Details

sample299.0ms

Algorithm

intervals

Results

19.0ms	47×	body	1280	valid
13.0ms	51×	body	640	valid
8.0ms	126×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	10×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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))

rewrite28.0ms

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:

9.0ms	(/ (- 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))

series219.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (35.0ms)

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

prune247.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
2.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series76.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
23.0ms	(pow (sin x) 2)

simplify61.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1590	240
3	5001	236

prune221.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(pow (* (tan x) (tan x)) 3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`tan-quot`
13×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

6.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(pow (* (tan x) (tan x)) 3)

series166.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))
67.0ms	(pow (* (tan x) (tan x)) 3)

simplify41.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	211	452
1	971	401
2	5001	384

prune307.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

43.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(- (sqrt 1.0) (tan x))
15.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))

series358.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
36.0ms	(- (sqrt 1.0) (tan x))
93.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))

simplify81.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	561	1675
1	2802	1512
2	5001	1496

prune329.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes173.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	15	9
2	15	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

668.0ms	1521×	body	1280	valid
333.0ms	1285×	body	640	valid
244.0ms	4286×	body	80	valid
114.0ms	606×	body	320	valid
38.0ms	302×	body	160	valid