Details

analyze4.0ms

Algorithm: search

sample25.0ms

Algorithm

intervals

Results

7.0ms	48×	body	1280	valid
6.0ms	50×	body	640	valid
4.0ms	125×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify19.0ms

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

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: 30.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune178.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0.0b

Counts

114 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
0.4b	(/ (neg 1.0) (pow x 2))
0.5b	(/ 3.0 (pow x 3))
6.2b	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

51.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
6.0ms	(/ (neg 1.0) (pow x 2))
5.0ms	(/ 3.0 (pow x 3))
75.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series19.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
6.0ms	(/ (neg 1.0) (pow x 2))
3.0ms	(/ 3.0 (pow x 3))
4.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify98.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	738	1746
1	3422	1585
2	5002	1567

prune300.0ms

Filtered

129 candidates to 246 candidates (-90.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	245	5	250

Merged error: 0b

Counts

250 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
80×	`times-frac`
64×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod`
30×	`distribute-lft-out`
18×	`add-cube-cbrt`
17×	`log-pow` `difference-of-squares`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum` `associate-/l*`
3×	`sub-neg`
2×	`flip3--` `exp-diff` `diff-log` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

4 → 130

Calls

4 calls:

31.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
7.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	404	1009
1	1249	941
2	5001	931

prune191.0ms

Filtered

87 candidates to 142 candidates (-63.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	142	5	147

Merged error: 0b

Counts

147 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (+ x 1.0) (- x 1.0))))
0.0b	(exp (/ (+ x 1.0) (- x 1.0)))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
61×	`times-frac`
52×	`exp-prod`
37×	`add-cube-cbrt`
28×	`log-pow`
16×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-prod` `associate-/r/` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`flip3--` `flip--` `associate-/l*`
3×	`div-inv` `associate--r+`
2×	`associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip-+` `rem-exp-log`

Counts

4 → 136

Calls

4 calls:

11.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
8.0ms	(exp (/ (+ x 1.0) (- x 1.0)))
7.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
4.0ms	(exp (/ (+ x 1.0) (- x 1.0)))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	412	978
1	1201	907
2	5001	888

prune203.0ms

Filtered

102 candidates to 148 candidates (-45.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	148	5	153

Merged error: 0b

Counts

153 → 5

regimes80.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms

analyze4.0ms

Algorithm: search

sample720.0ms

Algorithm

intervals

Results

256.0ms	1690×	body	1280	valid
157.0ms	1285×	body	640	valid
132.0ms	4109×	body	80	valid
56.0ms	594×	body	320	valid
20.0ms	322×	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

analyze4.0ms

sample25.0ms

simplify19.0ms

prune2.0ms

localize6.0ms

rewrite45.0ms

series12.0ms

simplify43.0ms

prune178.0ms

localize11.0ms

rewrite146.0ms

series19.0ms

simplify98.0ms

prune300.0ms

localize9.0ms

rewrite103.0ms

series24.0ms

simplify43.0ms

prune191.0ms

localize10.0ms

rewrite65.0ms

series17.0ms

simplify42.0ms

prune203.0ms

regimes80.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample720.0ms

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