Details

sample57.0ms

Algorithm

intervals

Results

14.0ms	55×	body	1280	valid
10.0ms	211×	body	80	nan
9.0ms	46×	body	640	valid
7.0ms	132×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.1b	(- (sqrt (+ x 1)) (sqrt x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

7.0ms	(sqrt (+ x 1))
49.0ms	(- (sqrt (+ x 1)) (sqrt x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(sqrt (+ x 1))
87.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.7s

Counts

43 → 43

Iterations

Iter	Nodes
done	5000
4	2095
3	848
2	350
1	165
0	81

prune145.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.2b	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`insert-posit16`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

7.0ms	(sqrt (+ x 1))
38.0ms	(+ (sqrt (+ x 1)) (sqrt x))
82.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1))
55.0ms	(+ (sqrt (+ x 1)) (sqrt x))
79.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5003
4	3628
3	1475
2	606
1	273
0	133

prune360.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

rewrite553.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`insert-posit16` `add-log-exp` `associate-/l/`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 320

Calls

4 calls:

50.0ms	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
72.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
103.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
300.0ms	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
84.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
79.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
101.0ms	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

simplify2.7s

Counts

332 → 332

Iterations

Iter	Nodes
done	5000
3	2376
2	961
1	467
0	236

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ (/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite445.0ms

Algorithm

rewrite-expression-head

Rules

1122×	`*-un-lft-identity`
900×	`sqrt-prod`
774×	`times-frac`
460×	`distribute-lft-out`
294×	`add-sqr-sqrt`
292×	`add-cube-cbrt`
46×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 551

Calls

4 calls:

67.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
64.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
79.0ms	(/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
196.0ms	(/ (/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
136.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
182.0ms	(/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
102.0ms	(/ (/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.1s

Counts

563 → 563

Iterations

Iter	Nodes
done	5001
2	1566
1	859
0	373

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample1.6s

Algorithm

intervals

Results

436.0ms	1720×	body	1280	valid
363.0ms	7974×	body	80	nan
220.0ms	4071×	body	80	valid
213.0ms	1264×	body	640	valid
111.0ms	613×	body	320	valid
24.0ms	332×	body	160	valid