Details

sample298.0ms

Algorithm

intervals

Results

27.0ms	61×	body	1280	valid
10.0ms	136×	body	80	valid
9.0ms	32×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify13.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite27.0ms

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:

7.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series224.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune255.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(+ (sqrt 1.0) (tan x))
0.3b	(* (tan x) (tan x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

4.0ms	(- (sqrt 1.0) (tan x))
30.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series206.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (sqrt 1.0) (tan x))
102.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
36.0ms	(+ (sqrt 1.0) (tan x))
32.0ms	(* (tan x) (tan x))

simplify53.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	328	693
1	1582	618
2	5001	607

prune248.0ms

Filtered

101 candidates to 67 candidates (66.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (- (tan x)) (+ (sqrt 1.0) (tan x)))
0.2b	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`tan-quot` `pow1` `flip3-+` `associate-l` `flip-+`
12×	`add-cube-cbrt`
11×	`add-log-exp`
10×	`frac-add`
9×	`distribute-neg-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`frac-times` `associate-r/` `associate-r*`
4×	`associate-*l/` `sum-log`
3×	`distribute-lft-neg-out` `distribute-lft-neg-in` `distribute-rgt-neg-in` `swap-sqr` `distribute-lft-out`
2×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `neg-mul-1` `associate-+l+` `distribute-rgt-out` `pow-plus` `unsub-neg` `pow-sqr` `pow-prod-up`

Counts

4 → 102

Calls

4 calls:

7.0ms	(+ (sqrt 1.0) (tan x))
18.0ms	(* (- (tan x)) (+ (sqrt 1.0) (tan x)))
12.0ms	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))

series187.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (sqrt 1.0) (tan x))
84.0ms	(* (- (tan x)) (+ (sqrt 1.0) (tan x)))
35.0ms	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))
32.0ms	(* (tan x) (tan x))

simplify97.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	628	1201
1	3107	1136
2	5001	1094

prune345.0ms

Filtered

114 candidates to 82 candidates (71.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (+ (* (- (tan x)) (sqrt 1.0)) (* (- (tan x)) (tan x))))
0.3b	(* (- (tan x)) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(+ (* (- (tan x)) (sqrt 1.0)) (* (- (tan x)) (tan x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

29×	`tan-quot`
19×	`frac-add`
18×	`add-log-exp`
17×	`add-sqr-sqrt` `distribute-neg-frac`
14×	`-un-lft-identity` `associate-l/`
13×	`pow1` `associate-l`
12×	`add-cube-cbrt`
11×	`distribute-lft-neg-out`
9×	`flip3-+` `sum-log` `flip-+`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r`
5×	`frac-times` `associate-*r/`
4×	`distribute-lft-out`
3×	`distribute-lft-neg-in` `distribute-neg-out` `distribute-rgt-neg-in` `swap-sqr` `unsub-neg`
2×	`+-commutative` `associate-+r-` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `neg-mul-1` `associate-+l+` `associate-+r+` `distribute-rgt-out` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 107

Calls

4 calls:

21.0ms	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (+ (* (- (tan x)) (sqrt 1.0)) (* (- (tan x)) (tan x))))
7.0ms	(* (- (tan x)) (tan x))
5.0ms	(* (tan x) (tan x))
7.0ms	(+ (* (- (tan x)) (sqrt 1.0)) (* (- (tan x)) (tan x)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (+ (* (- (tan x)) (sqrt 1.0)) (* (- (tan x)) (tan x))))
47.0ms	(* (- (tan x)) (tan x))
35.0ms	(* (tan x) (tan x))
76.0ms	(+ (* (- (tan x)) (sqrt 1.0)) (* (- (tan x)) (tan x)))

simplify98.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	638	1469
1	3009	1352
2	5001	1330

prune335.0ms

Filtered

119 candidates to 83 candidates (69.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes246.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	14
1	15	14

end0.0ms

sample1.6s

Algorithm

intervals

Results

687.0ms	1515×	body	1280	valid
352.0ms	1216×	body	640	valid
250.0ms	4300×	body	80	valid
132.0ms	630×	body	320	valid
54.0ms	339×	body	160	valid