Details

sample297.0ms

Algorithm

intervals

Results

15.0ms	49×	body	1280	valid
7.0ms	40×	body	640	valid
5.0ms	136×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune3.0ms

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune232.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	104	13	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
92×	`add-sqr-sqrt`
72×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
21×	`add-exp-log`
19×	`pow1`
16×	`difference-of-squares`
15×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`tan-quot` `div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow2` `frac-times` `rec-exp` `frac-2neg` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

7.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
9.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series243.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
89.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
34.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

simplify83.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	579	2595
1	2779	2386
2	5001	2281

prune269.0ms

Filtered

199 candidates to 108 candidates (54.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	199	13	212

Merged error: 0.0b

Counts

212 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b	(/ (/ 1 (+ 1.0 (* (tan x) (tan x)))) (/ 1 (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

642×	`times-frac`
333×	`add-sqr-sqrt`
281×	`add-cube-cbrt` `*-un-lft-identity`
73×	`associate-/r/`
52×	`add-exp-log`
48×	`difference-of-squares`
37×	`div-inv`
34×	`div-exp`
22×	`add-cbrt-cube`
21×	`associate-/r*`
20×	`flip3-+` `flip-+`
19×	`pow1`
18×	`associate-/l*`
16×	`flip3--` `flip--`
9×	`cbrt-undiv` `rec-exp` `1-exp`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`add-log-exp`
2×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 424

Calls

4 calls:

5.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
19.0ms	(/ (/ 1 (+ 1.0 (* (tan x) (tan x)))) (/ 1 (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
90.0ms	(/ (/ 1 (+ 1.0 (* (tan x) (tan x)))) (/ 1 (- 1.0 (* (tan x) (tan x)))))
37.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify116.0ms

Algorithm

egg-herbie

Counts

436 → 436

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1938	8764
1	5001	8143

prune563.0ms

Filtered

436 candidates to 215 candidates (49.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	434	2	436
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	436	13	449

Merged error: 0.0b

Counts

449 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.4b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
14.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
152.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	266	869
1	914	806
2	5002	790

prune157.0ms

Filtered

118 candidates to 69 candidates (58.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	118	13	131

Merged error: 0.0b

Counts

131 → 13

regimes168.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms

sample999.0ms

Algorithm

intervals

Results

407.0ms	1558×	body	1280	valid
211.0ms	1238×	body	640	valid
159.0ms	4225×	body	80	valid
77.0ms	642×	body	320	valid
29.0ms	337×	body	160	valid