d0 + t_5)) - t_6) + (0.5d0 / t_12)) + t_14
    else if (t_16 <= 2.999995d0) then
        tmp = ((1.0d0 + sqrt((1.0d0 + t_10))) - t_6) - (t_15 - t_13)
    else
        tmp = ((2.0d0 - (t_6 + t_15)) + (1.0d0 - t_12)) + t_14
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = fmax(t_2, t_8);
	double t_12 = Math.sqrt(t_9);
	double t_13 = Math.sqrt((t_9 + 1.0)) - t_12;
	double t_14 = Math.sqrt((t_11 + 1.0)) - Math.sqrt(t_11);
	double t_15 = Math.sqrt(t_10);
	double t_16 = ((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_10 + 1.0)) - t_15)) + t_13;
	double tmp;
	if (t_16 <= 1.0) {
		tmp = ((Math.sqrt((1.0 + t_5)) - t_6) + (0.5 / t_12)) + t_14;
	} else if (t_16 <= 2.999995) {
		tmp = ((1.0 + Math.sqrt((1.0 + t_10))) - t_6) - (t_15 - t_13);
	} else {
		tmp = ((2.0 - (t_6 + t_15)) + (1.0 - t_12)) + t_14;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = fmax(t_2, t_8)
	t_12 = math.sqrt(t_9)
	t_13 = math.sqrt((t_9 + 1.0)) - t_12
	t_14 = math.sqrt((t_11 + 1.0)) - math.sqrt(t_11)
	t_15 = math.sqrt(t_10)
	t_16 = ((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_10 + 1.0)) - t_15)) + t_13
	tmp = 0
	if t_16 <= 1.0:
		tmp = ((math.sqrt((1.0 + t_5)) - t_6) + (0.5 / t_12)) + t_14
	elif t_16 <= 2.999995:
		tmp = ((1.0 + math.sqrt((1.0 + t_10))) - t_6) - (t_15 - t_13)
	else:
		tmp = ((2.0 - (t_6 + t_15)) + (1.0 - t_12)) + t_14
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = fmax(t_2, t_8)
	t_12 = sqrt(t_9)
	t_13 = Float64(sqrt(Float64(t_9 + 1.0)) - t_12)
	t_14 = Float64(sqrt(Float64(t_11 + 1.0)) - sqrt(t_11))
	t_15 = sqrt(t_10)
	t_16 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_10 + 1.0)) - t_15)) + t_13)
	tmp = 0.0
	if (t_16 <= 1.0)
		tmp = Float64(Float64(Float64(sqrt(Float64(1.0 + t_5)) - t_6) + Float64(0.5 / t_12)) + t_14);
	elseif (t_16 <= 2.999995)
		tmp = Float64(Float64(Float64(1.0 + sqrt(Float64(1.0 + t_10))) - t_6) - Float64(t_15 - t_13));
	else
		tmp = Float64(Float64(Float64(2.0 - Float64(t_6 + t_15)) + Float64(1.0 - t_12)) + t_14);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = min(t_3, t_7);
	t_11 = max(t_2, t_8);
	t_12 = sqrt(t_9);
	t_13 = sqrt((t_9 + 1.0)) - t_12;
	t_14 = sqrt((t_11 + 1.0)) - sqrt(t_11);
	t_15 = sqrt(t_10);
	t_16 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_15)) + t_13;
	tmp = 0.0;
	if (t_16 <= 1.0)
		tmp = ((sqrt((1.0 + t_5)) - t_6) + (0.5 / t_12)) + t_14;
	elseif (t_16 <= 2.999995)
		tmp = ((1.0 + sqrt((1.0 + t_10))) - t_6) - (t_15 - t_13);
	else
		tmp = ((2.0 - (t_6 + t_15)) + (1.0 - t_12)) + t_14;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$11 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$12 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$13 = N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$11], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$15 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$15), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]}, If[LessEqual[t$95$16, 1.0], N[(N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(0.5 / t$95$12), $MachinePrecision]), $MachinePrecision] + t$95$14), $MachinePrecision], If[LessEqual[t$95$16, 2.999995], N[(N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] - N[(t$95$15 - t$95$13), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 - N[(t$95$6 + t$95$15), $MachinePrecision]), $MachinePrecision] + N[(1.0 - t$95$12), $MachinePrecision]), $MachinePrecision] + t$95$14), $MachinePrecision]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
										LET t_10 = tmp_20 IN
											LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
											LET t_11 = tmp_21 IN
												LET t_12 = (sqrt(t_9)) IN
													LET t_13 = ((sqrt((t_9 + (1)))) - t_12) IN
														LET t_14 = ((sqrt((t_11 + (1)))) - (sqrt(t_11))) IN
															LET t_15 = (sqrt(t_10)) IN
																LET t_16 = ((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_10 + (1)))) - t_15)) + t_13) IN
																	LET tmp_23 = IF (t_16 <= (29999950000000001892885848064906895160675048828125e-49)) THEN ((((1) + (sqrt(((1) + t_10)))) - t_6) - (t_15 - t_13)) ELSE ((((2) - (t_6 + t_15)) + ((1) - t_12)) + t_14) ENDIF IN
																	LET tmp_22 = IF (t_16 <= (1)) THEN ((((sqrt(((1) + t_5))) - t_6) + ((5e-1) / t_12)) + t_14) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{\frac{1}{2}}{z \cdot \sqrt{\frac{1}{z}}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 47.5%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{0.5}{z \cdot \sqrt{\frac{1}{z}}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{\frac{1}{2}}{\sqrt{z}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 47.5%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{0.5}{\sqrt{z}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in y around inf

      \[\leadsto \left(\left(\sqrt{1 + x} - \sqrt{x}\right) + \frac{0.5}{\sqrt{z}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 26.9%

       \[\leadsto \left(\left(\sqrt{1 + x} - \sqrt{x}\right) + \frac{0.5}{\sqrt{z}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   if 1 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.9999950000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 54.5%

      \[\leadsto \left(\left(\sqrt{t + 1} - \sqrt{t}\right) + \left(\sqrt{y + 1} - \left(\sqrt{x} - \sqrt{1 + x}\right)\right)\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 20.8%

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 16.9%

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   if 2.9999950000000002 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 91.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_11 := \sqrt{t\_9}\\ t_12 := \sqrt{t\_9 + 1} - t\_11\\ t_13 := \sqrt{t\_10}\\ t_14 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_10 + 1} - t\_13\right)\right) + t\_12\\ t_15 := \mathsf{max}\left(t\_2, t\_8\right)\\ \mathbf{if}\;t\_14 \leq 1:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \frac{1}{1 + t\_11}\right) - t\_6\\ \mathbf{elif}\;t\_14 \leq 2.999995:\\ \;\;\;\;\left(\left(1 + \sqrt{1 + t\_10}\right) - t\_6\right) - \left(t\_13 - t\_12\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - \left(t\_6 + t\_13\right)\right) + \left(1 - t\_11\right)\right) + \left(\sqrt{t\_15 + 1} - \sqrt{t\_15}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (fmin t_3 t_7))
       (t_11 (sqrt t_9))
       (t_12 (- (sqrt (+ t_9 1.0)) t_11))
       (t_13 (sqrt t_10))
       (t_14
        (+
         (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_10 1.0)) t_13))
         t_12))
       (t_15 (fmax t_2 t_8)))
  (if (<= t_14 1.0)
    (- (+ (sqrt (+ 1.0 t_5)) (/ 1.0 (+ 1.0 t_11))) t_6)
    (if (<= t_14 2.999995)
      (- (- (+ 1.0 (sqrt (+ 1.0 t_10))) t_6) (- t_13 t_12))
      (+
       (+ (- 2.0 (+ t_6 t_13)) (- 1.0 t_11))
       (- (sqrt (+ t_15 1.0)) (sqrt t_15)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = sqrt(t_9);
	double t_12 = sqrt((t_9 + 1.0)) - t_11;
	double t_13 = sqrt(t_10);
	double t_14 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_13)) + t_12;
	double t_15 = fmax(t_2, t_8);
	double tmp;
	if (t_14 <= 1.0) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6;
	} else if (t_14 <= 2.999995) {
		tmp = ((1.0 + sqrt((1.0 + t_10))) - t_6) - (t_13 - t_12);
	} else {
		tmp = ((2.0 - (t_6 + t_13)) + (1.0 - t_11)) + (sqrt((t_15 + 1.0)) - sqrt(t_15));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = fmin(t_3, t_7)
    t_11 = sqrt(t_9)
    t_12 = sqrt((t_9 + 1.0d0)) - t_11
    t_13 = sqrt(t_10)
    t_14 = ((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_10 + 1.0d0)) - t_13)) + t_12
    t_15 = fmax(t_2, t_8)
    if (t_14 <= 1.0d0) then
        tmp = (sqrt((1.0d0 + t_5)) + (1.0d0 / (1.0d0 + t_11))) - t_6
    else if (t_14 <= 2.999995d0) then
        tmp = ((1.0d0 + sqrt((1.0d0 + t_10))) - t_6) - (t_13 - t_12)
    else
        tmp = ((2.0d0 - (t_6 + t_13)) + (1.0d0 - t_11)) + (sqrt((t_15 + 1.0d0)) - sqrt(t_15))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = Math.sqrt(t_9);
	double t_12 = Math.sqrt((t_9 + 1.0)) - t_11;
	double t_13 = Math.sqrt(t_10);
	double t_14 = ((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_10 + 1.0)) - t_13)) + t_12;
	double t_15 = fmax(t_2, t_8);
	double tmp;
	if (t_14 <= 1.0) {
		tmp = (Math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6;
	} else if (t_14 <= 2.999995) {
		tmp = ((1.0 + Math.sqrt((1.0 + t_10))) - t_6) - (t_13 - t_12);
	} else {
		tmp = ((2.0 - (t_6 + t_13)) + (1.0 - t_11)) + (Math.sqrt((t_15 + 1.0)) - Math.sqrt(t_15));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = math.sqrt(t_9)
	t_12 = math.sqrt((t_9 + 1.0)) - t_11
	t_13 = math.sqrt(t_10)
	t_14 = ((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_10 + 1.0)) - t_13)) + t_12
	t_15 = fmax(t_2, t_8)
	tmp = 0
	if t_14 <= 1.0:
		tmp = (math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6
	elif t_14 <= 2.999995:
		tmp = ((1.0 + math.sqrt((1.0 + t_10))) - t_6) - (t_13 - t_12)
	else:
		tmp = ((2.0 - (t_6 + t_13)) + (1.0 - t_11)) + (math.sqrt((t_15 + 1.0)) - math.sqrt(t_15))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = sqrt(t_9)
	t_12 = Float64(sqrt(Float64(t_9 + 1.0)) - t_11)
	t_13 = sqrt(t_10)
	t_14 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_10 + 1.0)) - t_13)) + t_12)
	t_15 = fmax(t_2, t_8)
	tmp = 0.0
	if (t_14 <= 1.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 / Float64(1.0 + t_11))) - t_6);
	elseif (t_14 <= 2.999995)
		tmp = Float64(Float64(Float64(1.0 + sqrt(Float64(1.0 + t_10))) - t_6) - Float64(t_13 - t_12));
	else
		tmp = Float64(Float64(Float64(2.0 - Float64(t_6 + t_13)) + Float64(1.0 - t_11)) + Float64(sqrt(Float64(t_15 + 1.0)) - sqrt(t_15)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = min(t_3, t_7);
	t_11 = sqrt(t_9);
	t_12 = sqrt((t_9 + 1.0)) - t_11;
	t_13 = sqrt(t_10);
	t_14 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_13)) + t_12;
	t_15 = max(t_2, t_8);
	tmp = 0.0;
	if (t_14 <= 1.0)
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6;
	elseif (t_14 <= 2.999995)
		tmp = ((1.0 + sqrt((1.0 + t_10))) - t_6) - (t_13 - t_12);
	else
		tmp = ((2.0 - (t_6 + t_13)) + (1.0 - t_11)) + (sqrt((t_15 + 1.0)) - sqrt(t_15));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$12 = N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$11), $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]), $MachinePrecision] + t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, If[LessEqual[t$95$14, 1.0], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision], If[LessEqual[t$95$14, 2.999995], N[(N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] - N[(t$95$13 - t$95$12), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 - N[(t$95$6 + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(1.0 - t$95$11), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$15 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$15], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
										LET t_10 = tmp_20 IN
											LET t_11 = (sqrt(t_9)) IN
												LET t_12 = ((sqrt((t_9 + (1)))) - t_11) IN
													LET t_13 = (sqrt(t_10)) IN
														LET t_14 = ((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_10 + (1)))) - t_13)) + t_12) IN
															LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
															LET t_15 = tmp_21 IN
																LET tmp_23 = IF (t_14 <= (29999950000000001892885848064906895160675048828125e-49)) THEN ((((1) + (sqrt(((1) + t_10)))) - t_6) - (t_13 - t_12)) ELSE ((((2) - (t_6 + t_13)) + ((1) - t_11)) + ((sqrt((t_15 + (1)))) - (sqrt(t_15)))) ENDIF IN
																LET tmp_22 = IF (t_14 <= (1)) THEN (((sqrt(((1) + t_5))) + ((1) / ((1) + t_11))) - t_6) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in z around 0

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]
   11. Step-by-step derivation

   12. Applied rewrites 21.3%

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]

   if 1 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.9999950000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 54.5%

      \[\leadsto \left(\left(\sqrt{t + 1} - \sqrt{t}\right) + \left(\sqrt{y + 1} - \left(\sqrt{x} - \sqrt{1 + x}\right)\right)\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 20.8%

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 16.9%

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   if 2.9999950000000002 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_2, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_3, t\_8\right)\\ t_10 := \mathsf{min}\left(t\_2, t\_7\right)\\ t_11 := \sqrt{t\_9}\\ t_12 := \sqrt{t\_9 + 1} - t\_11\\ t_13 := \mathsf{max}\left(t\_3, t\_8\right)\\ t_14 := \sqrt{t\_10}\\ t_15 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_10 + 1} - t\_14\right)\right) + t\_12\\ t_16 := t\_6 + t\_14\\ \mathbf{if}\;t\_15 \leq 1:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \frac{1}{1 + t\_11}\right) - t\_6\\ \mathbf{elif}\;t\_15 \leq 1.9998:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_10}\right) - t\_16\\ \mathbf{elif}\;t\_15 \leq 2.999995:\\ \;\;\;\;\left(\left(2 + 0.5 \cdot t\_10\right) - t\_6\right) - \left(t\_14 - t\_12\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 - t\_16\right) + \left(1 - t\_11\right)\right) + \left(\sqrt{t\_13 + 1} - \sqrt{t\_13}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmin (fmax x y) t_1))
       (t_3 (fmax (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_2 t_7))
       (t_9 (fmin t_3 t_8))
       (t_10 (fmin t_2 t_7))
       (t_11 (sqrt t_9))
       (t_12 (- (sqrt (+ t_9 1.0)) t_11))
       (t_13 (fmax t_3 t_8))
       (t_14 (sqrt t_10))
       (t_15
        (+
         (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_10 1.0)) t_14))
         t_12))
       (t_16 (+ t_6 t_14)))
  (if (<= t_15 1.0)
    (- (+ (sqrt (+ 1.0 t_5)) (/ 1.0 (+ 1.0 t_11))) t_6)
    (if (<= t_15 1.9998)
      (- (+ 1.0 (sqrt (+ 1.0 t_10))) t_16)
      (if (<= t_15 2.999995)
        (- (- (+ 2.0 (* 0.5 t_10)) t_6) (- t_14 t_12))
        (+
         (+ (- 2.0 t_16) (- 1.0 t_11))
         (- (sqrt (+ t_13 1.0)) (sqrt t_13))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmin(fmax(x, y), t_1);
	double t_3 = fmax(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_2, t_7);
	double t_9 = fmin(t_3, t_8);
	double t_10 = fmin(t_2, t_7);
	double t_11 = sqrt(t_9);
	double t_12 = sqrt((t_9 + 1.0)) - t_11;
	double t_13 = fmax(t_3, t_8);
	double t_14 = sqrt(t_10);
	double t_15 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_14)) + t_12;
	double t_16 = t_6 + t_14;
	double tmp;
	if (t_15 <= 1.0) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6;
	} else if (t_15 <= 1.9998) {
		tmp = (1.0 + sqrt((1.0 + t_10))) - t_16;
	} else if (t_15 <= 2.999995) {
		tmp = ((2.0 + (0.5 * t_10)) - t_6) - (t_14 - t_12);
	} else {
		tmp = ((2.0 - t_16) + (1.0 - t_11)) + (sqrt((t_13 + 1.0)) - sqrt(t_13));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmin(fmax(x, y), t_1)
    t_3 = fmax(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_2, t_7)
    t_9 = fmin(t_3, t_8)
    t_10 = fmin(t_2, t_7)
    t_11 = sqrt(t_9)
    t_12 = sqrt((t_9 + 1.0d0)) - t_11
    t_13 = fmax(t_3, t_8)
    t_14 = sqrt(t_10)
    t_15 = ((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_10 + 1.0d0)) - t_14)) + t_12
    t_16 = t_6 + t_14
    if (t_15 <= 1.0d0) then
        tmp = (sqrt((1.0d0 + t_5)) + (1.0d0 / (1.0d0 + t_11))) - t_6
    else if (t_15 <= 1.9998d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_10))) - t_16
    else if (t_15 <= 2.999995d0) then
        tmp = ((2.0d0 + (0.5d0 * t_10)) - t_6) - (t_14 - t_12)
    else
        tmp = ((2.0d0 - t_16) + (1.0d0 - t_11)) + (sqrt((t_13 + 1.0d0)) - sqrt(t_13))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmin(fmax(x, y), t_1);
	double t_3 = fmax(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_2, t_7);
	double t_9 = fmin(t_3, t_8);
	double t_10 = fmin(t_2, t_7);
	double t_11 = Math.sqrt(t_9);
	double t_12 = Math.sqrt((t_9 + 1.0)) - t_11;
	double t_13 = fmax(t_3, t_8);
	double t_14 = Math.sqrt(t_10);
	double t_15 = ((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_10 + 1.0)) - t_14)) + t_12;
	double t_16 = t_6 + t_14;
	double tmp;
	if (t_15 <= 1.0) {
		tmp = (Math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6;
	} else if (t_15 <= 1.9998) {
		tmp = (1.0 + Math.sqrt((1.0 + t_10))) - t_16;
	} else if (t_15 <= 2.999995) {
		tmp = ((2.0 + (0.5 * t_10)) - t_6) - (t_14 - t_12);
	} else {
		tmp = ((2.0 - t_16) + (1.0 - t_11)) + (Math.sqrt((t_13 + 1.0)) - Math.sqrt(t_13));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmin(fmax(x, y), t_1)
	t_3 = fmax(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_2, t_7)
	t_9 = fmin(t_3, t_8)
	t_10 = fmin(t_2, t_7)
	t_11 = math.sqrt(t_9)
	t_12 = math.sqrt((t_9 + 1.0)) - t_11
	t_13 = fmax(t_3, t_8)
	t_14 = math.sqrt(t_10)
	t_15 = ((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_10 + 1.0)) - t_14)) + t_12
	t_16 = t_6 + t_14
	tmp = 0
	if t_15 <= 1.0:
		tmp = (math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6
	elif t_15 <= 1.9998:
		tmp = (1.0 + math.sqrt((1.0 + t_10))) - t_16
	elif t_15 <= 2.999995:
		tmp = ((2.0 + (0.5 * t_10)) - t_6) - (t_14 - t_12)
	else:
		tmp = ((2.0 - t_16) + (1.0 - t_11)) + (math.sqrt((t_13 + 1.0)) - math.sqrt(t_13))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmin(fmax(x, y), t_1)
	t_3 = fmax(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_2, t_7)
	t_9 = fmin(t_3, t_8)
	t_10 = fmin(t_2, t_7)
	t_11 = sqrt(t_9)
	t_12 = Float64(sqrt(Float64(t_9 + 1.0)) - t_11)
	t_13 = fmax(t_3, t_8)
	t_14 = sqrt(t_10)
	t_15 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_10 + 1.0)) - t_14)) + t_12)
	t_16 = Float64(t_6 + t_14)
	tmp = 0.0
	if (t_15 <= 1.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 / Float64(1.0 + t_11))) - t_6);
	elseif (t_15 <= 1.9998)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_10))) - t_16);
	elseif (t_15 <= 2.999995)
		tmp = Float64(Float64(Float64(2.0 + Float64(0.5 * t_10)) - t_6) - Float64(t_14 - t_12));
	else
		tmp = Float64(Float64(Float64(2.0 - t_16) + Float64(1.0 - t_11)) + Float64(sqrt(Float64(t_13 + 1.0)) - sqrt(t_13)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = min(max(x, y), t_1);
	t_3 = max(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_2, t_7);
	t_9 = min(t_3, t_8);
	t_10 = min(t_2, t_7);
	t_11 = sqrt(t_9);
	t_12 = sqrt((t_9 + 1.0)) - t_11;
	t_13 = max(t_3, t_8);
	t_14 = sqrt(t_10);
	t_15 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_14)) + t_12;
	t_16 = t_6 + t_14;
	tmp = 0.0;
	if (t_15 <= 1.0)
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_11))) - t_6;
	elseif (t_15 <= 1.9998)
		tmp = (1.0 + sqrt((1.0 + t_10))) - t_16;
	elseif (t_15 <= 2.999995)
		tmp = ((2.0 + (0.5 * t_10)) - t_6) - (t_14 - t_12);
	else
		tmp = ((2.0 - t_16) + (1.0 - t_11)) + (sqrt((t_13 + 1.0)) - sqrt(t_13));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$2, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$3, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$2, t$95$7], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$12 = N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$11), $MachinePrecision]}, Block[{t$95$13 = N[Max[t$95$3, t$95$8], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + t$95$12), $MachinePrecision]}, Block[{t$95$16 = N[(t$95$6 + t$95$14), $MachinePrecision]}, If[LessEqual[t$95$15, 1.0], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision], If[LessEqual[t$95$15, 1.9998], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$16), $MachinePrecision], If[LessEqual[t$95$15, 2.999995], N[(N[(N[(2.0 + N[(0.5 * t$95$10), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] - N[(t$95$14 - t$95$12), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 - t$95$16), $MachinePrecision] + N[(1.0 - t$95$11), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$13 + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t$95$13], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 < t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 > t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_2 > t_7) THEN t_2 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_3 < t_8) THEN t_3 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET tmp_20 = IF (t_2 < t_7) THEN t_2 ELSE t_7 ENDIF IN
										LET t_10 = tmp_20 IN
											LET t_11 = (sqrt(t_9)) IN
												LET t_12 = ((sqrt((t_9 + (1)))) - t_11) IN
													LET tmp_21 = IF (t_3 > t_8) THEN t_3 ELSE t_8 ENDIF IN
													LET t_13 = tmp_21 IN
														LET t_14 = (sqrt(t_10)) IN
															LET t_15 = ((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_10 + (1)))) - t_14)) + t_12) IN
																LET t_16 = (t_6 + t_14) IN
																	LET tmp_24 = IF (t_15 <= (29999950000000001892885848064906895160675048828125e-49)) THEN ((((2) + ((5e-1) * t_10)) - t_6) - (t_14 - t_12)) ELSE ((((2) - t_16) + ((1) - t_11)) + ((sqrt((t_13 + (1)))) - (sqrt(t_13)))) ENDIF IN
																	LET tmp_23 = IF (t_15 <= (1999800000000000022026824808563105762004852294921875e-51)) THEN (((1) + (sqrt(((1) + t_10)))) - t_16) ELSE tmp_24 ENDIF IN
																	LET tmp_22 = IF (t_15 <= (1)) THEN (((sqrt(((1) + t_5))) + ((1) / ((1) + t_11))) - t_6) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in z around 0

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]
   11. Step-by-step derivation

   12. Applied rewrites 21.3%

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]

   if 1 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1.9998

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 1.9998 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.9999950000000002

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 54.5%

      \[\leadsto \left(\left(\sqrt{t + 1} - \sqrt{t}\right) + \left(\sqrt{y + 1} - \left(\sqrt{x} - \sqrt{1 + x}\right)\right)\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 20.8%

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 16.9%

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   10. Taylor expanded in y around 0

       \[\leadsto \left(\left(2 + \frac{1}{2} \cdot y\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 16.5%

       \[\leadsto \left(\left(2 + 0.5 \cdot y\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   if 2.9999950000000002 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 36.9%

      \[\leadsto \left(\left(\left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 24.5%

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.0%

       \[\leadsto \left(\left(2 - \left(\sqrt{x} + \sqrt{y}\right)\right) + \left(1 - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 19: 90.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \sqrt{t\_9 + 1} - t\_10\\ t_12 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_13 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_14 := \sqrt{t\_13}\\ t_15 := \sqrt{t\_12}\\ t_16 := \left(\left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_12 + 1} - t\_15\right)\right) + t\_11\right) + \left(\sqrt{t\_13 + 1} - t\_14\right)\\ \mathbf{if}\;t\_16 \leq 1:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \frac{1}{1 + t\_10}\right) - t\_6\\ \mathbf{elif}\;t\_16 \leq 1.9998:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_12}\right) - \left(t\_6 + t\_15\right)\\ \mathbf{elif}\;t\_16 \leq 3.5:\\ \;\;\;\;\left(\left(2 + 0.5 \cdot t\_12\right) - t\_6\right) - \left(t\_15 - t\_11\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4 + 0.5 \cdot t\_5\right) - \left(t\_14 + \left(t\_6 + \left(t\_15 + t\_10\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (sqrt t_9))
       (t_11 (- (sqrt (+ t_9 1.0)) t_10))
       (t_12 (fmin t_3 t_7))
       (t_13 (fmax t_2 t_8))
       (t_14 (sqrt t_13))
       (t_15 (sqrt t_12))
       (t_16
        (+
         (+
          (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_12 1.0)) t_15))
          t_11)
         (- (sqrt (+ t_13 1.0)) t_14))))
  (if (<= t_16 1.0)
    (- (+ (sqrt (+ 1.0 t_5)) (/ 1.0 (+ 1.0 t_10))) t_6)
    (if (<= t_16 1.9998)
      (- (+ 1.0 (sqrt (+ 1.0 t_12))) (+ t_6 t_15))
      (if (<= t_16 3.5)
        (- (- (+ 2.0 (* 0.5 t_12)) t_6) (- t_15 t_11))
        (- (+ 4.0 (* 0.5 t_5)) (+ t_14 (+ t_6 (+ t_15 t_10)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = sqrt((t_9 + 1.0)) - t_10;
	double t_12 = fmin(t_3, t_7);
	double t_13 = fmax(t_2, t_8);
	double t_14 = sqrt(t_13);
	double t_15 = sqrt(t_12);
	double t_16 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_12 + 1.0)) - t_15)) + t_11) + (sqrt((t_13 + 1.0)) - t_14);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_16 <= 1.9998) {
		tmp = (1.0 + sqrt((1.0 + t_12))) - (t_6 + t_15);
	} else if (t_16 <= 3.5) {
		tmp = ((2.0 + (0.5 * t_12)) - t_6) - (t_15 - t_11);
	} else {
		tmp = (4.0 + (0.5 * t_5)) - (t_14 + (t_6 + (t_15 + t_10)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = sqrt(t_9)
    t_11 = sqrt((t_9 + 1.0d0)) - t_10
    t_12 = fmin(t_3, t_7)
    t_13 = fmax(t_2, t_8)
    t_14 = sqrt(t_13)
    t_15 = sqrt(t_12)
    t_16 = (((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_12 + 1.0d0)) - t_15)) + t_11) + (sqrt((t_13 + 1.0d0)) - t_14)
    if (t_16 <= 1.0d0) then
        tmp = (sqrt((1.0d0 + t_5)) + (1.0d0 / (1.0d0 + t_10))) - t_6
    else if (t_16 <= 1.9998d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_12))) - (t_6 + t_15)
    else if (t_16 <= 3.5d0) then
        tmp = ((2.0d0 + (0.5d0 * t_12)) - t_6) - (t_15 - t_11)
    else
        tmp = (4.0d0 + (0.5d0 * t_5)) - (t_14 + (t_6 + (t_15 + t_10)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = Math.sqrt(t_9);
	double t_11 = Math.sqrt((t_9 + 1.0)) - t_10;
	double t_12 = fmin(t_3, t_7);
	double t_13 = fmax(t_2, t_8);
	double t_14 = Math.sqrt(t_13);
	double t_15 = Math.sqrt(t_12);
	double t_16 = (((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_12 + 1.0)) - t_15)) + t_11) + (Math.sqrt((t_13 + 1.0)) - t_14);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = (Math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_16 <= 1.9998) {
		tmp = (1.0 + Math.sqrt((1.0 + t_12))) - (t_6 + t_15);
	} else if (t_16 <= 3.5) {
		tmp = ((2.0 + (0.5 * t_12)) - t_6) - (t_15 - t_11);
	} else {
		tmp = (4.0 + (0.5 * t_5)) - (t_14 + (t_6 + (t_15 + t_10)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = math.sqrt(t_9)
	t_11 = math.sqrt((t_9 + 1.0)) - t_10
	t_12 = fmin(t_3, t_7)
	t_13 = fmax(t_2, t_8)
	t_14 = math.sqrt(t_13)
	t_15 = math.sqrt(t_12)
	t_16 = (((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_12 + 1.0)) - t_15)) + t_11) + (math.sqrt((t_13 + 1.0)) - t_14)
	tmp = 0
	if t_16 <= 1.0:
		tmp = (math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6
	elif t_16 <= 1.9998:
		tmp = (1.0 + math.sqrt((1.0 + t_12))) - (t_6 + t_15)
	elif t_16 <= 3.5:
		tmp = ((2.0 + (0.5 * t_12)) - t_6) - (t_15 - t_11)
	else:
		tmp = (4.0 + (0.5 * t_5)) - (t_14 + (t_6 + (t_15 + t_10)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = sqrt(t_9)
	t_11 = Float64(sqrt(Float64(t_9 + 1.0)) - t_10)
	t_12 = fmin(t_3, t_7)
	t_13 = fmax(t_2, t_8)
	t_14 = sqrt(t_13)
	t_15 = sqrt(t_12)
	t_16 = Float64(Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_12 + 1.0)) - t_15)) + t_11) + Float64(sqrt(Float64(t_13 + 1.0)) - t_14))
	tmp = 0.0
	if (t_16 <= 1.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 / Float64(1.0 + t_10))) - t_6);
	elseif (t_16 <= 1.9998)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_12))) - Float64(t_6 + t_15));
	elseif (t_16 <= 3.5)
		tmp = Float64(Float64(Float64(2.0 + Float64(0.5 * t_12)) - t_6) - Float64(t_15 - t_11));
	else
		tmp = Float64(Float64(4.0 + Float64(0.5 * t_5)) - Float64(t_14 + Float64(t_6 + Float64(t_15 + t_10))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = sqrt(t_9);
	t_11 = sqrt((t_9 + 1.0)) - t_10;
	t_12 = min(t_3, t_7);
	t_13 = max(t_2, t_8);
	t_14 = sqrt(t_13);
	t_15 = sqrt(t_12);
	t_16 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_12 + 1.0)) - t_15)) + t_11) + (sqrt((t_13 + 1.0)) - t_14);
	tmp = 0.0;
	if (t_16 <= 1.0)
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	elseif (t_16 <= 1.9998)
		tmp = (1.0 + sqrt((1.0 + t_12))) - (t_6 + t_15);
	elseif (t_16 <= 3.5)
		tmp = ((2.0 + (0.5 * t_12)) - t_6) - (t_15 - t_11);
	else
		tmp = (4.0 + (0.5 * t_5)) - (t_14 + (t_6 + (t_15 + t_10)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]}, Block[{t$95$12 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$13 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$13], $MachinePrecision]}, Block[{t$95$15 = N[Sqrt[t$95$12], $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$15), $MachinePrecision]), $MachinePrecision] + t$95$11), $MachinePrecision] + N[(N[Sqrt[N[(t$95$13 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$16, 1.0], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision], If[LessEqual[t$95$16, 1.9998], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$12), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$15), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$16, 3.5], N[(N[(N[(2.0 + N[(0.5 * t$95$12), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision] - N[(t$95$15 - t$95$11), $MachinePrecision]), $MachinePrecision], N[(N[(4.0 + N[(0.5 * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$14 + N[(t$95$6 + N[(t$95$15 + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET t_11 = ((sqrt((t_9 + (1)))) - t_10) IN
												LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
												LET t_12 = tmp_20 IN
													LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
													LET t_13 = tmp_21 IN
														LET t_14 = (sqrt(t_13)) IN
															LET t_15 = (sqrt(t_12)) IN
																LET t_16 = (((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_12 + (1)))) - t_15)) + t_11) + ((sqrt((t_13 + (1)))) - t_14)) IN
																	LET tmp_24 = IF (t_16 <= (35e-1)) THEN ((((2) + ((5e-1) * t_12)) - t_6) - (t_15 - t_11)) ELSE (((4) + ((5e-1) * t_5)) - (t_14 + (t_6 + (t_15 + t_10)))) ENDIF IN
																	LET tmp_23 = IF (t_16 <= (1999800000000000022026824808563105762004852294921875e-51)) THEN (((1) + (sqrt(((1) + t_12)))) - (t_6 + t_15)) ELSE tmp_24 ENDIF IN
																	LET tmp_22 = IF (t_16 <= (1)) THEN (((sqrt(((1) + t_5))) + ((1) / ((1) + t_10))) - t_6) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in z around 0

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]
   11. Step-by-step derivation

   12. Applied rewrites 21.3%

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]

   if 1 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1.9998

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 1.9998 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 3.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 54.5%

      \[\leadsto \left(\left(\sqrt{t + 1} - \sqrt{t}\right) + \left(\sqrt{y + 1} - \left(\sqrt{x} - \sqrt{1 + x}\right)\right)\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 20.8%

      \[\leadsto \left(\left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 16.9%

      \[\leadsto \left(\left(1 + \sqrt{1 + y}\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   10. Taylor expanded in y around 0

       \[\leadsto \left(\left(2 + \frac{1}{2} \cdot y\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 16.5%

       \[\leadsto \left(\left(2 + 0.5 \cdot y\right) - \sqrt{x}\right) - \left(\sqrt{y} - \left(\sqrt{z + 1} - \sqrt{z}\right)\right) \]

   if 3.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 10.2%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.1%

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 8.0%

       \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto \left(4 + \frac{1}{2} \cdot x\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 8.2%

       \[\leadsto \left(4 + 0.5 \cdot x\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 20: 90.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_12 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_13 := \sqrt{t\_12}\\ t_14 := \sqrt{t\_11}\\ t_15 := \left(\left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_11 + 1} - t\_14\right)\right) + \left(\sqrt{t\_9 + 1} - t\_10\right)\right) + \left(\sqrt{t\_12 + 1} - t\_13\right)\\ t_16 := t\_6 + \left(t\_14 + t\_10\right)\\ \mathbf{if}\;t\_15 \leq 1:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \frac{1}{1 + t\_10}\right) - t\_6\\ \mathbf{elif}\;t\_15 \leq 2:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_11}\right) - \left(t\_6 + t\_14\right)\\ \mathbf{elif}\;t\_15 \leq 3.5:\\ \;\;\;\;\left(2 + \sqrt{1 + t\_9}\right) - t\_16\\ \mathbf{else}:\\ \;\;\;\;4 - \left(t\_13 + t\_16\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (sqrt t_9))
       (t_11 (fmin t_3 t_7))
       (t_12 (fmax t_2 t_8))
       (t_13 (sqrt t_12))
       (t_14 (sqrt t_11))
       (t_15
        (+
         (+
          (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_11 1.0)) t_14))
          (- (sqrt (+ t_9 1.0)) t_10))
         (- (sqrt (+ t_12 1.0)) t_13)))
       (t_16 (+ t_6 (+ t_14 t_10))))
  (if (<= t_15 1.0)
    (- (+ (sqrt (+ 1.0 t_5)) (/ 1.0 (+ 1.0 t_10))) t_6)
    (if (<= t_15 2.0)
      (- (+ 1.0 (sqrt (+ 1.0 t_11))) (+ t_6 t_14))
      (if (<= t_15 3.5)
        (- (+ 2.0 (sqrt (+ 1.0 t_9))) t_16)
        (- 4.0 (+ t_13 t_16)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = sqrt(t_12);
	double t_14 = sqrt(t_11);
	double t_15 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_14)) + (sqrt((t_9 + 1.0)) - t_10)) + (sqrt((t_12 + 1.0)) - t_13);
	double t_16 = t_6 + (t_14 + t_10);
	double tmp;
	if (t_15 <= 1.0) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_15 <= 2.0) {
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_14);
	} else if (t_15 <= 3.5) {
		tmp = (2.0 + sqrt((1.0 + t_9))) - t_16;
	} else {
		tmp = 4.0 - (t_13 + t_16);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = sqrt(t_9)
    t_11 = fmin(t_3, t_7)
    t_12 = fmax(t_2, t_8)
    t_13 = sqrt(t_12)
    t_14 = sqrt(t_11)
    t_15 = (((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_11 + 1.0d0)) - t_14)) + (sqrt((t_9 + 1.0d0)) - t_10)) + (sqrt((t_12 + 1.0d0)) - t_13)
    t_16 = t_6 + (t_14 + t_10)
    if (t_15 <= 1.0d0) then
        tmp = (sqrt((1.0d0 + t_5)) + (1.0d0 / (1.0d0 + t_10))) - t_6
    else if (t_15 <= 2.0d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_11))) - (t_6 + t_14)
    else if (t_15 <= 3.5d0) then
        tmp = (2.0d0 + sqrt((1.0d0 + t_9))) - t_16
    else
        tmp = 4.0d0 - (t_13 + t_16)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = Math.sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = Math.sqrt(t_12);
	double t_14 = Math.sqrt(t_11);
	double t_15 = (((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_11 + 1.0)) - t_14)) + (Math.sqrt((t_9 + 1.0)) - t_10)) + (Math.sqrt((t_12 + 1.0)) - t_13);
	double t_16 = t_6 + (t_14 + t_10);
	double tmp;
	if (t_15 <= 1.0) {
		tmp = (Math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_15 <= 2.0) {
		tmp = (1.0 + Math.sqrt((1.0 + t_11))) - (t_6 + t_14);
	} else if (t_15 <= 3.5) {
		tmp = (2.0 + Math.sqrt((1.0 + t_9))) - t_16;
	} else {
		tmp = 4.0 - (t_13 + t_16);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = math.sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = math.sqrt(t_12)
	t_14 = math.sqrt(t_11)
	t_15 = (((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_11 + 1.0)) - t_14)) + (math.sqrt((t_9 + 1.0)) - t_10)) + (math.sqrt((t_12 + 1.0)) - t_13)
	t_16 = t_6 + (t_14 + t_10)
	tmp = 0
	if t_15 <= 1.0:
		tmp = (math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6
	elif t_15 <= 2.0:
		tmp = (1.0 + math.sqrt((1.0 + t_11))) - (t_6 + t_14)
	elif t_15 <= 3.5:
		tmp = (2.0 + math.sqrt((1.0 + t_9))) - t_16
	else:
		tmp = 4.0 - (t_13 + t_16)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = sqrt(t_12)
	t_14 = sqrt(t_11)
	t_15 = Float64(Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_11 + 1.0)) - t_14)) + Float64(sqrt(Float64(t_9 + 1.0)) - t_10)) + Float64(sqrt(Float64(t_12 + 1.0)) - t_13))
	t_16 = Float64(t_6 + Float64(t_14 + t_10))
	tmp = 0.0
	if (t_15 <= 1.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 / Float64(1.0 + t_10))) - t_6);
	elseif (t_15 <= 2.0)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_11))) - Float64(t_6 + t_14));
	elseif (t_15 <= 3.5)
		tmp = Float64(Float64(2.0 + sqrt(Float64(1.0 + t_9))) - t_16);
	else
		tmp = Float64(4.0 - Float64(t_13 + t_16));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = sqrt(t_9);
	t_11 = min(t_3, t_7);
	t_12 = max(t_2, t_8);
	t_13 = sqrt(t_12);
	t_14 = sqrt(t_11);
	t_15 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_14)) + (sqrt((t_9 + 1.0)) - t_10)) + (sqrt((t_12 + 1.0)) - t_13);
	t_16 = t_6 + (t_14 + t_10);
	tmp = 0.0;
	if (t_15 <= 1.0)
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	elseif (t_15 <= 2.0)
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_14);
	elseif (t_15 <= 3.5)
		tmp = (2.0 + sqrt((1.0 + t_9))) - t_16;
	else
		tmp = 4.0 - (t_13 + t_16);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$12 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$12], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(t$95$6 + N[(t$95$14 + t$95$10), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$15, 1.0], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision], If[LessEqual[t$95$15, 2.0], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$11), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$14), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$15, 3.5], N[(N[(2.0 + N[Sqrt[N[(1.0 + t$95$9), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$16), $MachinePrecision], N[(4.0 - N[(t$95$13 + t$95$16), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
											LET t_11 = tmp_20 IN
												LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
												LET t_12 = tmp_21 IN
													LET t_13 = (sqrt(t_12)) IN
														LET t_14 = (sqrt(t_11)) IN
															LET t_15 = (((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_11 + (1)))) - t_14)) + ((sqrt((t_9 + (1)))) - t_10)) + ((sqrt((t_12 + (1)))) - t_13)) IN
																LET t_16 = (t_6 + (t_14 + t_10)) IN
																	LET tmp_24 = IF (t_15 <= (35e-1)) THEN (((2) + (sqrt(((1) + t_9)))) - t_16) ELSE ((4) - (t_13 + t_16)) ENDIF IN
																	LET tmp_23 = IF (t_15 <= (2)) THEN (((1) + (sqrt(((1) + t_11)))) - (t_6 + t_14)) ELSE tmp_24 ENDIF IN
																	LET tmp_22 = IF (t_15 <= (1)) THEN (((sqrt(((1) + t_5))) + ((1) / ((1) + t_10))) - t_6) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in z around 0

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]
   11. Step-by-step derivation

   12. Applied rewrites 21.3%

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]

   if 1 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 2

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 3.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   if 3.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 10.2%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.1%

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 8.0%

       \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 7.0%

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 21: 90.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_12 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_13 := \sqrt{t\_12}\\ t_14 := \sqrt{t\_11}\\ t_15 := \left(\left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_11 + 1} - t\_14\right)\right) + \left(\sqrt{t\_9 + 1} - t\_10\right)\right) + \left(\sqrt{t\_12 + 1} - t\_13\right)\\ t_16 := t\_6 + \left(t\_14 + t\_10\right)\\ \mathbf{if}\;t\_15 \leq 1:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \frac{1}{1 + t\_10}\right) - t\_6\\ \mathbf{elif}\;t\_15 \leq 2:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_11}\right) - \left(t\_6 + t\_14\right)\\ \mathbf{elif}\;t\_15 \leq 3.5:\\ \;\;\;\;\left(2 + \sqrt{1 + t\_9}\right) - t\_16\\ \mathbf{else}:\\ \;\;\;\;\left(4 + 0.5 \cdot t\_5\right) - \left(t\_13 + t\_16\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (sqrt t_9))
       (t_11 (fmin t_3 t_7))
       (t_12 (fmax t_2 t_8))
       (t_13 (sqrt t_12))
       (t_14 (sqrt t_11))
       (t_15
        (+
         (+
          (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_11 1.0)) t_14))
          (- (sqrt (+ t_9 1.0)) t_10))
         (- (sqrt (+ t_12 1.0)) t_13)))
       (t_16 (+ t_6 (+ t_14 t_10))))
  (if (<= t_15 1.0)
    (- (+ (sqrt (+ 1.0 t_5)) (/ 1.0 (+ 1.0 t_10))) t_6)
    (if (<= t_15 2.0)
      (- (+ 1.0 (sqrt (+ 1.0 t_11))) (+ t_6 t_14))
      (if (<= t_15 3.5)
        (- (+ 2.0 (sqrt (+ 1.0 t_9))) t_16)
        (- (+ 4.0 (* 0.5 t_5)) (+ t_13 t_16)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = sqrt(t_12);
	double t_14 = sqrt(t_11);
	double t_15 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_14)) + (sqrt((t_9 + 1.0)) - t_10)) + (sqrt((t_12 + 1.0)) - t_13);
	double t_16 = t_6 + (t_14 + t_10);
	double tmp;
	if (t_15 <= 1.0) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_15 <= 2.0) {
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_14);
	} else if (t_15 <= 3.5) {
		tmp = (2.0 + sqrt((1.0 + t_9))) - t_16;
	} else {
		tmp = (4.0 + (0.5 * t_5)) - (t_13 + t_16);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = sqrt(t_9)
    t_11 = fmin(t_3, t_7)
    t_12 = fmax(t_2, t_8)
    t_13 = sqrt(t_12)
    t_14 = sqrt(t_11)
    t_15 = (((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_11 + 1.0d0)) - t_14)) + (sqrt((t_9 + 1.0d0)) - t_10)) + (sqrt((t_12 + 1.0d0)) - t_13)
    t_16 = t_6 + (t_14 + t_10)
    if (t_15 <= 1.0d0) then
        tmp = (sqrt((1.0d0 + t_5)) + (1.0d0 / (1.0d0 + t_10))) - t_6
    else if (t_15 <= 2.0d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_11))) - (t_6 + t_14)
    else if (t_15 <= 3.5d0) then
        tmp = (2.0d0 + sqrt((1.0d0 + t_9))) - t_16
    else
        tmp = (4.0d0 + (0.5d0 * t_5)) - (t_13 + t_16)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = Math.sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = Math.sqrt(t_12);
	double t_14 = Math.sqrt(t_11);
	double t_15 = (((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_11 + 1.0)) - t_14)) + (Math.sqrt((t_9 + 1.0)) - t_10)) + (Math.sqrt((t_12 + 1.0)) - t_13);
	double t_16 = t_6 + (t_14 + t_10);
	double tmp;
	if (t_15 <= 1.0) {
		tmp = (Math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_15 <= 2.0) {
		tmp = (1.0 + Math.sqrt((1.0 + t_11))) - (t_6 + t_14);
	} else if (t_15 <= 3.5) {
		tmp = (2.0 + Math.sqrt((1.0 + t_9))) - t_16;
	} else {
		tmp = (4.0 + (0.5 * t_5)) - (t_13 + t_16);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = math.sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = math.sqrt(t_12)
	t_14 = math.sqrt(t_11)
	t_15 = (((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_11 + 1.0)) - t_14)) + (math.sqrt((t_9 + 1.0)) - t_10)) + (math.sqrt((t_12 + 1.0)) - t_13)
	t_16 = t_6 + (t_14 + t_10)
	tmp = 0
	if t_15 <= 1.0:
		tmp = (math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6
	elif t_15 <= 2.0:
		tmp = (1.0 + math.sqrt((1.0 + t_11))) - (t_6 + t_14)
	elif t_15 <= 3.5:
		tmp = (2.0 + math.sqrt((1.0 + t_9))) - t_16
	else:
		tmp = (4.0 + (0.5 * t_5)) - (t_13 + t_16)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = sqrt(t_12)
	t_14 = sqrt(t_11)
	t_15 = Float64(Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_11 + 1.0)) - t_14)) + Float64(sqrt(Float64(t_9 + 1.0)) - t_10)) + Float64(sqrt(Float64(t_12 + 1.0)) - t_13))
	t_16 = Float64(t_6 + Float64(t_14 + t_10))
	tmp = 0.0
	if (t_15 <= 1.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 / Float64(1.0 + t_10))) - t_6);
	elseif (t_15 <= 2.0)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_11))) - Float64(t_6 + t_14));
	elseif (t_15 <= 3.5)
		tmp = Float64(Float64(2.0 + sqrt(Float64(1.0 + t_9))) - t_16);
	else
		tmp = Float64(Float64(4.0 + Float64(0.5 * t_5)) - Float64(t_13 + t_16));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = sqrt(t_9);
	t_11 = min(t_3, t_7);
	t_12 = max(t_2, t_8);
	t_13 = sqrt(t_12);
	t_14 = sqrt(t_11);
	t_15 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_14)) + (sqrt((t_9 + 1.0)) - t_10)) + (sqrt((t_12 + 1.0)) - t_13);
	t_16 = t_6 + (t_14 + t_10);
	tmp = 0.0;
	if (t_15 <= 1.0)
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	elseif (t_15 <= 2.0)
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_14);
	elseif (t_15 <= 3.5)
		tmp = (2.0 + sqrt((1.0 + t_9))) - t_16;
	else
		tmp = (4.0 + (0.5 * t_5)) - (t_13 + t_16);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$12 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$12], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(t$95$6 + N[(t$95$14 + t$95$10), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$15, 1.0], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision], If[LessEqual[t$95$15, 2.0], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$11), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$14), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$15, 3.5], N[(N[(2.0 + N[Sqrt[N[(1.0 + t$95$9), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$16), $MachinePrecision], N[(N[(4.0 + N[(0.5 * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$13 + t$95$16), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
											LET t_11 = tmp_20 IN
												LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
												LET t_12 = tmp_21 IN
													LET t_13 = (sqrt(t_12)) IN
														LET t_14 = (sqrt(t_11)) IN
															LET t_15 = (((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_11 + (1)))) - t_14)) + ((sqrt((t_9 + (1)))) - t_10)) + ((sqrt((t_12 + (1)))) - t_13)) IN
																LET t_16 = (t_6 + (t_14 + t_10)) IN
																	LET tmp_24 = IF (t_15 <= (35e-1)) THEN (((2) + (sqrt(((1) + t_9)))) - t_16) ELSE (((4) + ((5e-1) * t_5)) - (t_13 + t_16)) ENDIF IN
																	LET tmp_23 = IF (t_15 <= (2)) THEN (((1) + (sqrt(((1) + t_11)))) - (t_6 + t_14)) ELSE tmp_24 ENDIF IN
																	LET tmp_22 = IF (t_15 <= (1)) THEN (((sqrt(((1) + t_5))) + ((1) / ((1) + t_10))) - t_6) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in z around 0

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]
   11. Step-by-step derivation

   12. Applied rewrites 21.3%

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]

   if 1 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 2

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 3.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   if 3.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 10.2%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.1%

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 8.0%

       \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto \left(4 + \frac{1}{2} \cdot x\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 8.2%

       \[\leadsto \left(4 + 0.5 \cdot x\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 22: 88.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_12 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_13 := \sqrt{t\_12}\\ t_14 := \sqrt{t\_11}\\ t_15 := t\_6 + \left(t\_14 + t\_10\right)\\ t_16 := \left(\left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_11 + 1} - t\_14\right)\right) + \left(\sqrt{t\_9 + 1} - t\_10\right)\right) + \left(\sqrt{t\_12 + 1} - t\_13\right)\\ \mathbf{if}\;t\_16 \leq 1:\\ \;\;\;\;\left(\sqrt{1 + t\_5} + \frac{1}{1 + t\_10}\right) - t\_6\\ \mathbf{elif}\;t\_16 \leq 2.5:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_11}\right) - \left(t\_6 + t\_14\right)\\ \mathbf{elif}\;t\_16 \leq 3.5:\\ \;\;\;\;\left(3 + 0.5 \cdot t\_9\right) - t\_15\\ \mathbf{else}:\\ \;\;\;\;4 - \left(t\_13 + t\_15\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (sqrt t_9))
       (t_11 (fmin t_3 t_7))
       (t_12 (fmax t_2 t_8))
       (t_13 (sqrt t_12))
       (t_14 (sqrt t_11))
       (t_15 (+ t_6 (+ t_14 t_10)))
       (t_16
        (+
         (+
          (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_11 1.0)) t_14))
          (- (sqrt (+ t_9 1.0)) t_10))
         (- (sqrt (+ t_12 1.0)) t_13))))
  (if (<= t_16 1.0)
    (- (+ (sqrt (+ 1.0 t_5)) (/ 1.0 (+ 1.0 t_10))) t_6)
    (if (<= t_16 2.5)
      (- (+ 1.0 (sqrt (+ 1.0 t_11))) (+ t_6 t_14))
      (if (<= t_16 3.5)
        (- (+ 3.0 (* 0.5 t_9)) t_15)
        (- 4.0 (+ t_13 t_15)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = sqrt(t_12);
	double t_14 = sqrt(t_11);
	double t_15 = t_6 + (t_14 + t_10);
	double t_16 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_14)) + (sqrt((t_9 + 1.0)) - t_10)) + (sqrt((t_12 + 1.0)) - t_13);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_16 <= 2.5) {
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_14);
	} else if (t_16 <= 3.5) {
		tmp = (3.0 + (0.5 * t_9)) - t_15;
	} else {
		tmp = 4.0 - (t_13 + t_15);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = sqrt(t_9)
    t_11 = fmin(t_3, t_7)
    t_12 = fmax(t_2, t_8)
    t_13 = sqrt(t_12)
    t_14 = sqrt(t_11)
    t_15 = t_6 + (t_14 + t_10)
    t_16 = (((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_11 + 1.0d0)) - t_14)) + (sqrt((t_9 + 1.0d0)) - t_10)) + (sqrt((t_12 + 1.0d0)) - t_13)
    if (t_16 <= 1.0d0) then
        tmp = (sqrt((1.0d0 + t_5)) + (1.0d0 / (1.0d0 + t_10))) - t_6
    else if (t_16 <= 2.5d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_11))) - (t_6 + t_14)
    else if (t_16 <= 3.5d0) then
        tmp = (3.0d0 + (0.5d0 * t_9)) - t_15
    else
        tmp = 4.0d0 - (t_13 + t_15)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = Math.sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = Math.sqrt(t_12);
	double t_14 = Math.sqrt(t_11);
	double t_15 = t_6 + (t_14 + t_10);
	double t_16 = (((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_11 + 1.0)) - t_14)) + (Math.sqrt((t_9 + 1.0)) - t_10)) + (Math.sqrt((t_12 + 1.0)) - t_13);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = (Math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	} else if (t_16 <= 2.5) {
		tmp = (1.0 + Math.sqrt((1.0 + t_11))) - (t_6 + t_14);
	} else if (t_16 <= 3.5) {
		tmp = (3.0 + (0.5 * t_9)) - t_15;
	} else {
		tmp = 4.0 - (t_13 + t_15);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = math.sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = math.sqrt(t_12)
	t_14 = math.sqrt(t_11)
	t_15 = t_6 + (t_14 + t_10)
	t_16 = (((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_11 + 1.0)) - t_14)) + (math.sqrt((t_9 + 1.0)) - t_10)) + (math.sqrt((t_12 + 1.0)) - t_13)
	tmp = 0
	if t_16 <= 1.0:
		tmp = (math.sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6
	elif t_16 <= 2.5:
		tmp = (1.0 + math.sqrt((1.0 + t_11))) - (t_6 + t_14)
	elif t_16 <= 3.5:
		tmp = (3.0 + (0.5 * t_9)) - t_15
	else:
		tmp = 4.0 - (t_13 + t_15)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = sqrt(t_12)
	t_14 = sqrt(t_11)
	t_15 = Float64(t_6 + Float64(t_14 + t_10))
	t_16 = Float64(Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_11 + 1.0)) - t_14)) + Float64(sqrt(Float64(t_9 + 1.0)) - t_10)) + Float64(sqrt(Float64(t_12 + 1.0)) - t_13))
	tmp = 0.0
	if (t_16 <= 1.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t_5)) + Float64(1.0 / Float64(1.0 + t_10))) - t_6);
	elseif (t_16 <= 2.5)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_11))) - Float64(t_6 + t_14));
	elseif (t_16 <= 3.5)
		tmp = Float64(Float64(3.0 + Float64(0.5 * t_9)) - t_15);
	else
		tmp = Float64(4.0 - Float64(t_13 + t_15));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = sqrt(t_9);
	t_11 = min(t_3, t_7);
	t_12 = max(t_2, t_8);
	t_13 = sqrt(t_12);
	t_14 = sqrt(t_11);
	t_15 = t_6 + (t_14 + t_10);
	t_16 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_14)) + (sqrt((t_9 + 1.0)) - t_10)) + (sqrt((t_12 + 1.0)) - t_13);
	tmp = 0.0;
	if (t_16 <= 1.0)
		tmp = (sqrt((1.0 + t_5)) + (1.0 / (1.0 + t_10))) - t_6;
	elseif (t_16 <= 2.5)
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_14);
	elseif (t_16 <= 3.5)
		tmp = (3.0 + (0.5 * t_9)) - t_15;
	else
		tmp = 4.0 - (t_13 + t_15);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$12 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$12], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$15 = N[(t$95$6 + N[(t$95$14 + t$95$10), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$16, 1.0], N[(N[(N[Sqrt[N[(1.0 + t$95$5), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$6), $MachinePrecision], If[LessEqual[t$95$16, 2.5], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$11), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$14), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$16, 3.5], N[(N[(3.0 + N[(0.5 * t$95$9), $MachinePrecision]), $MachinePrecision] - t$95$15), $MachinePrecision], N[(4.0 - N[(t$95$13 + t$95$15), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
											LET t_11 = tmp_20 IN
												LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
												LET t_12 = tmp_21 IN
													LET t_13 = (sqrt(t_12)) IN
														LET t_14 = (sqrt(t_11)) IN
															LET t_15 = (t_6 + (t_14 + t_10)) IN
																LET t_16 = (((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_11 + (1)))) - t_14)) + ((sqrt((t_9 + (1)))) - t_10)) + ((sqrt((t_12 + (1)))) - t_13)) IN
																	LET tmp_24 = IF (t_16 <= (35e-1)) THEN (((3) + ((5e-1) * t_9)) - t_15) ELSE ((4) - (t_13 + t_15)) ENDIF IN
																	LET tmp_23 = IF (t_16 <= (25e-1)) THEN (((1) + (sqrt(((1) + t_11)))) - (t_6 + t_14)) ELSE tmp_24 ENDIF IN
																	LET tmp_22 = IF (t_16 <= (1)) THEN (((sqrt(((1) + t_5))) + ((1) / ((1) + t_10))) - t_6) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in z around 0

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]
   11. Step-by-step derivation

   12. Applied rewrites 21.3%

       \[\leadsto \left(\sqrt{1 + x} + \frac{1}{1 + \sqrt{z}}\right) - \sqrt{x} \]

   if 1 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 2.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 3.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   11. Taylor expanded in z around 0

       \[\leadsto \left(3 + \frac{1}{2} \cdot z\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 9.6%

       \[\leadsto \left(3 + 0.5 \cdot z\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   if 3.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 10.2%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.1%

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 8.0%

       \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 7.0%

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 23: 81.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_12 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_13 := \sqrt{t\_12 + 1}\\ t_14 := \sqrt{t\_12}\\ t_15 := \sqrt{t\_11}\\ t_16 := \left(\left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_11 + 1} - t\_15\right)\right) + \left(\sqrt{t\_9 + 1} - t\_10\right)\right) + \left(t\_13 - t\_14\right)\\ t_17 := t\_6 + \left(t\_15 + t\_10\right)\\ \mathbf{if}\;t\_16 \leq 1:\\ \;\;\;\;1 + \left(t\_13 - \left(t\_14 + t\_10\right)\right)\\ \mathbf{elif}\;t\_16 \leq 2.5:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_11}\right) - \left(t\_6 + t\_15\right)\\ \mathbf{elif}\;t\_16 \leq 3.5:\\ \;\;\;\;\left(3 + 0.5 \cdot t\_9\right) - t\_17\\ \mathbf{else}:\\ \;\;\;\;4 - \left(t\_14 + t\_17\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (sqrt t_9))
       (t_11 (fmin t_3 t_7))
       (t_12 (fmax t_2 t_8))
       (t_13 (sqrt (+ t_12 1.0)))
       (t_14 (sqrt t_12))
       (t_15 (sqrt t_11))
       (t_16
        (+
         (+
          (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_11 1.0)) t_15))
          (- (sqrt (+ t_9 1.0)) t_10))
         (- t_13 t_14)))
       (t_17 (+ t_6 (+ t_15 t_10))))
  (if (<= t_16 1.0)
    (+ 1.0 (- t_13 (+ t_14 t_10)))
    (if (<= t_16 2.5)
      (- (+ 1.0 (sqrt (+ 1.0 t_11))) (+ t_6 t_15))
      (if (<= t_16 3.5)
        (- (+ 3.0 (* 0.5 t_9)) t_17)
        (- 4.0 (+ t_14 t_17)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = sqrt((t_12 + 1.0));
	double t_14 = sqrt(t_12);
	double t_15 = sqrt(t_11);
	double t_16 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_15)) + (sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14);
	double t_17 = t_6 + (t_15 + t_10);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = 1.0 + (t_13 - (t_14 + t_10));
	} else if (t_16 <= 2.5) {
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_15);
	} else if (t_16 <= 3.5) {
		tmp = (3.0 + (0.5 * t_9)) - t_17;
	} else {
		tmp = 4.0 - (t_14 + t_17);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = sqrt(t_9)
    t_11 = fmin(t_3, t_7)
    t_12 = fmax(t_2, t_8)
    t_13 = sqrt((t_12 + 1.0d0))
    t_14 = sqrt(t_12)
    t_15 = sqrt(t_11)
    t_16 = (((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_11 + 1.0d0)) - t_15)) + (sqrt((t_9 + 1.0d0)) - t_10)) + (t_13 - t_14)
    t_17 = t_6 + (t_15 + t_10)
    if (t_16 <= 1.0d0) then
        tmp = 1.0d0 + (t_13 - (t_14 + t_10))
    else if (t_16 <= 2.5d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_11))) - (t_6 + t_15)
    else if (t_16 <= 3.5d0) then
        tmp = (3.0d0 + (0.5d0 * t_9)) - t_17
    else
        tmp = 4.0d0 - (t_14 + t_17)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = Math.sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = Math.sqrt((t_12 + 1.0));
	double t_14 = Math.sqrt(t_12);
	double t_15 = Math.sqrt(t_11);
	double t_16 = (((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_11 + 1.0)) - t_15)) + (Math.sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14);
	double t_17 = t_6 + (t_15 + t_10);
	double tmp;
	if (t_16 <= 1.0) {
		tmp = 1.0 + (t_13 - (t_14 + t_10));
	} else if (t_16 <= 2.5) {
		tmp = (1.0 + Math.sqrt((1.0 + t_11))) - (t_6 + t_15);
	} else if (t_16 <= 3.5) {
		tmp = (3.0 + (0.5 * t_9)) - t_17;
	} else {
		tmp = 4.0 - (t_14 + t_17);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = math.sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = math.sqrt((t_12 + 1.0))
	t_14 = math.sqrt(t_12)
	t_15 = math.sqrt(t_11)
	t_16 = (((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_11 + 1.0)) - t_15)) + (math.sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14)
	t_17 = t_6 + (t_15 + t_10)
	tmp = 0
	if t_16 <= 1.0:
		tmp = 1.0 + (t_13 - (t_14 + t_10))
	elif t_16 <= 2.5:
		tmp = (1.0 + math.sqrt((1.0 + t_11))) - (t_6 + t_15)
	elif t_16 <= 3.5:
		tmp = (3.0 + (0.5 * t_9)) - t_17
	else:
		tmp = 4.0 - (t_14 + t_17)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = sqrt(Float64(t_12 + 1.0))
	t_14 = sqrt(t_12)
	t_15 = sqrt(t_11)
	t_16 = Float64(Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_11 + 1.0)) - t_15)) + Float64(sqrt(Float64(t_9 + 1.0)) - t_10)) + Float64(t_13 - t_14))
	t_17 = Float64(t_6 + Float64(t_15 + t_10))
	tmp = 0.0
	if (t_16 <= 1.0)
		tmp = Float64(1.0 + Float64(t_13 - Float64(t_14 + t_10)));
	elseif (t_16 <= 2.5)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_11))) - Float64(t_6 + t_15));
	elseif (t_16 <= 3.5)
		tmp = Float64(Float64(3.0 + Float64(0.5 * t_9)) - t_17);
	else
		tmp = Float64(4.0 - Float64(t_14 + t_17));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = sqrt(t_9);
	t_11 = min(t_3, t_7);
	t_12 = max(t_2, t_8);
	t_13 = sqrt((t_12 + 1.0));
	t_14 = sqrt(t_12);
	t_15 = sqrt(t_11);
	t_16 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_15)) + (sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14);
	t_17 = t_6 + (t_15 + t_10);
	tmp = 0.0;
	if (t_16 <= 1.0)
		tmp = 1.0 + (t_13 - (t_14 + t_10));
	elseif (t_16 <= 2.5)
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_15);
	elseif (t_16 <= 3.5)
		tmp = (3.0 + (0.5 * t_9)) - t_17;
	else
		tmp = 4.0 - (t_14 + t_17);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$12 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$12], $MachinePrecision]}, Block[{t$95$15 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$15), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]), $MachinePrecision] + N[(t$95$13 - t$95$14), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(t$95$6 + N[(t$95$15 + t$95$10), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$16, 1.0], N[(1.0 + N[(t$95$13 - N[(t$95$14 + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$16, 2.5], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$11), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$15), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$16, 3.5], N[(N[(3.0 + N[(0.5 * t$95$9), $MachinePrecision]), $MachinePrecision] - t$95$17), $MachinePrecision], N[(4.0 - N[(t$95$14 + t$95$17), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
											LET t_11 = tmp_20 IN
												LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
												LET t_12 = tmp_21 IN
													LET t_13 = (sqrt((t_12 + (1)))) IN
														LET t_14 = (sqrt(t_12)) IN
															LET t_15 = (sqrt(t_11)) IN
																LET t_16 = (((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_11 + (1)))) - t_15)) + ((sqrt((t_9 + (1)))) - t_10)) + (t_13 - t_14)) IN
																	LET t_17 = (t_6 + (t_15 + t_10)) IN
																		LET tmp_24 = IF (t_16 <= (35e-1)) THEN (((3) + ((5e-1) * t_9)) - t_17) ELSE ((4) - (t_14 + t_17)) ENDIF IN
																		LET tmp_23 = IF (t_16 <= (25e-1)) THEN (((1) + (sqrt(((1) + t_11)))) - (t_6 + t_15)) ELSE tmp_24 ENDIF IN
																		LET tmp_22 = IF (t_16 <= (1)) THEN ((1) + (t_13 - (t_14 + t_10))) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.1%

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 13.4%

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 11.7%

       \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.1%

       \[\leadsto 1 + \left(\sqrt{t + 1} - \left(\sqrt{t} + \sqrt{z}\right)\right) \]

   if 1 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 2.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 3.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + z}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   11. Taylor expanded in z around 0

       \[\leadsto \left(3 + \frac{1}{2} \cdot z\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 9.6%

       \[\leadsto \left(3 + 0.5 \cdot z\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   if 3.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 10.2%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.1%

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 8.0%

       \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 7.0%

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 24: 80.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \sqrt{t\_9}\\ t_11 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_12 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_13 := \sqrt{t\_12 + 1}\\ t_14 := \sqrt{t\_12}\\ t_15 := \sqrt{t\_11}\\ t_16 := t\_6 + \left(t\_15 + t\_10\right)\\ t_17 := \left(\left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_11 + 1} - t\_15\right)\right) + \left(\sqrt{t\_9 + 1} - t\_10\right)\right) + \left(t\_13 - t\_14\right)\\ \mathbf{if}\;t\_17 \leq 1:\\ \;\;\;\;1 + \left(t\_13 - \left(t\_14 + t\_10\right)\right)\\ \mathbf{elif}\;t\_17 \leq 2.5:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_11}\right) - \left(t\_6 + t\_15\right)\\ \mathbf{elif}\;t\_17 \leq 3.5:\\ \;\;\;\;3 - t\_16\\ \mathbf{else}:\\ \;\;\;\;4 - \left(t\_14 + t\_16\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (sqrt t_9))
       (t_11 (fmin t_3 t_7))
       (t_12 (fmax t_2 t_8))
       (t_13 (sqrt (+ t_12 1.0)))
       (t_14 (sqrt t_12))
       (t_15 (sqrt t_11))
       (t_16 (+ t_6 (+ t_15 t_10)))
       (t_17
        (+
         (+
          (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_11 1.0)) t_15))
          (- (sqrt (+ t_9 1.0)) t_10))
         (- t_13 t_14))))
  (if (<= t_17 1.0)
    (+ 1.0 (- t_13 (+ t_14 t_10)))
    (if (<= t_17 2.5)
      (- (+ 1.0 (sqrt (+ 1.0 t_11))) (+ t_6 t_15))
      (if (<= t_17 3.5) (- 3.0 t_16) (- 4.0 (+ t_14 t_16)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = sqrt((t_12 + 1.0));
	double t_14 = sqrt(t_12);
	double t_15 = sqrt(t_11);
	double t_16 = t_6 + (t_15 + t_10);
	double t_17 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_15)) + (sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14);
	double tmp;
	if (t_17 <= 1.0) {
		tmp = 1.0 + (t_13 - (t_14 + t_10));
	} else if (t_17 <= 2.5) {
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_15);
	} else if (t_17 <= 3.5) {
		tmp = 3.0 - t_16;
	} else {
		tmp = 4.0 - (t_14 + t_16);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = sqrt(t_9)
    t_11 = fmin(t_3, t_7)
    t_12 = fmax(t_2, t_8)
    t_13 = sqrt((t_12 + 1.0d0))
    t_14 = sqrt(t_12)
    t_15 = sqrt(t_11)
    t_16 = t_6 + (t_15 + t_10)
    t_17 = (((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_11 + 1.0d0)) - t_15)) + (sqrt((t_9 + 1.0d0)) - t_10)) + (t_13 - t_14)
    if (t_17 <= 1.0d0) then
        tmp = 1.0d0 + (t_13 - (t_14 + t_10))
    else if (t_17 <= 2.5d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_11))) - (t_6 + t_15)
    else if (t_17 <= 3.5d0) then
        tmp = 3.0d0 - t_16
    else
        tmp = 4.0d0 - (t_14 + t_16)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = Math.sqrt(t_9);
	double t_11 = fmin(t_3, t_7);
	double t_12 = fmax(t_2, t_8);
	double t_13 = Math.sqrt((t_12 + 1.0));
	double t_14 = Math.sqrt(t_12);
	double t_15 = Math.sqrt(t_11);
	double t_16 = t_6 + (t_15 + t_10);
	double t_17 = (((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_11 + 1.0)) - t_15)) + (Math.sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14);
	double tmp;
	if (t_17 <= 1.0) {
		tmp = 1.0 + (t_13 - (t_14 + t_10));
	} else if (t_17 <= 2.5) {
		tmp = (1.0 + Math.sqrt((1.0 + t_11))) - (t_6 + t_15);
	} else if (t_17 <= 3.5) {
		tmp = 3.0 - t_16;
	} else {
		tmp = 4.0 - (t_14 + t_16);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = math.sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = math.sqrt((t_12 + 1.0))
	t_14 = math.sqrt(t_12)
	t_15 = math.sqrt(t_11)
	t_16 = t_6 + (t_15 + t_10)
	t_17 = (((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_11 + 1.0)) - t_15)) + (math.sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14)
	tmp = 0
	if t_17 <= 1.0:
		tmp = 1.0 + (t_13 - (t_14 + t_10))
	elif t_17 <= 2.5:
		tmp = (1.0 + math.sqrt((1.0 + t_11))) - (t_6 + t_15)
	elif t_17 <= 3.5:
		tmp = 3.0 - t_16
	else:
		tmp = 4.0 - (t_14 + t_16)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = sqrt(t_9)
	t_11 = fmin(t_3, t_7)
	t_12 = fmax(t_2, t_8)
	t_13 = sqrt(Float64(t_12 + 1.0))
	t_14 = sqrt(t_12)
	t_15 = sqrt(t_11)
	t_16 = Float64(t_6 + Float64(t_15 + t_10))
	t_17 = Float64(Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_11 + 1.0)) - t_15)) + Float64(sqrt(Float64(t_9 + 1.0)) - t_10)) + Float64(t_13 - t_14))
	tmp = 0.0
	if (t_17 <= 1.0)
		tmp = Float64(1.0 + Float64(t_13 - Float64(t_14 + t_10)));
	elseif (t_17 <= 2.5)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_11))) - Float64(t_6 + t_15));
	elseif (t_17 <= 3.5)
		tmp = Float64(3.0 - t_16);
	else
		tmp = Float64(4.0 - Float64(t_14 + t_16));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = sqrt(t_9);
	t_11 = min(t_3, t_7);
	t_12 = max(t_2, t_8);
	t_13 = sqrt((t_12 + 1.0));
	t_14 = sqrt(t_12);
	t_15 = sqrt(t_11);
	t_16 = t_6 + (t_15 + t_10);
	t_17 = (((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_11 + 1.0)) - t_15)) + (sqrt((t_9 + 1.0)) - t_10)) + (t_13 - t_14);
	tmp = 0.0;
	if (t_17 <= 1.0)
		tmp = 1.0 + (t_13 - (t_14 + t_10));
	elseif (t_17 <= 2.5)
		tmp = (1.0 + sqrt((1.0 + t_11))) - (t_6 + t_15);
	elseif (t_17 <= 3.5)
		tmp = 3.0 - t_16;
	else
		tmp = 4.0 - (t_14 + t_16);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$11 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$12 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$14 = N[Sqrt[t$95$12], $MachinePrecision]}, Block[{t$95$15 = N[Sqrt[t$95$11], $MachinePrecision]}, Block[{t$95$16 = N[(t$95$6 + N[(t$95$15 + t$95$10), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$11 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$15), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$10), $MachinePrecision]), $MachinePrecision] + N[(t$95$13 - t$95$14), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$17, 1.0], N[(1.0 + N[(t$95$13 - N[(t$95$14 + t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$17, 2.5], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$11), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$15), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$17, 3.5], N[(3.0 - t$95$16), $MachinePrecision], N[(4.0 - N[(t$95$14 + t$95$16), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET t_10 = (sqrt(t_9)) IN
											LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
											LET t_11 = tmp_20 IN
												LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
												LET t_12 = tmp_21 IN
													LET t_13 = (sqrt((t_12 + (1)))) IN
														LET t_14 = (sqrt(t_12)) IN
															LET t_15 = (sqrt(t_11)) IN
																LET t_16 = (t_6 + (t_15 + t_10)) IN
																	LET t_17 = (((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_11 + (1)))) - t_15)) + ((sqrt((t_9 + (1)))) - t_10)) + (t_13 - t_14)) IN
																		LET tmp_24 = IF (t_17 <= (35e-1)) THEN ((3) - t_16) ELSE ((4) - (t_14 + t_16)) ENDIF IN
																		LET tmp_23 = IF (t_17 <= (25e-1)) THEN (((1) + (sqrt(((1) + t_11)))) - (t_6 + t_15)) ELSE tmp_24 ENDIF IN
																		LET tmp_22 = IF (t_17 <= (1)) THEN ((1) + (t_13 - (t_14 + t_10))) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.1%

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 13.4%

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 11.7%

       \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.1%

       \[\leadsto 1 + \left(\sqrt{t + 1} - \left(\sqrt{t} + \sqrt{z}\right)\right) \]

   if 1 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 2.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t))) < 3.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 8.2%

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   if 3.5 < (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t #s(literal 1 binary64))) (sqrt.f64 t)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 10.2%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   5. Taylor expanded in z around 0

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.1%

      \[\leadsto \left(2 + \left(\sqrt{1 + x} + \sqrt{1 + y}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 8.0%

       \[\leadsto \left(3 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 7.0%

       \[\leadsto 4 - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 25: 76.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(x, y\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_5 := \mathsf{min}\left(t\_4, t\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left(t\_4, t\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_7\right)\\ t_9 := \mathsf{min}\left(t\_2, t\_8\right)\\ t_10 := \mathsf{min}\left(t\_3, t\_7\right)\\ t_11 := \sqrt{t\_9}\\ t_12 := \mathsf{max}\left(t\_2, t\_8\right)\\ t_13 := \sqrt{t\_10}\\ t_14 := \left(\left(\sqrt{t\_5 + 1} - t\_6\right) + \left(\sqrt{t\_10 + 1} - t\_13\right)\right) + \left(\sqrt{t\_9 + 1} - t\_11\right)\\ \mathbf{if}\;t\_14 \leq 1:\\ \;\;\;\;1 + \left(\sqrt{t\_12 + 1} - \left(\sqrt{t\_12} + t\_11\right)\right)\\ \mathbf{elif}\;t\_14 \leq 2.5:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_10}\right) - \left(t\_6 + t\_13\right)\\ \mathbf{else}:\\ \;\;\;\;3 - \left(t\_6 + \left(t\_13 + t\_11\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x y) z))
       (t_2 (fmax (fmax x y) t_1))
       (t_3 (fmin (fmax x y) t_1))
       (t_4 (fmin (fmin x y) z))
       (t_5 (fmin t_4 t))
       (t_6 (sqrt t_5))
       (t_7 (fmax t_4 t))
       (t_8 (fmax t_3 t_7))
       (t_9 (fmin t_2 t_8))
       (t_10 (fmin t_3 t_7))
       (t_11 (sqrt t_9))
       (t_12 (fmax t_2 t_8))
       (t_13 (sqrt t_10))
       (t_14
        (+
         (+ (- (sqrt (+ t_5 1.0)) t_6) (- (sqrt (+ t_10 1.0)) t_13))
         (- (sqrt (+ t_9 1.0)) t_11))))
  (if (<= t_14 1.0)
    (+ 1.0 (- (sqrt (+ t_12 1.0)) (+ (sqrt t_12) t_11)))
    (if (<= t_14 2.5)
      (- (+ 1.0 (sqrt (+ 1.0 t_10))) (+ t_6 t_13))
      (- 3.0 (+ t_6 (+ t_13 t_11)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = sqrt(t_9);
	double t_12 = fmax(t_2, t_8);
	double t_13 = sqrt(t_10);
	double t_14 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_13)) + (sqrt((t_9 + 1.0)) - t_11);
	double tmp;
	if (t_14 <= 1.0) {
		tmp = 1.0 + (sqrt((t_12 + 1.0)) - (sqrt(t_12) + t_11));
	} else if (t_14 <= 2.5) {
		tmp = (1.0 + sqrt((1.0 + t_10))) - (t_6 + t_13);
	} else {
		tmp = 3.0 - (t_6 + (t_13 + t_11));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, y), z)
    t_2 = fmax(fmax(x, y), t_1)
    t_3 = fmin(fmax(x, y), t_1)
    t_4 = fmin(fmin(x, y), z)
    t_5 = fmin(t_4, t)
    t_6 = sqrt(t_5)
    t_7 = fmax(t_4, t)
    t_8 = fmax(t_3, t_7)
    t_9 = fmin(t_2, t_8)
    t_10 = fmin(t_3, t_7)
    t_11 = sqrt(t_9)
    t_12 = fmax(t_2, t_8)
    t_13 = sqrt(t_10)
    t_14 = ((sqrt((t_5 + 1.0d0)) - t_6) + (sqrt((t_10 + 1.0d0)) - t_13)) + (sqrt((t_9 + 1.0d0)) - t_11)
    if (t_14 <= 1.0d0) then
        tmp = 1.0d0 + (sqrt((t_12 + 1.0d0)) - (sqrt(t_12) + t_11))
    else if (t_14 <= 2.5d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_10))) - (t_6 + t_13)
    else
        tmp = 3.0d0 - (t_6 + (t_13 + t_11))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, y), z);
	double t_2 = fmax(fmax(x, y), t_1);
	double t_3 = fmin(fmax(x, y), t_1);
	double t_4 = fmin(fmin(x, y), z);
	double t_5 = fmin(t_4, t);
	double t_6 = Math.sqrt(t_5);
	double t_7 = fmax(t_4, t);
	double t_8 = fmax(t_3, t_7);
	double t_9 = fmin(t_2, t_8);
	double t_10 = fmin(t_3, t_7);
	double t_11 = Math.sqrt(t_9);
	double t_12 = fmax(t_2, t_8);
	double t_13 = Math.sqrt(t_10);
	double t_14 = ((Math.sqrt((t_5 + 1.0)) - t_6) + (Math.sqrt((t_10 + 1.0)) - t_13)) + (Math.sqrt((t_9 + 1.0)) - t_11);
	double tmp;
	if (t_14 <= 1.0) {
		tmp = 1.0 + (Math.sqrt((t_12 + 1.0)) - (Math.sqrt(t_12) + t_11));
	} else if (t_14 <= 2.5) {
		tmp = (1.0 + Math.sqrt((1.0 + t_10))) - (t_6 + t_13);
	} else {
		tmp = 3.0 - (t_6 + (t_13 + t_11));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = math.sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = math.sqrt(t_9)
	t_12 = fmax(t_2, t_8)
	t_13 = math.sqrt(t_10)
	t_14 = ((math.sqrt((t_5 + 1.0)) - t_6) + (math.sqrt((t_10 + 1.0)) - t_13)) + (math.sqrt((t_9 + 1.0)) - t_11)
	tmp = 0
	if t_14 <= 1.0:
		tmp = 1.0 + (math.sqrt((t_12 + 1.0)) - (math.sqrt(t_12) + t_11))
	elif t_14 <= 2.5:
		tmp = (1.0 + math.sqrt((1.0 + t_10))) - (t_6 + t_13)
	else:
		tmp = 3.0 - (t_6 + (t_13 + t_11))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, y), z)
	t_2 = fmax(fmax(x, y), t_1)
	t_3 = fmin(fmax(x, y), t_1)
	t_4 = fmin(fmin(x, y), z)
	t_5 = fmin(t_4, t)
	t_6 = sqrt(t_5)
	t_7 = fmax(t_4, t)
	t_8 = fmax(t_3, t_7)
	t_9 = fmin(t_2, t_8)
	t_10 = fmin(t_3, t_7)
	t_11 = sqrt(t_9)
	t_12 = fmax(t_2, t_8)
	t_13 = sqrt(t_10)
	t_14 = Float64(Float64(Float64(sqrt(Float64(t_5 + 1.0)) - t_6) + Float64(sqrt(Float64(t_10 + 1.0)) - t_13)) + Float64(sqrt(Float64(t_9 + 1.0)) - t_11))
	tmp = 0.0
	if (t_14 <= 1.0)
		tmp = Float64(1.0 + Float64(sqrt(Float64(t_12 + 1.0)) - Float64(sqrt(t_12) + t_11)));
	elseif (t_14 <= 2.5)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_10))) - Float64(t_6 + t_13));
	else
		tmp = Float64(3.0 - Float64(t_6 + Float64(t_13 + t_11)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, y), z);
	t_2 = max(max(x, y), t_1);
	t_3 = min(max(x, y), t_1);
	t_4 = min(min(x, y), z);
	t_5 = min(t_4, t);
	t_6 = sqrt(t_5);
	t_7 = max(t_4, t);
	t_8 = max(t_3, t_7);
	t_9 = min(t_2, t_8);
	t_10 = min(t_3, t_7);
	t_11 = sqrt(t_9);
	t_12 = max(t_2, t_8);
	t_13 = sqrt(t_10);
	t_14 = ((sqrt((t_5 + 1.0)) - t_6) + (sqrt((t_10 + 1.0)) - t_13)) + (sqrt((t_9 + 1.0)) - t_11);
	tmp = 0.0;
	if (t_14 <= 1.0)
		tmp = 1.0 + (sqrt((t_12 + 1.0)) - (sqrt(t_12) + t_11));
	elseif (t_14 <= 2.5)
		tmp = (1.0 + sqrt((1.0 + t_10))) - (t_6 + t_13);
	else
		tmp = 3.0 - (t_6 + (t_13 + t_11));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[x, y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$5 = N[Min[t$95$4, t], $MachinePrecision]}, Block[{t$95$6 = N[Sqrt[t$95$5], $MachinePrecision]}, Block[{t$95$7 = N[Max[t$95$4, t], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$9 = N[Min[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$3, t$95$7], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[t$95$9], $MachinePrecision]}, Block[{t$95$12 = N[Max[t$95$2, t$95$8], $MachinePrecision]}, Block[{t$95$13 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(N[Sqrt[N[(t$95$5 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$6), $MachinePrecision] + N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$9 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$11), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$14, 1.0], N[(1.0 + N[(N[Sqrt[N[(t$95$12 + 1.0), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[t$95$12], $MachinePrecision] + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$14, 2.5], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$10), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$6 + t$95$13), $MachinePrecision]), $MachinePrecision], N[(3.0 - N[(t$95$6 + N[(t$95$13 + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (tmp_2 > z) THEN tmp_3 ELSE z ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_5 = IF (tmp_6 > t_1) THEN tmp_7 ELSE t_1 ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_9 = IF (tmp_10 < t_1) THEN tmp_11 ELSE t_1 ENDIF IN
			LET t_3 = tmp_9 IN
				LET tmp_14 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_15 = IF (x < y) THEN x ELSE y ENDIF IN
				LET tmp_13 = IF (tmp_14 < z) THEN tmp_15 ELSE z ENDIF IN
				LET t_4 = tmp_13 IN
					LET tmp_16 = IF (t_4 < t) THEN t_4 ELSE t ENDIF IN
					LET t_5 = tmp_16 IN
						LET t_6 = (sqrt(t_5)) IN
							LET tmp_17 = IF (t_4 > t) THEN t_4 ELSE t ENDIF IN
							LET t_7 = tmp_17 IN
								LET tmp_18 = IF (t_3 > t_7) THEN t_3 ELSE t_7 ENDIF IN
								LET t_8 = tmp_18 IN
									LET tmp_19 = IF (t_2 < t_8) THEN t_2 ELSE t_8 ENDIF IN
									LET t_9 = tmp_19 IN
										LET tmp_20 = IF (t_3 < t_7) THEN t_3 ELSE t_7 ENDIF IN
										LET t_10 = tmp_20 IN
											LET t_11 = (sqrt(t_9)) IN
												LET tmp_21 = IF (t_2 > t_8) THEN t_2 ELSE t_8 ENDIF IN
												LET t_12 = tmp_21 IN
													LET t_13 = (sqrt(t_10)) IN
														LET t_14 = ((((sqrt((t_5 + (1)))) - t_6) + ((sqrt((t_10 + (1)))) - t_13)) + ((sqrt((t_9 + (1)))) - t_11)) IN
															LET tmp_23 = IF (t_14 <= (25e-1)) THEN (((1) + (sqrt(((1) + t_10)))) - (t_6 + t_13)) ELSE ((3) - (t_6 + (t_13 + t_11))) ENDIF IN
															LET tmp_22 = IF (t_14 <= (1)) THEN ((1) + ((sqrt((t_12 + (1)))) - ((sqrt(t_12)) + t_11))) ELSE tmp_23 ENDIF IN
	tmp_22
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.1%

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 13.4%

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 11.7%

       \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.1%

       \[\leadsto 1 + \left(\sqrt{t + 1} - \left(\sqrt{t} + \sqrt{z}\right)\right) \]

   if 1 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.6%

       \[\leadsto \left(1 + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.5 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 8.2%

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 26: 73.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(x, z\right), t\right)\\ t_2 := \mathsf{min}\left(\mathsf{min}\left(x, z\right), t\right)\\ t_3 := \mathsf{max}\left(y, \mathsf{max}\left(x, z\right)\right)\\ t_4 := \sqrt{t\_2}\\ t_5 := \mathsf{min}\left(y, \mathsf{max}\left(x, z\right)\right)\\ t_6 := \mathsf{max}\left(t\_5, t\_1\right)\\ t_7 := \mathsf{min}\left(t\_5, t\_1\right)\\ t_8 := \mathsf{max}\left(t\_3, t\_6\right)\\ t_9 := \sqrt{t\_7}\\ t_10 := \mathsf{min}\left(t\_3, t\_6\right)\\ t_11 := \sqrt{t\_10}\\ t_12 := \left(\left(\sqrt{t\_2 + 1} - t\_4\right) + \left(\sqrt{t\_7 + 1} - t\_9\right)\right) + \left(\sqrt{t\_10 + 1} - t\_11\right)\\ \mathbf{if}\;t\_12 \leq 1.5:\\ \;\;\;\;1 + \left(\sqrt{t\_8 + 1} - \left(\sqrt{t\_8} + t\_11\right)\right)\\ \mathbf{elif}\;t\_12 \leq 2.5:\\ \;\;\;\;\left(1 + \sqrt{1 + t\_2}\right) - \left(t\_4 + t\_9\right)\\ \mathbf{else}:\\ \;\;\;\;3 - \left(t\_4 + \left(t\_9 + t\_11\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmin x z) t))
       (t_2 (fmin (fmin x z) t))
       (t_3 (fmax y (fmax x z)))
       (t_4 (sqrt t_2))
       (t_5 (fmin y (fmax x z)))
       (t_6 (fmax t_5 t_1))
       (t_7 (fmin t_5 t_1))
       (t_8 (fmax t_3 t_6))
       (t_9 (sqrt t_7))
       (t_10 (fmin t_3 t_6))
       (t_11 (sqrt t_10))
       (t_12
        (+
         (+ (- (sqrt (+ t_2 1.0)) t_4) (- (sqrt (+ t_7 1.0)) t_9))
         (- (sqrt (+ t_10 1.0)) t_11))))
  (if (<= t_12 1.5)
    (+ 1.0 (- (sqrt (+ t_8 1.0)) (+ (sqrt t_8) t_11)))
    (if (<= t_12 2.5)
      (- (+ 1.0 (sqrt (+ 1.0 t_2))) (+ t_4 t_9))
      (- 3.0 (+ t_4 (+ t_9 t_11)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, z), t);
	double t_2 = fmin(fmin(x, z), t);
	double t_3 = fmax(y, fmax(x, z));
	double t_4 = sqrt(t_2);
	double t_5 = fmin(y, fmax(x, z));
	double t_6 = fmax(t_5, t_1);
	double t_7 = fmin(t_5, t_1);
	double t_8 = fmax(t_3, t_6);
	double t_9 = sqrt(t_7);
	double t_10 = fmin(t_3, t_6);
	double t_11 = sqrt(t_10);
	double t_12 = ((sqrt((t_2 + 1.0)) - t_4) + (sqrt((t_7 + 1.0)) - t_9)) + (sqrt((t_10 + 1.0)) - t_11);
	double tmp;
	if (t_12 <= 1.5) {
		tmp = 1.0 + (sqrt((t_8 + 1.0)) - (sqrt(t_8) + t_11));
	} else if (t_12 <= 2.5) {
		tmp = (1.0 + sqrt((1.0 + t_2))) - (t_4 + t_9);
	} else {
		tmp = 3.0 - (t_4 + (t_9 + t_11));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = fmax(fmin(x, z), t)
    t_2 = fmin(fmin(x, z), t)
    t_3 = fmax(y, fmax(x, z))
    t_4 = sqrt(t_2)
    t_5 = fmin(y, fmax(x, z))
    t_6 = fmax(t_5, t_1)
    t_7 = fmin(t_5, t_1)
    t_8 = fmax(t_3, t_6)
    t_9 = sqrt(t_7)
    t_10 = fmin(t_3, t_6)
    t_11 = sqrt(t_10)
    t_12 = ((sqrt((t_2 + 1.0d0)) - t_4) + (sqrt((t_7 + 1.0d0)) - t_9)) + (sqrt((t_10 + 1.0d0)) - t_11)
    if (t_12 <= 1.5d0) then
        tmp = 1.0d0 + (sqrt((t_8 + 1.0d0)) - (sqrt(t_8) + t_11))
    else if (t_12 <= 2.5d0) then
        tmp = (1.0d0 + sqrt((1.0d0 + t_2))) - (t_4 + t_9)
    else
        tmp = 3.0d0 - (t_4 + (t_9 + t_11))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmin(x, z), t);
	double t_2 = fmin(fmin(x, z), t);
	double t_3 = fmax(y, fmax(x, z));
	double t_4 = Math.sqrt(t_2);
	double t_5 = fmin(y, fmax(x, z));
	double t_6 = fmax(t_5, t_1);
	double t_7 = fmin(t_5, t_1);
	double t_8 = fmax(t_3, t_6);
	double t_9 = Math.sqrt(t_7);
	double t_10 = fmin(t_3, t_6);
	double t_11 = Math.sqrt(t_10);
	double t_12 = ((Math.sqrt((t_2 + 1.0)) - t_4) + (Math.sqrt((t_7 + 1.0)) - t_9)) + (Math.sqrt((t_10 + 1.0)) - t_11);
	double tmp;
	if (t_12 <= 1.5) {
		tmp = 1.0 + (Math.sqrt((t_8 + 1.0)) - (Math.sqrt(t_8) + t_11));
	} else if (t_12 <= 2.5) {
		tmp = (1.0 + Math.sqrt((1.0 + t_2))) - (t_4 + t_9);
	} else {
		tmp = 3.0 - (t_4 + (t_9 + t_11));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmin(x, z), t)
	t_2 = fmin(fmin(x, z), t)
	t_3 = fmax(y, fmax(x, z))
	t_4 = math.sqrt(t_2)
	t_5 = fmin(y, fmax(x, z))
	t_6 = fmax(t_5, t_1)
	t_7 = fmin(t_5, t_1)
	t_8 = fmax(t_3, t_6)
	t_9 = math.sqrt(t_7)
	t_10 = fmin(t_3, t_6)
	t_11 = math.sqrt(t_10)
	t_12 = ((math.sqrt((t_2 + 1.0)) - t_4) + (math.sqrt((t_7 + 1.0)) - t_9)) + (math.sqrt((t_10 + 1.0)) - t_11)
	tmp = 0
	if t_12 <= 1.5:
		tmp = 1.0 + (math.sqrt((t_8 + 1.0)) - (math.sqrt(t_8) + t_11))
	elif t_12 <= 2.5:
		tmp = (1.0 + math.sqrt((1.0 + t_2))) - (t_4 + t_9)
	else:
		tmp = 3.0 - (t_4 + (t_9 + t_11))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmin(x, z), t)
	t_2 = fmin(fmin(x, z), t)
	t_3 = fmax(y, fmax(x, z))
	t_4 = sqrt(t_2)
	t_5 = fmin(y, fmax(x, z))
	t_6 = fmax(t_5, t_1)
	t_7 = fmin(t_5, t_1)
	t_8 = fmax(t_3, t_6)
	t_9 = sqrt(t_7)
	t_10 = fmin(t_3, t_6)
	t_11 = sqrt(t_10)
	t_12 = Float64(Float64(Float64(sqrt(Float64(t_2 + 1.0)) - t_4) + Float64(sqrt(Float64(t_7 + 1.0)) - t_9)) + Float64(sqrt(Float64(t_10 + 1.0)) - t_11))
	tmp = 0.0
	if (t_12 <= 1.5)
		tmp = Float64(1.0 + Float64(sqrt(Float64(t_8 + 1.0)) - Float64(sqrt(t_8) + t_11)));
	elseif (t_12 <= 2.5)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + t_2))) - Float64(t_4 + t_9));
	else
		tmp = Float64(3.0 - Float64(t_4 + Float64(t_9 + t_11)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(min(x, z), t);
	t_2 = min(min(x, z), t);
	t_3 = max(y, max(x, z));
	t_4 = sqrt(t_2);
	t_5 = min(y, max(x, z));
	t_6 = max(t_5, t_1);
	t_7 = min(t_5, t_1);
	t_8 = max(t_3, t_6);
	t_9 = sqrt(t_7);
	t_10 = min(t_3, t_6);
	t_11 = sqrt(t_10);
	t_12 = ((sqrt((t_2 + 1.0)) - t_4) + (sqrt((t_7 + 1.0)) - t_9)) + (sqrt((t_10 + 1.0)) - t_11);
	tmp = 0.0;
	if (t_12 <= 1.5)
		tmp = 1.0 + (sqrt((t_8 + 1.0)) - (sqrt(t_8) + t_11));
	elseif (t_12 <= 2.5)
		tmp = (1.0 + sqrt((1.0 + t_2))) - (t_4 + t_9);
	else
		tmp = 3.0 - (t_4 + (t_9 + t_11));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Min[x, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Min[x, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$3 = N[Max[y, N[Max[x, z], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[t$95$2], $MachinePrecision]}, Block[{t$95$5 = N[Min[y, N[Max[x, z], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$6 = N[Max[t$95$5, t$95$1], $MachinePrecision]}, Block[{t$95$7 = N[Min[t$95$5, t$95$1], $MachinePrecision]}, Block[{t$95$8 = N[Max[t$95$3, t$95$6], $MachinePrecision]}, Block[{t$95$9 = N[Sqrt[t$95$7], $MachinePrecision]}, Block[{t$95$10 = N[Min[t$95$3, t$95$6], $MachinePrecision]}, Block[{t$95$11 = N[Sqrt[t$95$10], $MachinePrecision]}, Block[{t$95$12 = N[(N[(N[(N[Sqrt[N[(t$95$2 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$4), $MachinePrecision] + N[(N[Sqrt[N[(t$95$7 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$9), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t$95$10 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$11), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$12, 1.5], N[(1.0 + N[(N[Sqrt[N[(t$95$8 + 1.0), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[t$95$8], $MachinePrecision] + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$12, 2.5], N[(N[(1.0 + N[Sqrt[N[(1.0 + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(t$95$4 + t$95$9), $MachinePrecision]), $MachinePrecision], N[(3.0 - N[(t$95$4 + N[(t$95$9 + t$95$11), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (x < z) THEN x ELSE z ENDIF IN
	LET tmp_3 = IF (x < z) THEN x ELSE z ENDIF IN
	LET tmp_1 = IF (tmp_2 > t) THEN tmp_3 ELSE t ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_6 = IF (x < z) THEN x ELSE z ENDIF IN
		LET tmp_7 = IF (x < z) THEN x ELSE z ENDIF IN
		LET tmp_5 = IF (tmp_6 < t) THEN tmp_7 ELSE t ENDIF IN
		LET t_2 = tmp_5 IN
			LET tmp_9 = IF (x > z) THEN x ELSE z ENDIF IN
			LET tmp_10 = IF (x > z) THEN x ELSE z ENDIF IN
			LET tmp_8 = IF (y > tmp_9) THEN y ELSE tmp_10 ENDIF IN
			LET t_3 = tmp_8 IN
				LET t_4 = (sqrt(t_2)) IN
					LET tmp_12 = IF (x > z) THEN x ELSE z ENDIF IN
					LET tmp_13 = IF (x > z) THEN x ELSE z ENDIF IN
					LET tmp_11 = IF (y < tmp_12) THEN y ELSE tmp_13 ENDIF IN
					LET t_5 = tmp_11 IN
						LET tmp_14 = IF (t_5 > t_1) THEN t_5 ELSE t_1 ENDIF IN
						LET t_6 = tmp_14 IN
							LET tmp_15 = IF (t_5 < t_1) THEN t_5 ELSE t_1 ENDIF IN
							LET t_7 = tmp_15 IN
								LET tmp_16 = IF (t_3 > t_6) THEN t_3 ELSE t_6 ENDIF IN
								LET t_8 = tmp_16 IN
									LET t_9 = (sqrt(t_7)) IN
										LET tmp_17 = IF (t_3 < t_6) THEN t_3 ELSE t_6 ENDIF IN
										LET t_10 = tmp_17 IN
											LET t_11 = (sqrt(t_10)) IN
												LET t_12 = ((((sqrt((t_2 + (1)))) - t_4) + ((sqrt((t_7 + (1)))) - t_9)) + ((sqrt((t_10 + (1)))) - t_11)) IN
													LET tmp_19 = IF (t_12 <= (25e-1)) THEN (((1) + (sqrt(((1) + t_2)))) - (t_4 + t_9)) ELSE ((3) - (t_4 + (t_9 + t_11))) ENDIF IN
													LET tmp_18 = IF (t_12 <= (15e-1)) THEN ((1) + ((sqrt((t_8 + (1)))) - ((sqrt(t_8)) + t_11))) ELSE tmp_19 ENDIF IN
	tmp_18
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 1.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.1%

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 13.4%

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 11.7%

       \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.1%

       \[\leadsto 1 + \left(\sqrt{t + 1} - \left(\sqrt{t} + \sqrt{z}\right)\right) \]

   if 1.5 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))) < 2.5

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in z around inf

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 13.3%

      \[\leadsto \left(\sqrt{1 + x} + \sqrt{1 + y}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   10. Taylor expanded in y around 0

       \[\leadsto \left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 11.5%

       \[\leadsto \left(1 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   if 2.5 < (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y #s(literal 1 binary64))) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 8.2%

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 27: 46.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), \mathsf{max}\left(x, t\right)\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), \mathsf{max}\left(x, t\right)\right)\\ t_3 := \sqrt{t\_2}\\ \mathbf{if}\;\sqrt{t\_2 + 1} - t\_3 \leq 0.2:\\ \;\;\;\;1 + \left(\sqrt{t\_1 + 1} - \left(\sqrt{t\_1} + t\_3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 - \left(\sqrt{\mathsf{min}\left(x, t\right)} + \left(\sqrt{\mathsf{min}\left(y, z\right)} + t\_3\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmax (fmax y z) (fmax x t)))
       (t_2 (fmin (fmax y z) (fmax x t)))
       (t_3 (sqrt t_2)))
  (if (<= (- (sqrt (+ t_2 1.0)) t_3) 0.2)
    (+ 1.0 (- (sqrt (+ t_1 1.0)) (+ (sqrt t_1) t_3)))
    (- 3.0 (+ (sqrt (fmin x t)) (+ (sqrt (fmin y z)) t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmax(y, z), fmax(x, t));
	double t_2 = fmin(fmax(y, z), fmax(x, t));
	double t_3 = sqrt(t_2);
	double tmp;
	if ((sqrt((t_2 + 1.0)) - t_3) <= 0.2) {
		tmp = 1.0 + (sqrt((t_1 + 1.0)) - (sqrt(t_1) + t_3));
	} else {
		tmp = 3.0 - (sqrt(fmin(x, t)) + (sqrt(fmin(y, z)) + t_3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = fmax(fmax(y, z), fmax(x, t))
    t_2 = fmin(fmax(y, z), fmax(x, t))
    t_3 = sqrt(t_2)
    if ((sqrt((t_2 + 1.0d0)) - t_3) <= 0.2d0) then
        tmp = 1.0d0 + (sqrt((t_1 + 1.0d0)) - (sqrt(t_1) + t_3))
    else
        tmp = 3.0d0 - (sqrt(fmin(x, t)) + (sqrt(fmin(y, z)) + t_3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmax(fmax(y, z), fmax(x, t));
	double t_2 = fmin(fmax(y, z), fmax(x, t));
	double t_3 = Math.sqrt(t_2);
	double tmp;
	if ((Math.sqrt((t_2 + 1.0)) - t_3) <= 0.2) {
		tmp = 1.0 + (Math.sqrt((t_1 + 1.0)) - (Math.sqrt(t_1) + t_3));
	} else {
		tmp = 3.0 - (Math.sqrt(fmin(x, t)) + (Math.sqrt(fmin(y, z)) + t_3));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmax(fmax(y, z), fmax(x, t))
	t_2 = fmin(fmax(y, z), fmax(x, t))
	t_3 = math.sqrt(t_2)
	tmp = 0
	if (math.sqrt((t_2 + 1.0)) - t_3) <= 0.2:
		tmp = 1.0 + (math.sqrt((t_1 + 1.0)) - (math.sqrt(t_1) + t_3))
	else:
		tmp = 3.0 - (math.sqrt(fmin(x, t)) + (math.sqrt(fmin(y, z)) + t_3))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmax(fmax(y, z), fmax(x, t))
	t_2 = fmin(fmax(y, z), fmax(x, t))
	t_3 = sqrt(t_2)
	tmp = 0.0
	if (Float64(sqrt(Float64(t_2 + 1.0)) - t_3) <= 0.2)
		tmp = Float64(1.0 + Float64(sqrt(Float64(t_1 + 1.0)) - Float64(sqrt(t_1) + t_3)));
	else
		tmp = Float64(3.0 - Float64(sqrt(fmin(x, t)) + Float64(sqrt(fmin(y, z)) + t_3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = max(max(y, z), max(x, t));
	t_2 = min(max(y, z), max(x, t));
	t_3 = sqrt(t_2);
	tmp = 0.0;
	if ((sqrt((t_2 + 1.0)) - t_3) <= 0.2)
		tmp = 1.0 + (sqrt((t_1 + 1.0)) - (sqrt(t_1) + t_3));
	else
		tmp = 3.0 - (sqrt(min(x, t)) + (sqrt(min(y, z)) + t_3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Max[N[Max[y, z], $MachinePrecision], N[Max[x, t], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[y, z], $MachinePrecision], N[Max[x, t], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[t$95$2], $MachinePrecision]}, If[LessEqual[N[(N[Sqrt[N[(t$95$2 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$3), $MachinePrecision], 0.2], N[(1.0 + N[(N[Sqrt[N[(t$95$1 + 1.0), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[t$95$1], $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.0 - N[(N[Sqrt[N[Min[x, t], $MachinePrecision]], $MachinePrecision] + N[(N[Sqrt[N[Min[y, z], $MachinePrecision]], $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (y > z) THEN y ELSE z ENDIF IN
	LET tmp_3 = IF (x > t) THEN x ELSE t ENDIF IN
	LET tmp_4 = IF (y > z) THEN y ELSE z ENDIF IN
	LET tmp_5 = IF (x > t) THEN x ELSE t ENDIF IN
	LET tmp_1 = IF (tmp_2 > tmp_3) THEN tmp_4 ELSE tmp_5 ENDIF IN
	LET t_1 = tmp_1 IN
		LET tmp_8 = IF (y > z) THEN y ELSE z ENDIF IN
		LET tmp_9 = IF (x > t) THEN x ELSE t ENDIF IN
		LET tmp_10 = IF (y > z) THEN y ELSE z ENDIF IN
		LET tmp_11 = IF (x > t) THEN x ELSE t ENDIF IN
		LET tmp_7 = IF (tmp_8 < tmp_9) THEN tmp_10 ELSE tmp_11 ENDIF IN
		LET t_2 = tmp_7 IN
			LET t_3 = (sqrt(t_2)) IN
				LET tmp_13 = IF (x < t) THEN x ELSE t ENDIF IN
				LET tmp_14 = IF (y < z) THEN y ELSE z ENDIF IN
				LET tmp_12 = IF (((sqrt((t_2 + (1)))) - t_3) <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((1) + ((sqrt((t_1 + (1)))) - ((sqrt(t_1)) + t_3))) ELSE ((3) - ((sqrt(tmp_13)) + ((sqrt(tmp_14)) + t_3))) ENDIF IN
	tmp_12
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)) < 0.20000000000000001

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.1%

      \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 13.4%

      \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + z}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 11.7%

       \[\leadsto \left(1 + \sqrt{1 + t}\right) - \left(\sqrt{t} + \sqrt{z}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.1%

       \[\leadsto 1 + \left(\sqrt{t + 1} - \left(\sqrt{t} + \sqrt{z}\right)\right) \]

   if 0.20000000000000001 < (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 8.2%

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 29.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(y, \mathsf{max}\left(x, z\right)\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(x, z\right), t\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(y, \mathsf{max}\left(x, z\right)\right), \mathsf{max}\left(t\_1, t\_2\right)\right)\\ t_4 := \sqrt{t\_3}\\ \mathbf{if}\;\sqrt{t\_3 + 1} - t\_4 \leq 0.2:\\ \;\;\;\;\frac{1}{t\_4 + \sqrt{1 + t\_3}}\\ \mathbf{else}:\\ \;\;\;\;3 - \left(\sqrt{\mathsf{min}\left(\mathsf{min}\left(x, z\right), t\right)} + \left(\sqrt{\mathsf{min}\left(t\_1, t\_2\right)} + t\_4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin y (fmax x z)))
       (t_2 (fmax (fmin x z) t))
       (t_3 (fmin (fmax y (fmax x z)) (fmax t_1 t_2)))
       (t_4 (sqrt t_3)))
  (if (<= (- (sqrt (+ t_3 1.0)) t_4) 0.2)
    (/ 1.0 (+ t_4 (sqrt (+ 1.0 t_3))))
    (-
     3.0
     (+ (sqrt (fmin (fmin x z) t)) (+ (sqrt (fmin t_1 t_2)) t_4))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(y, fmax(x, z));
	double t_2 = fmax(fmin(x, z), t);
	double t_3 = fmin(fmax(y, fmax(x, z)), fmax(t_1, t_2));
	double t_4 = sqrt(t_3);
	double tmp;
	if ((sqrt((t_3 + 1.0)) - t_4) <= 0.2) {
		tmp = 1.0 / (t_4 + sqrt((1.0 + t_3)));
	} else {
		tmp = 3.0 - (sqrt(fmin(fmin(x, z), t)) + (sqrt(fmin(t_1, t_2)) + t_4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = fmin(y, fmax(x, z))
    t_2 = fmax(fmin(x, z), t)
    t_3 = fmin(fmax(y, fmax(x, z)), fmax(t_1, t_2))
    t_4 = sqrt(t_3)
    if ((sqrt((t_3 + 1.0d0)) - t_4) <= 0.2d0) then
        tmp = 1.0d0 / (t_4 + sqrt((1.0d0 + t_3)))
    else
        tmp = 3.0d0 - (sqrt(fmin(fmin(x, z), t)) + (sqrt(fmin(t_1, t_2)) + t_4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(y, fmax(x, z));
	double t_2 = fmax(fmin(x, z), t);
	double t_3 = fmin(fmax(y, fmax(x, z)), fmax(t_1, t_2));
	double t_4 = Math.sqrt(t_3);
	double tmp;
	if ((Math.sqrt((t_3 + 1.0)) - t_4) <= 0.2) {
		tmp = 1.0 / (t_4 + Math.sqrt((1.0 + t_3)));
	} else {
		tmp = 3.0 - (Math.sqrt(fmin(fmin(x, z), t)) + (Math.sqrt(fmin(t_1, t_2)) + t_4));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = fmin(y, fmax(x, z))
	t_2 = fmax(fmin(x, z), t)
	t_3 = fmin(fmax(y, fmax(x, z)), fmax(t_1, t_2))
	t_4 = math.sqrt(t_3)
	tmp = 0
	if (math.sqrt((t_3 + 1.0)) - t_4) <= 0.2:
		tmp = 1.0 / (t_4 + math.sqrt((1.0 + t_3)))
	else:
		tmp = 3.0 - (math.sqrt(fmin(fmin(x, z), t)) + (math.sqrt(fmin(t_1, t_2)) + t_4))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = fmin(y, fmax(x, z))
	t_2 = fmax(fmin(x, z), t)
	t_3 = fmin(fmax(y, fmax(x, z)), fmax(t_1, t_2))
	t_4 = sqrt(t_3)
	tmp = 0.0
	if (Float64(sqrt(Float64(t_3 + 1.0)) - t_4) <= 0.2)
		tmp = Float64(1.0 / Float64(t_4 + sqrt(Float64(1.0 + t_3))));
	else
		tmp = Float64(3.0 - Float64(sqrt(fmin(fmin(x, z), t)) + Float64(sqrt(fmin(t_1, t_2)) + t_4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(y, max(x, z));
	t_2 = max(min(x, z), t);
	t_3 = min(max(y, max(x, z)), max(t_1, t_2));
	t_4 = sqrt(t_3);
	tmp = 0.0;
	if ((sqrt((t_3 + 1.0)) - t_4) <= 0.2)
		tmp = 1.0 / (t_4 + sqrt((1.0 + t_3)));
	else
		tmp = 3.0 - (sqrt(min(min(x, z), t)) + (sqrt(min(t_1, t_2)) + t_4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[y, N[Max[x, z], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[x, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[y, N[Max[x, z], $MachinePrecision]], $MachinePrecision], N[Max[t$95$1, t$95$2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[t$95$3], $MachinePrecision]}, If[LessEqual[N[(N[Sqrt[N[(t$95$3 + 1.0), $MachinePrecision]], $MachinePrecision] - t$95$4), $MachinePrecision], 0.2], N[(1.0 / N[(t$95$4 + N[Sqrt[N[(1.0 + t$95$3), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.0 - N[(N[Sqrt[N[Min[N[Min[x, z], $MachinePrecision], t], $MachinePrecision]], $MachinePrecision] + N[(N[Sqrt[N[Min[t$95$1, t$95$2], $MachinePrecision]], $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (x > z) THEN x ELSE z ENDIF IN
	LET tmp_2 = IF (x > z) THEN x ELSE z ENDIF IN
	LET tmp = IF (y < tmp_1) THEN y ELSE tmp_2 ENDIF IN
	LET t_1 = tmp IN
		LET tmp_5 = IF (x < z) THEN x ELSE z ENDIF IN
		LET tmp_6 = IF (x < z) THEN x ELSE z ENDIF IN
		LET tmp_4 = IF (tmp_5 > t) THEN tmp_6 ELSE t ENDIF IN
		LET t_2 = tmp_4 IN
			LET tmp_12 = IF (x > z) THEN x ELSE z ENDIF IN
			LET tmp_13 = IF (x > z) THEN x ELSE z ENDIF IN
			LET tmp_11 = IF (y > tmp_12) THEN y ELSE tmp_13 ENDIF IN
			LET tmp_14 = IF (t_1 > t_2) THEN t_1 ELSE t_2 ENDIF IN
			LET tmp_16 = IF (x > z) THEN x ELSE z ENDIF IN
			LET tmp_17 = IF (x > z) THEN x ELSE z ENDIF IN
			LET tmp_15 = IF (y > tmp_16) THEN y ELSE tmp_17 ENDIF IN
			LET tmp_18 = IF (t_1 > t_2) THEN t_1 ELSE t_2 ENDIF IN
			LET tmp_10 = IF (tmp_11 < tmp_14) THEN tmp_15 ELSE tmp_18 ENDIF IN
			LET t_3 = tmp_10 IN
				LET t_4 = (sqrt(t_3)) IN
					LET tmp_22 = IF (x < z) THEN x ELSE z ENDIF IN
					LET tmp_23 = IF (x < z) THEN x ELSE z ENDIF IN
					LET tmp_21 = IF (tmp_22 < t) THEN tmp_23 ELSE t ENDIF IN
					LET tmp_24 = IF (t_1 < t_2) THEN t_1 ELSE t_2 ENDIF IN
					LET tmp_19 = IF (((sqrt((t_3 + (1)))) - t_4) <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((1) / (t_4 + (sqrt(((1) + t_3))))) ELSE ((3) - ((sqrt(tmp_21)) + ((sqrt(tmp_24)) + t_4))) ENDIF IN
	tmp_19
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z)) < 0.20000000000000001

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
   2. Step-by-step derivation

   3. Applied rewrites 93.8%

      \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   4. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 19.3%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
   8. Step-by-step derivation

   9. Applied rewrites 21.6%

      \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]
   11. Step-by-step derivation

   12. Applied rewrites 18.1%

       \[\leadsto \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]

   if 0.20000000000000001 < (-.f64 (sqrt.f64 (+.f64 z #s(literal 1 binary64))) (sqrt.f64 z))

   1. Initial program 92.0%

      \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.2%

      \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.7%

      \[\leadsto \left(1 + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 9.4%

       \[\leadsto \left(2 + \sqrt{1 + x}\right) - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]

   11. Taylor expanded in x around 0

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 8.2%

       \[\leadsto 3 - \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 26.6% accurate, 2.3× speedup

Math

\[\frac{1}{\sqrt{\mathsf{min}\left(z, t\right)} + \sqrt{1 + \mathsf{min}\left(z, t\right)}} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (/ 1.0 (+ (sqrt (fmin z t)) (sqrt (+ 1.0 (fmin z t))))))

C

double code(double x, double y, double z, double t) {
	return 1.0 / (sqrt(fmin(z, t)) + sqrt((1.0 + fmin(z, t))));
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 / (sqrt(fmin(z, t)) + sqrt((1.0d0 + fmin(z, t))))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 / (Math.sqrt(fmin(z, t)) + Math.sqrt((1.0 + fmin(z, t))));
}

Python

def code(x, y, z, t):
	return 1.0 / (math.sqrt(fmin(z, t)) + math.sqrt((1.0 + fmin(z, t))))

Julia

function code(x, y, z, t)
	return Float64(1.0 / Float64(sqrt(fmin(z, t)) + sqrt(Float64(1.0 + fmin(z, t)))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 / (sqrt(min(z, t)) + sqrt((1.0 + min(z, t))));
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 / N[(N[Sqrt[N[Min[z, t], $MachinePrecision]], $MachinePrecision] + N[Sqrt[N[(1.0 + N[Min[z, t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_1 = IF (z < t) THEN z ELSE t ENDIF IN
	(1) / ((sqrt(tmp)) + (sqrt(((1) + tmp_1))))
END code

Derivation

1. Initial program 92.0%

   \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]
2. Step-by-step derivation

3. Applied rewrites 93.8%

   \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \frac{1}{\sqrt{z} + \sqrt{z + 1}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

4. Taylor expanded in t around inf

   \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]
5. Step-by-step derivation

6. Applied rewrites 19.3%

   \[\leadsto \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right)\right) - \left(\sqrt{x} + \sqrt{y}\right) \]

7. Taylor expanded in y around inf

   \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]
8. Step-by-step derivation

9. Applied rewrites 21.6%

   \[\leadsto \left(\sqrt{1 + x} + \frac{1}{\sqrt{z} + \sqrt{1 + z}}\right) - \sqrt{x} \]

10. Taylor expanded in x around inf

    \[\leadsto \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]
11. Step-by-step derivation

12. Applied rewrites 18.1%

    \[\leadsto \frac{1}{\sqrt{z} + \sqrt{1 + z}} \]
13. Add Preprocessing

Alternative 30: 16.7% accurate, 4.5× speedup

Math

\[\sqrt{1 + t} - \sqrt{t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (- (sqrt (+ 1.0 t)) (sqrt t)))

C

double code(double x, double y, double z, double t) {
	return sqrt((1.0 + t)) - sqrt(t);
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = sqrt((1.0d0 + t)) - sqrt(t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.sqrt((1.0 + t)) - Math.sqrt(t);
}

Python

def code(x, y, z, t):
	return math.sqrt((1.0 + t)) - math.sqrt(t)

Julia

function code(x, y, z, t)
	return Float64(sqrt(Float64(1.0 + t)) - sqrt(t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = sqrt((1.0 + t)) - sqrt(t);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(sqrt(((1) + t))) - (sqrt(t))
END code

Derivation

1. Initial program 92.0%

   \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

2. Taylor expanded in y around inf

   \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
3. Step-by-step derivation

4. Applied rewrites 12.1%

   \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

5. Taylor expanded in z around inf

   \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]
6. Step-by-step derivation

7. Applied rewrites 13.2%

   \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]

8. Taylor expanded in x around inf

   \[\leadsto \sqrt{1 + t} - \sqrt{t} \]
9. Step-by-step derivation

10. Applied rewrites 15.3%

    \[\leadsto \sqrt{1 + t} - \sqrt{t} \]
11. Add Preprocessing

Alternative 31: 15.3% accurate, 3.5× speedup

Math

\[2 - \left(\sqrt{t} + \sqrt{\mathsf{min}\left(x, z\right)}\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (- 2.0 (+ (sqrt t) (sqrt (fmin x z)))))

C

double code(double x, double y, double z, double t) {
	return 2.0 - (sqrt(t) + sqrt(fmin(x, z)));
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 2.0d0 - (sqrt(t) + sqrt(fmin(x, z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 2.0 - (Math.sqrt(t) + Math.sqrt(fmin(x, z)));
}

Python

def code(x, y, z, t):
	return 2.0 - (math.sqrt(t) + math.sqrt(fmin(x, z)))

Julia

function code(x, y, z, t)
	return Float64(2.0 - Float64(sqrt(t) + sqrt(fmin(x, z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 2.0 - (sqrt(t) + sqrt(min(x, z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(2.0 - N[(N[Sqrt[t], $MachinePrecision] + N[Sqrt[N[Min[x, z], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp = IF (x < z) THEN x ELSE z ENDIF IN
	(2) - ((sqrt(t)) + (sqrt(tmp)))
END code

Derivation

1. Initial program 92.0%

   \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

2. Taylor expanded in y around inf

   \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
3. Step-by-step derivation

4. Applied rewrites 12.1%

   \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

5. Taylor expanded in z around inf

   \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]
6. Step-by-step derivation

7. Applied rewrites 13.2%

   \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]

8. Taylor expanded in t around 0

   \[\leadsto \left(1 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]
9. Step-by-step derivation

10. Applied rewrites 11.5%

    \[\leadsto \left(1 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]

11. Taylor expanded in x around 0

    \[\leadsto 2 - \left(\sqrt{t} + \sqrt{x}\right) \]
12. Step-by-step derivation

13. Applied rewrites 10.1%

    \[\leadsto 2 - \left(\sqrt{t} + \sqrt{x}\right) \]
14. Add Preprocessing

Alternative 32: 14.0% accurate, 8.1× speedup

Math

\[1 - \sqrt{t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (- 1.0 (sqrt t)))

C

double code(double x, double y, double z, double t) {
	return 1.0 - sqrt(t);
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - sqrt(t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 - Math.sqrt(t);
}

Python

def code(x, y, z, t):
	return 1.0 - math.sqrt(t)

Julia

function code(x, y, z, t)
	return Float64(1.0 - sqrt(t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 - sqrt(t);
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(1) - (sqrt(t))
END code

Derivation

1. Initial program 92.0%

   \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

2. Taylor expanded in y around inf

   \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]
3. Step-by-step derivation

4. Applied rewrites 12.1%

   \[\leadsto \left(\sqrt{1 + t} + \left(\sqrt{1 + x} + \sqrt{1 + z}\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \sqrt{z}\right)\right) \]

5. Taylor expanded in z around inf

   \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]
6. Step-by-step derivation

7. Applied rewrites 13.2%

   \[\leadsto \left(\sqrt{1 + t} + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]

8. Taylor expanded in t around 0

   \[\leadsto \left(1 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]
9. Step-by-step derivation

10. Applied rewrites 11.5%

    \[\leadsto \left(1 + \sqrt{1 + x}\right) - \left(\sqrt{t} + \sqrt{x}\right) \]

11. Taylor expanded in x around inf

    \[\leadsto 1 - \sqrt{t} \]
12. Step-by-step derivation

13. Applied rewrites 14.0%

    \[\leadsto 1 - \sqrt{t} \]
14. Add Preprocessing

Alternative 33: 1.6% accurate, 11.4× speedup

Math

\[-\sqrt{t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (- (sqrt t)))

C

double code(double x, double y, double z, double t) {
	return -sqrt(t);
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = -sqrt(t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return -Math.sqrt(t);
}

Python

def code(x, y, z, t):
	return -math.sqrt(t)

Julia

function code(x, y, z, t)
	return Float64(-sqrt(t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -sqrt(t);
end

Wolfram

code[x_, y_, z_, t_] := (-N[Sqrt[t], $MachinePrecision])

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	- (sqrt(t))
END code

Derivation

1. Initial program 92.0%

   \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

2. Taylor expanded in t around 0

   \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]
3. Step-by-step derivation

4. Applied rewrites 10.2%

   \[\leadsto \left(1 + \left(\sqrt{1 + x} + \left(\sqrt{1 + y} + \sqrt{1 + z}\right)\right)\right) - \left(\sqrt{t} + \left(\sqrt{x} + \left(\sqrt{y} + \sqrt{z}\right)\right)\right) \]

5. Taylor expanded in t around inf

   \[\leadsto -1 \cdot \left(t \cdot \sqrt{\frac{1}{t}}\right) \]
6. Step-by-step derivation

7. Applied rewrites 1.6%

   \[\leadsto -1 \cdot \left(t \cdot \sqrt{\frac{1}{t}}\right) \]

8. Taylor expanded in t around 0

   \[\leadsto -1 \cdot \sqrt{t} \]
9. Step-by-step derivation

10. Applied rewrites 1.6%

    \[\leadsto -1 \cdot \sqrt{t} \]

12. Applied rewrites 1.6%

    \[\leadsto -\sqrt{t} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Main:z from "
  :precision binary64
  (+ (+ (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y))) (- (sqrt (+ z 1.0)) (sqrt z))) (- (sqrt (+ t 1.0)) (sqrt t))))