Details

sample299.0ms

Algorithm

intervals

Results

16.0ms	58×	body	1280	valid
6.0ms	38×	body	640	valid
5.0ms	135×	body	80	valid
2.0ms	16×	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:

0.2b	(/ (- 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))

rewrite25.0ms

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:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series220.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (tan x) (tan x))
57.0ms	(* (tan x) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune256.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

14 alts after pruning (14 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)

rewrite11.0ms

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:

2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)
2.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series75.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
22.0ms	(pow (sin x) 2)

simplify60.0ms

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

prune231.0ms

Filtered

84 candidates to 48 candidates (57.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

6.0ms	(/ (* (tan x) (sin x)) (cos x))
11.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(* (tan x) (tan x))

series256.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* (tan x) (sin x)) (cos x))
110.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
54.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
33.0ms	(* (tan x) (tan x))

simplify60.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	432	1210
1	1837	1122
2	5001	1116

prune326.0ms

Filtered

116 candidates to 80 candidates (69.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ 1 (/ (cos x) (* (tan x) (sin x)))))
0.3b	(/ (cos x) (* (tan x) (sin x)))
0.3b	(* (tan x) (tan x))
0.7b	(/ 1 (/ (cos x) (* (tan x) (sin x))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

41×	`times-frac`
36×	`add-sqr-sqrt`
32×	`add-exp-log`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
20×	`add-cbrt-cube`
14×	`div-exp`
12×	`pow1`
9×	`tan-quot` `associate-/r*`
7×	`cbrt-undiv` `div-inv`
6×	`associate-l/` `associate-/r/` `associate-/l` `add-log-exp`
5×	`prod-exp`
3×	`rec-exp` `1-exp` `swap-sqr` `associate-r` `associate-l` `cbrt-unprod` `difference-of-squares`
2×	`frac-2neg` `clear-num` `distribute-lft-out--`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `pow-flip` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `flip--` `inv-pow` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

11.0ms	(- 1.0 (/ 1 (/ (cos x) (* (tan x) (sin x)))))
8.0ms	(/ (cos x) (* (tan x) (sin x)))
5.0ms	(* (tan x) (tan x))
8.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- 1.0 (/ 1 (/ (cos x) (* (tan x) (sin x)))))
66.0ms	(/ (cos x) (* (tan x) (sin x)))
35.0ms	(* (tan x) (tan x))
58.0ms	(/ 1 (/ (cos x) (* (tan x) (sin x))))

simplify57.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	445	1108
1	2094	942
2	5001	933

prune282.0ms

Filtered

139 candidates to 78 candidates (56.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes201.0ms

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	17	12
1	17	12

end0.0ms

sample959.0ms

Algorithm

intervals

Results

378.0ms	1507×	body	1280	valid
211.0ms	1293×	body	640	valid
155.0ms	4301×	body	80	valid
75.0ms	613×	body	320	valid
24.0ms	286×	body	160	valid