Details

sample54.0ms

Algorithm

intervals

Results

12.0ms	271×	body	80	nan
11.0ms	50×	body	1280	valid
11.0ms	133×	body	80	valid
8.0ms	49×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.5b	(- (sqrt (+ x 1)) (sqrt x))

rewrite71.0ms

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:

19.0ms	(sqrt (+ x 1))
51.0ms	(- (sqrt (+ x 1)) (sqrt x))

series129.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(sqrt (+ x 1))
96.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.7s

Counts

43 → 43

Iterations

Iter	Nodes
5	4263
4	1592
3	732
2	350
1	159
0	81

prune305.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 78

Calls

3 calls:

35.0ms	(+ (sqrt (+ x 1)) (sqrt x))
9.0ms	(sqrt (+ x 1))
47.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (sqrt (+ x 1)) (sqrt x))
24.0ms	(sqrt (+ x 1))
98.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.6s

Counts

87 → 87

Iterations

Iter	Nodes
4	2200
3	1031
2	525
1	237
0	120

prune714.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 169

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ x 1)))
9.0ms	(sqrt (sqrt (+ x 1)))
33.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
36.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (sqrt (+ x 1)))
51.0ms	(sqrt (sqrt (+ x 1)))
85.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
39.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify1.8s

Counts

181 → 181

Iterations

Iter	Nodes
3	2049
2	964
1	432
0	211

prune1.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 99

Calls

4 calls:

34.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))

series237.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
59.0ms	(cbrt (+ x 1))
59.0ms	(cbrt (+ x 1))
62.0ms	(cbrt (+ x 1))

simplify1.5s

Counts

111 → 111

Iterations

Iter	Nodes
4	3020
3	1274
2	606
1	269
0	123

prune1.9s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes166.0ms

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
2	9
1	9
0	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	1718×	body	1280	valid
451.0ms	8041×	body	80	nan
350.0ms	1286×	body	640	valid
286.0ms	4111×	body	80	valid
95.0ms	595×	body	320	valid
32.0ms	290×	body	160	valid