Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	71×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series202.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ 1.0 (sqrt (+ x 1.0)))
155.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	274	394
1	1028	351
2	5002	347

prune76.0ms

Filtered

51 candidates to 38 candidates (25.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	3	52

Merged error: 0b

Counts

52 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
311×	`*-un-lft-identity`
236×	`sqrt-prod`
195×	`add-sqr-sqrt`
193×	`add-cube-cbrt`
59×	`distribute-lft-out`
33×	`associate-/l*`
24×	`sqrt-div`
21×	`associate-/r*`
20×	`associate-/r/`
13×	`associate-/l/`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 329

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
21.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series869.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
139.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
437.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
155.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	891	5653
1	3462	5110
2	5002	5016

prune369.0ms

Filtered

341 candidates to 151 candidates (55.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	341	3	344

Merged error: 0b

Counts

344 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
40×	`add-cube-cbrt`
38×	`sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
13×	`associate-r/` `associate-/l`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
6×	`associate-l` `unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`associate-/r/`
3×	`flip3-+` `clear-num` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `prod-exp` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative`

Counts

3 → 130

Calls

3 calls:

8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
18.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series500.0ms

Counts

3 → 9

Calls

3 calls:

305.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
146.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	503	1233
1	2188	1088
2	5001	1058

prune184.0ms

Filtered

139 candidates to 83 candidates (40.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Merged error: 0b

Counts

142 → 3

regimes30.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample333.0ms

Algorithm

intervals

Results

161.0ms	7999×	body	80	valid
52.0ms	2681×	body	80	nan
0.0ms	1×	body	1280	valid