Details

sample98.0ms

Algorithm

intervals

Results

26.0ms	36×	body	1280	valid
21.0ms	59×	body	640	valid
20.0ms	259×	body	80	nan
12.0ms	137×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	15
2	15
1	11
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.6b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
97×	`times-frac`
93×	`*-un-lft-identity`
60×	`sqrt-prod`
40×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*`
5×	`add-log-exp`
4×	`div-exp`
3×	`insert-posit16`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `associate-/r/` `inv-pow`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--`

Counts

3 → 150

Calls

3 calls:

18.0ms	(/ 1 (sqrt (+ x 1)))
23.0ms	(/ 1 (sqrt x))
44.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series177.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ 1 (sqrt (+ x 1)))
47.0ms	(/ 1 (sqrt x))
81.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify11.0s

Counts

159 → 159

Iterations

Iter	Nodes
4	3886
3	1930
2	885
1	369
0	196

prune550.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.1b

localize26.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
11.0b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`times-frac`
22×	`sqrt-prod`
18×	`add-cube-cbrt`
15×	`difference-of-squares`
7×	`associate-/r*`
6×	`add-exp-log`
5×	`unpow-prod-down` `sqr-pow`
4×	`pow1` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`pow-flip` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/` `insert-posit16` `div-inv` `distribute-lft-out--`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `1-exp` `flip-+` `flip--` `inv-pow`

Counts

2 → 82

Calls

2 calls:

18.0ms	(/ 1 (sqrt (+ x 1)))
21.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series108.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ 1 (sqrt (+ x 1)))
71.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify7.4s

Counts

88 → 88

Iterations

Iter	Nodes
4	4666
3	1626
2	710
1	316
0	156

prune246.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (pow x -1/2))
0.1b	(sqrt (pow x -1/2))
0.3b	(* (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
7.7b	(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

118×	`sqrt-prod`
116×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
32×	`times-frac`
30×	`associate-r`
20×	`unpow-prod-down`
16×	`sqr-pow`
10×	`add-cube-cbrt`
6×	`pow1` `rem-sqrt-square` `add-cbrt-cube` `associate-l` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`frac-times` `flip3--` `insert-posit16` `flip--`
3×	`sub-neg` `flip3-+` `flip-+` `div-inv` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

2.0ms	(sqrt (pow x -1/2))
2.0ms	(sqrt (pow x -1/2))
132.0ms	(* (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
21.0ms	(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))

series694.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt (pow x -1/2))
193.0ms	(sqrt (pow x -1/2))
207.0ms	(* (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
107.0ms	(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))

simplify2.2s

Counts

153 → 153

Iterations

Iter	Nodes
3	5554
2	1716
1	547
0	210

prune551.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(/ 1 (sqrt (sqrt (+ x 1))))
0.2b	(/ (/ 1 (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))
16.0b	(- (pow x -1/2) (/ (/ 1 (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1)))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

943×	`sqrt-prod`
837×	`times-frac`
564×	`add-sqr-sqrt`
539×	`*-un-lft-identity`
360×	`add-cube-cbrt`
75×	`distribute-lft-out`
69×	`difference-of-squares`
56×	`sqrt-div`
39×	`associate-/l*`
26×	`associate-/r/`
24×	`sqrt-pow1`
23×	`unpow-prod-down` `sqr-pow`
20×	`pow1` `associate-/r*`
17×	`add-exp-log`
16×	`div-inv`
14×	`flip3-+` `flip-+` `pow-flip`
12×	`pow1/2`
11×	`add-cbrt-cube`
10×	`pow-div`
8×	`div-exp`
6×	`add-log-exp`
4×	`cbrt-undiv` `insert-posit16`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 608

Calls

4 calls:

8.0ms	(sqrt (sqrt (+ x 1)))
15.0ms	(/ 1 (sqrt (sqrt (+ x 1))))
33.0ms	(/ (/ 1 (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))
53.0ms	(- (pow x -1/2) (/ (/ 1 (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1)))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (sqrt (+ x 1)))
42.0ms	(/ 1 (sqrt (sqrt (+ x 1))))
42.0ms	(/ (/ 1 (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))
70.0ms	(- (pow x -1/2) (/ (/ 1 (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1)))))

simplify3.7s

Counts

620 → 620

Iterations

Iter	Nodes
2	2539
1	1316
0	571

prune774.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.4b

regimes64.0ms

Accuracy

99.6% (0.0b remaining)

Error of 9.9b against oracle of 9.9b and baseline of 21.2b

bsearch73.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	318690.85562629136	4508.697553152039

simplify7.0ms

Iterations

Iter	Nodes
2	45
1	45
0	38

end0.0ms

sample2.3s

Algorithm

intervals

Results

751.0ms	8060×	body	80	nan
565.0ms	1830×	body	640	valid
360.0ms	1147×	body	1280	valid
285.0ms	4063×	body	80	valid
152.0ms	649×	body	320	valid
36.0ms	311×	body	160	valid