Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
3.0ms	136×	body	80	valid
3.0ms	37×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	11×	body	160	valid

simplify22.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite127.0ms

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:

23.0ms	(/ (+ x 1.0) (- x 1.0))
11.0ms	(/ x (+ x 1.0))
88.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(/ x (+ x 1.0))
116.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5002	716

prune213.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
3.3b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 303

Calls

4 calls:

21.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
48.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
14.0ms	(pow (/ x (+ x 1.0)) 3)
238.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series421.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
38.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
56.0ms	(pow (/ x (+ x 1.0)) 3)
266.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1164	2932
1	5002	2690

prune548.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ x (+ x 1.0)) 6)
0.1b	(pow (pow (/ x (+ x 1.0)) 3) 3)
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 6)
3.2b	(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))

rewrite830.0ms

Algorithm

rewrite-expression-head

Rules

853×	`*-un-lft-identity`
694×	`unpow-prod-down`
650×	`cube-prod`
487×	`add-sqr-sqrt`
448×	`times-frac`
217×	`distribute-lft-out--`
200×	`difference-of-squares`
148×	`distribute-lft-out`
89×	`sqr-pow`
59×	`add-cube-cbrt`
14×	`add-exp-log`
12×	`associate-/r/`
10×	`pow-exp`
9×	`pow-unpow`
6×	`pow1` `cube-div` `div-inv` `add-log-exp`
5×	`flip3-+` `add-cbrt-cube` `flip-+`
4×	`pow-to-exp`
3×	`cube-mult` `pow-pow` `unpow3` `div-exp`
2×	`flip3--` `flip--`
1×	`difference-cubes` `sub-neg` `diff-log` `frac-sub` `rem-cube-cbrt`

Counts

4 → 538

Calls

4 calls:

13.0ms	(pow (/ x (+ x 1.0)) 6)
27.0ms	(pow (pow (/ x (+ x 1.0)) 3) 3)
21.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 6)
718.0ms	(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))

series753.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ x (+ x 1.0)) 6)
77.0ms	(pow (pow (/ x (+ x 1.0)) 3) 3)
69.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 6)
548.0ms	(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))

simplify107.0ms

Algorithm

egg-herbie

Counts

550 → 550

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1243	8010
1	5002	7843

prune821.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
3.2b	(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))

rewrite773.0ms

Algorithm

rewrite-expression-head

Rules

759×	`*-un-lft-identity`
572×	`unpow-prod-down` `cube-prod`
427×	`add-sqr-sqrt`
368×	`times-frac`
213×	`distribute-lft-out--`
196×	`difference-of-squares`
131×	`distribute-lft-out`
84×	`sqr-pow`
12×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `cube-div` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 401

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
717.0ms	(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))

series978.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
80.0ms	(cbrt (+ x 1.0))
732.0ms	(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))

simplify137.0ms

Algorithm

egg-herbie

Counts

413 → 413

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	584	6870
1	2047	6826
2	5002	6820

prune778.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.6b

bsearch109.0ms

Steps

Iters	Range		Point
5	6330.810310882262	18189.836774986274	9075.837006323241
9	-11413.0783357711	-0.00024241826916865248	-9583.752190154746

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	62
1	66	62

end0.0ms

sample538.0ms

Algorithm

intervals

Results

173.0ms	1682×	body	1280	valid
99.0ms	4111×	body	80	valid
99.0ms	1257×	body	640	valid
38.0ms	642×	body	320	valid
13.0ms	308×	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