Details

sample206.0ms

Algorithm

intervals

Results

132.0ms	98×	body	2560	valid
40.0ms	79×	body	1280	valid
16.0ms	45×	body	640	valid
4.0ms	22×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	9×	body	160	valid
0.0ms	3×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

2.0ms	(/ 1.0 (tan x))
18.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series149.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ 1.0 (tan x))
115.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	232	342
1	610	327
2	1894	327
3	5001	326

prune118.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.022222222222222223 (pow x 3))
0.1b	(* 0.0021164021164021165 (pow x 5))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

3.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
9.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
9.0ms	(* 0.022222222222222223 (pow x 3))
6.0ms	(* 0.0021164021164021165 (pow x 5))

series306.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
69.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
43.0ms	(* 0.022222222222222223 (pow x 3))
50.0ms	(* 0.0021164021164021165 (pow x 5))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	355	465
1	1532	436
2	5001	436

prune211.0ms

Filtered

92 candidates to 59 candidates (64.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.022222222222222223 (pow x 3))
0.1b	(* 0.0021164021164021165 (pow x 5))
1.9b	(log (exp (* 0.022222222222222223 (pow x 3))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-r`
16×	`*-un-lft-identity`
14×	`add-exp-log`
13×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp`
4×	`cube-prod` `log-pow` `sqr-pow`
3×	`associate-+l+` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `cube-mult` `associate-+r+` `exp-prod` `exp-to-pow` `flip3-+` `unpow3` `rem-log-exp` `flip-+`

Counts

4 → 88

Calls

4 calls:

10.0ms	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
7.0ms	(* 0.022222222222222223 (pow x 3))
9.0ms	(* 0.0021164021164021165 (pow x 5))
1.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
38.0ms	(* 0.022222222222222223 (pow x 3))
55.0ms	(* 0.0021164021164021165 (pow x 5))
39.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	329	515
1	1345	456
2	5001	456

prune275.0ms

Filtered

100 candidates to 65 candidates (65.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.022222222222222223 (pow x 3))
0.1b	(* 0.0021164021164021165 (pow x 5))
1.2b	(log (exp (* 0.0021164021164021165 (pow x 5))))
1.9b	(log (exp (* 0.022222222222222223 (pow x 3))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp` `log-pow` `add-log-exp`
4×	`cube-prod` `sqr-pow`
2×	`pow-to-exp` `exp-prod` `exp-to-pow` `rem-log-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`cube-mult` `unpow3`

Counts

4 → 84

Calls

4 calls:

7.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(* 0.0021164021164021165 (pow x 5))
1.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))
1.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* 0.022222222222222223 (pow x 3))
51.0ms	(* 0.0021164021164021165 (pow x 5))
56.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))
43.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

simplify193.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	243	347
1	915	305
2	4712	305
3	5001	305

prune279.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

regimes33.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.3s	3166×	body	2560	valid
1.4s	2520×	body	1280	valid
500.0ms	1273×	body	640	valid
145.0ms	665×	body	320	valid
100.0ms	8000×	pre	80	true
41.0ms	319×	body	160	valid
4.0ms	57×	body	80	valid