Details

sample318.0ms

Algorithm

intervals

Results

14.0ms	48×	body	1280	valid
6.0ms	36×	body	640	valid
5.0ms	138×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	9×	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)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite45.0ms

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))))
25.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
98.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5002	824

prune229.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-r`
14×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`associate-l` `sqrt-prod` `distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`tan-quot` `associate-/r/`
3×	`frac-times` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `pow2` `flip3--` `frac-2neg` `pow-plus` `div-sub` `clear-num` `sum-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 132

Calls

4 calls:

16.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
8.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
91.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(+ (sqrt 1.0) (tan x))
35.0ms	(* (tan x) (tan x))

simplify81.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	558	1651
1	2783	1488
2	5002	1472

prune277.0ms

Filtered

144 candidates to 97 candidates (67.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	144	10	154

Merged error: 0b

Counts

154 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
184×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
19×	`sqrt-prod` `distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

8.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
4.0ms	(+ (sqrt 1.0) (tan x))
15.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))

series373.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
32.0ms	(+ (sqrt 1.0) (tan x))
193.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
37.0ms	(* (tan x) (tan x))

simplify122.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	735	4155
1	3740	3919
2	5002	3901

prune404.0ms

Filtered

236 candidates to 144 candidates (61.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	236	10	246

Merged error: 0b

Counts

246 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0))
0.2b	(/ (* (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (- (sqrt 1.0) (tan x))) (* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)))
0.2b	(* (tan x) (tan x))
0.4b	(pow (tan x) 3)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
15×	`flip3-+` `flip-+`
14×	`pow1`
13×	`frac-times` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/` `associate-/l/`
7×	`associate-r/` `associate-l/`
6×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod`
5×	`tan-quot`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `cube-prod` `swap-sqr` `flip--`
2×	`pow-prod-down` `*-commutative` `unswap-sqr`
1×	`cube-div` `pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `distribute-lft-in` `times-frac` `pow-plus` `unpow3` `pow-exp` `clear-num` `associate-/r` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

13.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0))
33.0ms	(/ (* (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (- (sqrt 1.0) (tan x))) (* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)))
5.0ms	(* (tan x) (tan x))
3.0ms	(pow (tan x) 3)

series596.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0))
396.0ms	(/ (* (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (- (sqrt 1.0) (tan x))) (* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)))
32.0ms	(* (tan x) (tan x))
50.0ms	(pow (tan x) 3)

simplify41.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	857	1899
1	5001	1596

prune341.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	129	10	139

Merged error: 0b

Counts

139 → 10

regimes164.0ms

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	12
1	13	12

end0.0ms

sample1.0s

Algorithm

intervals

Results

393.0ms	1508×	body	1280	valid
215.0ms	1251×	body	640	valid
174.0ms	4287×	body	80	valid
82.0ms	651×	body	320	valid
28.0ms	303×	body	160	valid

Details

sample318.0ms

simplify15.0ms

prune3.0ms

localize10.0ms

rewrite45.0ms

series211.0ms

simplify44.0ms

prune229.0ms

localize10.0ms

rewrite38.0ms

series351.0ms

simplify81.0ms

prune277.0ms

localize14.0ms

rewrite44.0ms

series373.0ms

simplify122.0ms

prune404.0ms

localize21.0ms

rewrite57.0ms

series596.0ms

simplify41.0ms

prune341.0ms

regimes164.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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