Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	55×	body	1280	valid
3.0ms	139×	body	80	valid
3.0ms	35×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	9×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 27.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series161.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (+ x 1.0) (- x 1.0))
125.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify139.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	317	591
1	1003	565
2	4494	559
3	5003	559

prune170.0ms

Filtered

77 candidates to 50 candidates (64.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Merged error: 0.2b

Counts

78 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
2.6b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

45.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
30.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
11.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
52.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
198.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify81.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1294	4957
1	5002	4719

prune561.0ms

Filtered

341 candidates to 173 candidates (50.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	338	3	341
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	340	5	345

Merged error: 0.2b

Counts

345 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(/ (log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
2.6b	(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
2.6b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

533×	`*-un-lft-identity`
304×	`times-frac`
171×	`distribute-lft-out`
89×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
70×	`log-pow`
56×	`exp-prod`
36×	`distribute-lft-out--`
25×	`pow1`
24×	`swap-sqr`
18×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
15×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/r/`
9×	`frac-sub`
8×	`associate-/l*`
7×	`frac-times` `associate-r/` `associate-l/`
6×	`add-log-exp`
5×	`cbrt-undiv` `log-prod` `flip3-+` `div-exp` `flip-+` `div-inv`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`sub-neg` `log-div` `exp-diff` `exp-sum`
1×	`pow2` `flip3--` `frac-2neg` `pow-plus` `diff-log` `div-sub` `rem-log-exp` `pow-prod-down` `frac-add` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 261

Calls

4 calls:

20.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
43.0ms	(/ (log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
11.0ms	(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
14.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
330.0ms	(/ (log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
197.0ms	(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
195.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify153.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	897	5698
1	4061	5095
2	5001	5069

prune466.0ms

Filtered

273 candidates to 129 candidates (47.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	273	5	278

Merged error: 0.2b

Counts

278 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))
0.3b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
20.6b	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
42×	`cbrt-prod`
21×	`times-frac`
16×	`cbrt-div` `difference-of-squares`
14×	`add-cube-cbrt`
11×	`pow1` `distribute-lft-out--`
10×	`swap-sqr`
9×	`flip3--` `flip--`
8×	`pow1/3` `associate-r` `associate-l`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 112

Calls

4 calls:

3.0ms	(cbrt (- x 1.0))
3.0ms	(cbrt (- x 1.0))
11.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
109.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (- x 1.0))
98.0ms	(cbrt (- x 1.0))
125.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
167.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	540	1361
1	1801	1261
2	5002	1191

prune350.0ms

Filtered

124 candidates to 91 candidates (73.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	124	5	129

Merged error: 0.2b

Counts

129 → 5

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.2b

bsearch111.0ms

Steps

Iters	Range		Point
9	911.8039404667869	114238954.84408061	16838.629846100426
10	-1087315822018.0432	-7.975708081780418	-13356.292489681631

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	35
1	68	35
2	81	35
3	83	35
4	83	35

end0.0ms

sample608.0ms

Algorithm

intervals

Results

207.0ms	1719×	body	1280	valid
117.0ms	1244×	body	640	valid
103.0ms	4114×	body	80	valid
41.0ms	605×	body	320	valid
15.0ms	318×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Details

sample24.0ms

simplify18.0ms

prune2.0ms

localize11.0ms

rewrite40.0ms

series161.0ms

simplify139.0ms

prune170.0ms

localize10.0ms

rewrite129.0ms

series623.0ms

simplify81.0ms

prune561.0ms

localize14.0ms

rewrite107.0ms

series767.0ms

simplify153.0ms

prune466.0ms

localize11.0ms

rewrite130.0ms

series486.0ms

simplify57.0ms

prune350.0ms

regimes49.0ms

bsearch111.0ms

simplify3.0ms

end0.0ms

sample608.0ms

Profiling

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6