Details

sample116.0ms

Algorithm

intervals

Results

27.0ms	298×	body	80	nan
22.0ms	51×	body	640	valid
21.0ms	37×	body	1280	valid
19.0ms	135×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	8×	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: 18.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.6b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
902×	`*-un-lft-identity`
788×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
74×	`distribute-lft-out`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 793

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
11.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
61.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series227.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1))
46.0ms	(/ 1 (sqrt (+ x 1)))
46.0ms	(/ 1 (sqrt x))
99.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.4s

Counts

805 → 805

Iterations

Iter	Nodes
2	2418
1	1414
0	651

prune3.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt x) 1)
0.1b	(/ 1 (hypot (sqrt x) 1))
0.2b	(/ 1 (sqrt x))
2.6b	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

505×	`times-frac`
406×	`add-sqr-sqrt`
386×	`*-un-lft-identity`
365×	`add-cube-cbrt`
286×	`prod-diff`
144×	`sqrt-prod`
42×	`div-inv`
22×	`fma-neg`
15×	`difference-of-squares`
12×	`add-exp-log`
9×	`associate-/r*`
8×	`add-cbrt-cube`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `pow-flip`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`hypot-udef` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 439

Calls

4 calls:

0.0ms	(hypot (sqrt x) 1)
4.0ms	(/ 1 (hypot (sqrt x) 1))
5.0ms	(/ 1 (sqrt x))
19.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

series771.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(hypot (sqrt x) 1)
240.0ms	(/ 1 (hypot (sqrt x) 1))
29.0ms	(/ 1 (sqrt x))
323.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

simplify1.8s

Counts

451 → 451

Iterations

Iter	Nodes
2	2272
1	1129
0	495

prune1.4s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 18.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
11.5b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

236×	`*-un-lft-identity`
209×	`add-sqr-sqrt`
189×	`prod-diff`
180×	`times-frac`
174×	`add-cube-cbrt`
110×	`sqrt-prod`
89×	`unpow-prod-down`
33×	`sqr-pow`
26×	`distribute-lft-out`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`difference-of-squares`
9×	`flip3-+` `flip-+` `div-inv`
7×	`associate-/r*` `fma-neg` `add-exp-log`
6×	`pow1`
5×	`add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `pow-flip` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

3 → 303

Calls

3 calls:

5.0ms	(sqrt (+ x 1))
9.0ms	(/ 1 (sqrt (+ x 1)))
25.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series116.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(sqrt (+ x 1))
30.0ms	(/ 1 (sqrt (+ x 1)))
62.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify2.3s

Counts

312 → 312

Iterations

Iter	Nodes
3	3597
2	1677
1	930
0	401

prune1.2s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 18.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt x))
0.6b	(cbrt (sqrt x))
28.6b	(fma (* (/ 1 (cbrt (sqrt x))) (/ 1 (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (/ (/ -1 (sqrt (cbrt (+ x 1)))) (fabs (cbrt (+ x 1)))))
30.8b	(fma (/ -1 (sqrt (cbrt (+ x 1)))) (/ 1 (fabs (cbrt (+ x 1)))) (/ (/ 1 (fabs (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (sqrt x))
1.0ms	(cbrt (sqrt x))
0.0ms	(fma (* (/ 1 (cbrt (sqrt x))) (/ 1 (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (/ (/ -1 (sqrt (cbrt (+ x 1)))) (fabs (cbrt (+ x 1)))))
0.0ms	(fma (/ -1 (sqrt (cbrt (+ x 1)))) (/ 1 (fabs (cbrt (+ x 1)))) (/ (/ 1 (fabs (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))

series908.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (sqrt x))
162.0ms	(cbrt (sqrt x))
203.0ms	(fma (* (/ 1 (cbrt (sqrt x))) (/ 1 (cbrt (sqrt x)))) (/ 1 (cbrt (sqrt x))) (/ (/ -1 (sqrt (cbrt (+ x 1)))) (fabs (cbrt (+ x 1)))))
379.0ms	(fma (/ -1 (sqrt (cbrt (+ x 1)))) (/ 1 (fabs (cbrt (+ x 1)))) (/ (/ 1 (fabs (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))

simplify1.4s

Counts

68 → 68

Iterations

Iter	Nodes
3	2892
2	850
1	306
0	133

prune600.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 18.1b

regimes140.0ms

Accuracy

0% (0.6b remaining)

Error of 19.5b against oracle of 18.9b and baseline of 19.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	7
0	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

714.0ms	8131×	body	80	nan
543.0ms	1831×	body	640	valid
348.0ms	1117×	body	1280	valid
319.0ms	4141×	body	80	valid
98.0ms	607×	body	320	valid
34.0ms	304×	body	160	valid