Details

sample368.0ms

Algorithm

intervals

Results

28.0ms	58×	body	1280	valid
14.0ms	50×	body	640	valid
8.0ms	129×	body	80	valid
2.0ms	9×	body	320	valid
1.0ms	10×	body	160	valid

simplify38.0ms

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: 0.4b

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))

rewrite68.0ms

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:

23.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series223.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
41.0ms	(- 1.0 (* (tan x) (tan x)))
35.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (37.0ms)

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

prune261.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

35.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
14.0ms	(* (tan x) (sin x))
9.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
18.0ms	(* (tan x) (tan x))

series261.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
46.0ms	(* (tan x) (sin x))
58.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
35.0ms	(* (tan x) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	402	1149
1	1438	1067
2	5001	1060

prune317.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)

rewrite16.0ms

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:

3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)

series78.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (59.0ms)

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

prune247.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(* (/ (* (tan x) (sin x)) (cos x)) (+ (/ (* (tan x) (sin x)) (cos x)) 1.0))
0.3b	(* (tan x) (tan x))
0.4b	(pow (/ (* (tan x) (sin x)) (cos x)) 3)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`add-exp-log` `add-cbrt-cube`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`pow1`
13×	`associate-l`
10×	`associate-r`
9×	`times-frac`
7×	`unpow-prod-down` `cube-prod` `prod-exp` `cbrt-unprod`
5×	`tan-quot`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-times` `pow-unpow` `associate-r/` `swap-sqr` `pow-prod-down` `associate-l/` `pow-exp` `*-commutative` `div-inv` `rem-cube-cbrt` `unswap-sqr`
2×	`flip3-+` `flip-+`
1×	`cube-div` `pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `pow-pow` `distribute-lft-in` `pow-plus` `unpow3` `pow-sqr` `pow-prod-up` `distribute-lft-out` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

16.0ms	(* (tan x) (sin x))
78.0ms	(* (/ (* (tan x) (sin x)) (cos x)) (+ (/ (* (tan x) (sin x)) (cos x)) 1.0))
16.0ms	(* (tan x) (tan x))
11.0ms	(pow (/ (* (tan x) (sin x)) (cos x)) 3)

series341.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (tan x) (sin x))
165.0ms	(* (/ (* (tan x) (sin x)) (cos x)) (+ (/ (* (tan x) (sin x)) (cos x)) 1.0))
34.0ms	(* (tan x) (tan x))
97.0ms	(pow (/ (* (tan x) (sin x)) (cos x)) 3)

simplify128.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	598	1119
1	3704	954
2	5003	945

prune388.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes229.0ms

Accuracy

0% (0.3b 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	13	10
1	13	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

653.0ms	1500×	body	1280	valid
341.0ms	1231×	body	640	valid
247.0ms	4304×	body	80	valid
127.0ms	636×	body	320	valid
48.0ms	329×	body	160	valid