Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	62×	body	640	valid
8.0ms	39×	body	1280	valid
7.0ms	211×	body	80	nan
6.0ms	132×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
2.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite259.0ms

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:

15.0ms	(sqrt (+ x 1))
23.0ms	(/ 1 (sqrt (+ x 1)))
12.0ms	(/ 1 (sqrt x))
136.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ x 1))
50.0ms	(/ 1 (sqrt (+ x 1)))
47.0ms	(/ 1 (sqrt x))
65.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.3s

Counts

805 → 805

Iterations

Iter	Nodes
done	5000
2	2463
1	1435
0	651

prune1.8s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt x) 1)
0.2b	(/ 1 (hypot (sqrt x) 1))
0.3b	(/ 1 (sqrt x))
2.1b	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

rewrite107.0ms

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)
6.0ms	(/ 1 (hypot (sqrt x) 1))
9.0ms	(/ 1 (sqrt x))
67.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

series973.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(hypot (sqrt x) 1)
341.0ms	(/ 1 (hypot (sqrt x) 1))
39.0ms	(/ 1 (sqrt x))
358.0ms	(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))

simplify2.5s

Counts

451 → 451

Iterations

Iter	Nodes
done	5000
2	2291
1	1139
0	495

prune1.3s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 18.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
8.8b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite122.0ms

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:

10.0ms	(sqrt (+ x 1))
14.0ms	(/ 1 (sqrt (+ x 1)))
67.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series158.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ x 1))
54.0ms	(/ 1 (sqrt (+ x 1)))
64.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify2.5s

Counts

312 → 312

Iterations

Iter	Nodes
done	5000
3	4518
2	1883
1	949
0	401

prune910.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 18.0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (+ x 1) -1/2)
2.1b	(- (pow x -1/2) (pow (+ x 1) -1/2))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

69×	`unpow-prod-down`
59×	`*-un-lft-identity`
56×	`prod-diff`
48×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
23×	`sqr-pow`
9×	`distribute-lft-out` `difference-of-squares`
7×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `pow-unpow` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

2 → 111

Calls

2 calls:

15.0ms	(pow (+ x 1) -1/2)
71.0ms	(- (pow x -1/2) (pow (+ x 1) -1/2))

series165.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(pow (+ x 1) -1/2)
124.0ms	(- (pow x -1/2) (pow (+ x 1) -1/2))

simplify2.2s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4299
2	1467
1	503
0	209

prune268.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

regimes44.0ms

Accuracy

98.1% (0.6b remaining)

Error of 1.5b against oracle of 0.9b and baseline of 30.0b

bsearch72.0ms

Steps

Iters	Range		Point
9	0.17679972651571432	94859.26993337883	6705.611752539598

simplify22.0ms

Iterations

Iter	Nodes
done	62
4	62
3	60
2	54
1	47
0	35

end0.0ms

sample2.0s

Algorithm

intervals

Results

654.0ms	1119×	body	1280	valid
403.0ms	7974×	body	80	nan
375.0ms	1873×	body	640	valid
234.0ms	4064×	body	80	valid
76.0ms	619×	body	320	valid
27.0ms	325×	body	160	valid