Details

sample270.0ms

Algorithm

intervals

Results

9.0ms	35×	body	1280	valid
7.0ms	41×	body	640	valid
6.0ms	145×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	17×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite25.0ms

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))
7.0ms	(* (tan x) (tan x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune219.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 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)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (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:

6.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
11.0ms	(/ 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))

series248.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
91.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify81.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (59.0ms)

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

prune259.0ms

Filtered

199 candidates to 110 candidates (55.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	201	9	210

Merged error: 0.0b

Counts

210 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
0.3b	(* (tan x) (tan x))
0.6b	(pow (tan x) 6)
12.3b	(cbrt (pow (tan x) 6))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
16×	`times-frac`
12×	`pow1`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`cbrt-prod`
6×	`unpow-prod-down`
5×	`distribute-lft-out` `difference-of-squares`
4×	`tan-quot` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow2` `frac-times` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow-plus` `pow1/3` `div-sub` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 6)
2.0ms	(cbrt (pow (tan x) 6))

series222.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (cbrt (pow (tan x) 6))))
32.0ms	(* (tan x) (tan x))
64.0ms	(pow (tan x) 6)
32.0ms	(cbrt (pow (tan x) 6))

simplify59.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	401	916
1	1610	848
2	5001	806

prune218.0ms

Filtered

113 candidates to 75 candidates (66.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Merged error: 0.0b

Counts

122 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (tan x) 6)
0.6b	(pow (tan x) 6)
12.3b	(cbrt (pow (tan x) 6))
12.3b	(cbrt (pow (tan x) 6))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `pow-unpow`
4×	`add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp`

Counts

4 → 64

Calls

4 calls:

3.0ms	(pow (tan x) 6)
3.0ms	(pow (tan x) 6)
2.0ms	(cbrt (pow (tan x) 6))
2.0ms	(cbrt (pow (tan x) 6))

series189.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (tan x) 6)
63.0ms	(pow (tan x) 6)
32.0ms	(cbrt (pow (tan x) 6))
35.0ms	(cbrt (pow (tan x) 6))

simplify101.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	141	372
1	465	330
2	2134	320
3	5001	286

prune165.0ms

Filtered

76 candidates to 50 candidates (65.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Merged error: 0.0b

Counts

84 → 8

regimes106.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms

sample910.0ms

Algorithm

intervals

Results

362.0ms	1518×	body	1280	valid
194.0ms	1239×	body	640	valid
147.0ms	4305×	body	80	valid
76.0ms	633×	body	320	valid
24.0ms	305×	body	160	valid