Details

sample307.0ms

Algorithm

intervals

Results

25.0ms	54×	body	1280	valid
11.0ms	41×	body	640	valid
8.0ms	140×	body	80	valid
3.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify14.0ms

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:

0.2b	(/ (- 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:

8.0ms	(/ (- 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))
7.0ms	(* (tan x) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
52.0ms	(* (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

prune246.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

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

series74.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
18.0ms	(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

prune225.0ms

Pruning

13 alts after pruning (13 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)) (/ (- (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))
0.3b	(* (tan x) (tan x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

41.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(- (sqrt 1.0) (tan x))
4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series301.0ms

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))
38.0ms	(+ (sqrt 1.0) (tan x))
32.0ms	(* (tan x) (tan x))

simplify69.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	490	1089
1	2418	957
2	5001	945

prune277.0ms

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))

series139.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify99.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	165	436
1	584	396
2	2750	386
3	5002	374

prune208.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes154.0ms

Accuracy

0% (0.4b 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	15	19
1	15	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

698.0ms	1544×	body	1280	valid
361.0ms	1276×	body	640	valid
240.0ms	4210×	body	80	valid
129.0ms	647×	body	320	valid
42.0ms	323×	body	160	valid