Details

sample79.0ms

Algorithm

intervals

Results

27.0ms	229×	body	80	nan
16.0ms	50×	body	1280	valid
10.0ms	39×	body	640	valid
9.0ms	144×	body	80	valid
3.0ms	13×	body	320	valid
1.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.7b	(- (sqrt (+ x 1)) (sqrt x))

rewrite84.0ms

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:

11.0ms	(sqrt (+ x 1))
72.0ms	(- (sqrt (+ x 1)) (sqrt x))

series121.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(sqrt (+ x 1))
87.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.8s

Counts

43 → 43

Iterations

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

prune183.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite140.0ms

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:

55.0ms	(+ (sqrt (+ x 1)) (sqrt x))
13.0ms	(sqrt (+ x 1))
69.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(+ (sqrt (+ x 1)) (sqrt x))
24.0ms	(sqrt (+ x 1))
93.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5004
4	4239
3	1697
2	688
1	274
0	133

prune306.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

1134×	`*-un-lft-identity`
910×	`sqrt-prod`
774×	`times-frac`
465×	`distribute-lft-out`
297×	`add-sqr-sqrt`
295×	`add-cube-cbrt`
50×	`associate-/l*`
28×	`sqrt-div`
27×	`associate-/r*`
24×	`associate-/r/`
22×	`associate-/l/`
16×	`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×	`clear-num` `frac-2neg`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 568

Calls

4 calls:

37.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
36.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
56.0ms	(/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
230.0ms	(/ (/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series529.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
124.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
155.0ms	(/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
96.0ms	(/ (/ (+ 1 0) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify4.0s

Counts

580 → 580

Iterations

Iter	Nodes
done	5008
3	4985
2	1552
1	876
0	382

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite871.0ms

Algorithm

rewrite-expression-head

Rules

960×	`*-un-lft-identity`
552×	`sqrt-prod`
495×	`sqrt-div`
421×	`distribute-lft-out`
247×	`times-frac`
225×	`frac-times`
210×	`associate-/r*`
196×	`add-sqr-sqrt`
165×	`add-cube-cbrt`
140×	`associate-/l*`
71×	`swap-sqr`
70×	`associate-/l/`
42×	`flip3-+` `flip-+`
35×	`clear-num` `frac-2neg`
33×	`associate-r` `associate-l`
20×	`pow1`
15×	`associate-l/` `associate-r/`
14×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`div-inv`
5×	`pow-prod-up`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 586

Calls

4 calls:

104.0ms	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
75.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
67.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
573.0ms	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
77.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
97.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
97.0ms	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

simplify2.8s

Counts

598 → 598

Iterations

Iter	Nodes
done	5000
3	3586
2	1490
1	806
0	472

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

653.0ms	4177×	body	80	valid
530.0ms	1657×	body	1280	valid
491.0ms	7961×	body	80	nan
311.0ms	1238×	body	640	valid
131.0ms	600×	body	320	valid
32.0ms	328×	body	160	valid