Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	49×	body	1280	valid
4.0ms	48×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	9×	body	160	valid

simplify20.0ms

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: 29.3b

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))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
140×	`frac-sub`
115×	`associate-/r*`
113×	`add-sqr-sqrt`
89×	`associate-/l*`
71×	`add-cube-cbrt`
52×	`times-frac`
42×	`distribute-lft-out`
28×	`distribute-lft-out--`
26×	`frac-2neg` `clear-num`
22×	`associate-/l/`
19×	`difference-of-squares`
12×	`flip3-+` `flip-+`
7×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `div-inv`
1×	`sub-neg` `diff-log`

Counts

3 → 243

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
41.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ x (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
140.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1416	3130
1	5001	3054

prune302.0ms

Filtered

252 candidates to 143 candidates (56.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	4	253

Merged error: 0.1b

Counts

253 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(* (+ x 1.0) (/ (- x 1.0) (+ x 1.0)))
0.0b	(/ (- (- (* (/ (- x 1.0) (+ x 1.0)) x) x) 1.0) (* (+ x 1.0) (/ (- x 1.0) (+ x 1.0))))
1.9b	(- (* (/ (- x 1.0) (+ x 1.0)) x) x)

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

715×	`*-un-lft-identity`
469×	`times-frac`
398×	`add-sqr-sqrt`
241×	`distribute-lft-out--`
237×	`associate-r`
174×	`add-cube-cbrt`
88×	`difference-of-squares`
75×	`associate-l`
67×	`associate-/r/`
66×	`distribute-lft-out`
65×	`associate-/r*`
56×	`frac-times`
46×	`associate-/l*`
40×	`flip3-+` `flip-+`
28×	`associate-*r/`
20×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
16×	`associate-/l/`
11×	`div-inv`
10×	`clear-num`
9×	`flip3--` `*-commutative` `flip--`
8×	`frac-2neg`
6×	`pow1` `cbrt-undiv` `div-exp` `un-div-inv` `add-log-exp`
4×	`distribute-rgt-out--` `associate-*l/` `prod-exp` `cbrt-unprod`
3×	`div-sub`
1×	`associate--l-` `sub-neg` `diff-log` `pow-prod-down`

Counts

4 → 529

Calls

4 calls:

8.0ms	(/ (- x 1.0) (+ x 1.0))
21.0ms	(* (+ x 1.0) (/ (- x 1.0) (+ x 1.0)))
58.0ms	(/ (- (- (* (/ (- x 1.0) (+ x 1.0)) x) x) 1.0) (* (+ x 1.0) (/ (- x 1.0) (+ x 1.0))))
27.0ms	(- (* (/ (- x 1.0) (+ x 1.0)) x) x)

series337.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- x 1.0) (+ x 1.0))
27.0ms	(* (+ x 1.0) (/ (- x 1.0) (+ x 1.0)))
155.0ms	(/ (- (- (* (/ (- x 1.0) (+ x 1.0)) x) x) 1.0) (* (+ x 1.0) (/ (- x 1.0) (+ x 1.0))))
113.0ms	(- (* (/ (- x 1.0) (+ x 1.0)) x) x)

simplify127.0ms

Algorithm

egg-herbie

Counts

541 → 541

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1666	8634
1	5002	8208

prune686.0ms

Filtered

541 candidates to 283 candidates (52.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	540	1	541
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	540	5	545

Merged error: 0.0b

Counts

545 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ (- x 1.0) (+ x 1.0)) (/ (+ x 1.0) x)) (* (/ (+ x 1.0) x) (/ (- x 1.0) (+ x 1.0))))
0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ (- x 1.0) (+ x 1.0))
2.3b	(- (/ (- x 1.0) (+ x 1.0)) (/ (+ x 1.0) x))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

3688×	`*-un-lft-identity`
2528×	`times-frac`
1631×	`add-sqr-sqrt`
805×	`distribute-lft-out--`
652×	`distribute-lft-out`
561×	`add-cube-cbrt`
442×	`associate-r`
385×	`associate-/l*`
336×	`associate-/r*` `frac-sub`
334×	`associate-/l/`
327×	`difference-of-squares`
272×	`associate-l`
235×	`associate-/r/`
168×	`frac-times`
84×	`clear-num`
83×	`frac-2neg`
68×	`unswap-sqr`
62×	`flip3-+` `flip-+`
41×	`flip3--` `flip--`
37×	`div-inv`
26×	`add-exp-log` `add-cbrt-cube`
17×	`*-commutative`
14×	`associate-*r/`
12×	`associate-*l/`
11×	`cbrt-undiv` `div-exp`
6×	`div-sub` `add-log-exp`
4×	`pow1` `prod-exp` `cbrt-unprod`
3×	`un-div-inv`
2×	`associate--l-`
1×	`sub-neg` `diff-log`

Counts

4 → 1558

Calls

4 calls:

112.0ms	(/ (- (/ (- x 1.0) (+ x 1.0)) (/ (+ x 1.0) x)) (* (/ (+ x 1.0) x) (/ (- x 1.0) (+ x 1.0))))
8.0ms	(/ (- x 1.0) (+ x 1.0))
8.0ms	(/ (- x 1.0) (+ x 1.0))
38.0ms	(- (/ (- x 1.0) (+ x 1.0)) (/ (+ x 1.0) x))

series362.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (- (/ (- x 1.0) (+ x 1.0)) (/ (+ x 1.0) x)) (* (/ (+ x 1.0) x) (/ (- x 1.0) (+ x 1.0))))
38.0ms	(/ (- x 1.0) (+ x 1.0))
42.0ms	(/ (- x 1.0) (+ x 1.0))
100.0ms	(- (/ (- x 1.0) (+ x 1.0)) (/ (+ x 1.0) x))

simplify305.0ms

Algorithm

egg-herbie

Counts

1570 → 1570

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	29081

prune2.0s

Filtered

1570 candidates to 706 candidates (45.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1570	0	1570
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1570	5	1575

Merged error: 0.0b

Counts

1575 → 5

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
0.0b	(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`distribute-lft-out`
9×	`add-log-exp`
6×	`associate-l`
4×	`sum-log`
3×	`+-commutative`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `associate-+r+` `flip3-+` `add-cbrt-cube` `flip-+`

Counts

2 → 33

Calls

2 calls:

7.0ms	(+ (* 3.0 x) 1.0)
19.0ms	(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

series59.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* 3.0 x) 1.0)
23.0ms	(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	159	217
1	571	205
2	2330	203
3	5001	203

prune44.0ms

Filtered

39 candidates to 22 candidates (56.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	39	5	44

Merged error: 0.0b

Counts

44 → 5

regimes31.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 24.6b

bsearch102.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	12664.160931741633
10	-1556119314.230081	-0.05767290693153419	-13967.117865521159

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	27
1	39	27

end0.0ms

sample516.0ms

Algorithm

intervals

Results

179.0ms	1656×	body	1280	valid
100.0ms	1191×	body	640	valid
97.0ms	4206×	body	80	valid
38.0ms	617×	body	320	valid
14.0ms	330×	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

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