Details

sample57.0ms

Algorithm

intervals

Results

28.0ms	51×	body	2560	valid
9.0ms	39×	body	1280	valid
6.0ms	46×	body	640	valid
3.0ms	30×	body	320	valid
2.0ms	68×	body	80	valid
2.0ms	22×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize6.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
15.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune107.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.4b	(- 1.0 (cos x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

22.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series107.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
44.0ms	(/ (- 1.0 (cos x)) x)
17.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690

prune224.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
0.4b	(cbrt (pow (- 1.0 (cos x)) 3))
0.4b	(pow (- 1.0 (cos x)) 3)
2.4b	(- 1.0 (cos x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
72×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
46×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3--` `flip--`
3×	`pow-unpow` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 163

Calls

4 calls:

17.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
5.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
5.0ms	(pow (- 1.0 (cos x)) 3)
3.0ms	(- 1.0 (cos x))

series128.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
17.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
46.0ms	(pow (- 1.0 (cos x)) 3)
18.0ms	(- 1.0 (cos x))

simplify55.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	409	1242
1	1611	1149
2	5002	1118

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (- 1.0 (cos x)) 3))
0.4b	(pow (- 1.0 (cos x)) 3)
0.4b	(pow (cbrt (pow (- 1.0 (cos x)) 3)) 3)
2.4b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-prod`
39×	`unpow-prod-down` `cube-prod`
37×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`cube-div`
6×	`pow1` `add-exp-log` `pow-unpow` `add-log-exp`
5×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
4×	`cbrt-div` `flip3--` `flip--`
3×	`pow-pow`
2×	`pow-to-exp` `pow1/3` `pow-exp` `rem-cube-cbrt`
1×	`sub-neg` `diff-log` `rem-cbrt-cube`

Counts

4 → 128

Calls

4 calls:

5.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
5.0ms	(pow (- 1.0 (cos x)) 3)
11.0ms	(pow (cbrt (pow (- 1.0 (cos x)) 3)) 3)
3.0ms	(- 1.0 (cos x))

series132.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
49.0ms	(pow (- 1.0 (cos x)) 3)
43.0ms	(pow (cbrt (pow (- 1.0 (cos x)) 3)) 3)
23.0ms	(- 1.0 (cos x))

simplify47.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	373	728
1	1047	678
2	5001	660

prune221.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes59.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.3b

bsearch63.0ms

Steps

Iters	Range		Point
9	0.004380743253548005	488.5072251079851	0.03299608739970331
9	-3.9934486818618	-6.3299436832828755e-06	-0.034500322172418156

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	19
1	37	19

end0.0ms

sample1.5s

Algorithm

intervals

Results

707.0ms	1551×	body	2560	valid
259.0ms	1180×	body	1280	valid
220.0ms	1552×	body	640	valid
121.0ms	950×	body	320	valid
74.0ms	2258×	body	80	valid
36.0ms	509×	body	160	valid