Details

sample296.0ms

Algorithm

intervals

Results

17.0ms	38×	body	1280	valid
11.0ms	160×	body	80	valid
8.0ms	29×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	13×	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: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

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

series218.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
98.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune246.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

17.0ms	(pow (cos x) 2)
17.0ms	(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 (54.0ms)

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

prune218.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- 1.0 (* (tan x) (tan x))) (- (/ (* 1.0 1.0) 1) (/ (pow (tan x) 4) 1))) (- 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.4b	(pow (tan x) 4)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

234×	`add-sqr-sqrt`
233×	`times-frac`
118×	`-un-lft-identity` `associate-l*`
111×	`difference-of-squares`
46×	`add-cube-cbrt`
27×	`unpow-prod-down`
25×	`sqr-pow`
21×	`pow1`
14×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-r`
9×	`div-inv`
8×	`tan-quot`
6×	`swap-sqr`
4×	`frac-times` `distribute-rgt-out--` `associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`
2×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `div-exp` `pow-exp` `frac-sub` `sub-div`

Counts

4 → 213

Calls

4 calls:

117.0ms	(* (/ (- 1.0 (* (tan x) (tan x))) (- (/ (* 1.0 1.0) 1) (/ (pow (tan x) 4) 1))) (- 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
2.0ms	(pow (tan x) 4)

series253.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (/ (- 1.0 (* (tan x) (tan x))) (- (/ (* 1.0 1.0) 1) (/ (pow (tan x) 4) 1))) (- 1.0 (* (tan x) (tan x))))
36.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
52.0ms	(pow (tan x) 4)

simplify110.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1044	2849
1	4909	2194
2	5001	2179

prune742.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(pow (tan x) 2)
0.4b	(pow (tan x) 4)
0.4b	(pow (tan x) 4)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `unpow-prod-down` `pow-unpow`
6×	`add-cbrt-cube`
4×	`tan-quot` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `swap-sqr` `associate-r` `associate-l` `pow-exp` `sqr-pow`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unpow2` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
2.0ms	(pow (tan x) 2)
2.0ms	(pow (tan x) 4)
2.0ms	(pow (tan x) 4)

series168.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
36.0ms	(pow (tan x) 2)
48.0ms	(pow (tan x) 4)
52.0ms	(pow (tan x) 4)

simplify161.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	215	319
1	902	299
2	4131	291
3	5001	291

prune244.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes179.0ms

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	12	13
1	12	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

678.0ms	1481×	body	1280	valid
333.0ms	1199×	body	640	valid
258.0ms	4338×	body	80	valid
129.0ms	647×	body	320	valid
44.0ms	335×	body	160	valid