Details

sample309.0ms

Algorithm

intervals

Results

22.0ms	49×	body	1280	valid
13.0ms	132×	body	80	valid
13.0ms	43×	body	640	valid
5.0ms	22×	body	320	valid
2.0ms	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)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

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))

series215.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune247.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
16.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)

simplify60.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1588	240
3	5001	236

prune244.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
92×	`add-sqr-sqrt`
72×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
21×	`add-exp-log`
19×	`pow1`
16×	`difference-of-squares`
15×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`tan-quot` `div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow2` `frac-times` `rec-exp` `frac-2neg` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

10.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
12.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series247.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
90.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
36.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	579	2595
1	2779	2386
2	5001	2281

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.4b	(pow (* (tan x) (tan x)) 3)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

236×	`tan-quot`
137×	`associate-*r/`
130×	`pow1`
97×	`frac-times`
78×	`associate-*l/`
45×	`frac-sub`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
21×	`add-exp-log` `add-cbrt-cube`
20×	`pow-plus`
15×	`pow2`
14×	`sub-div`
11×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow-pow` `add-log-exp`
4×	`swap-sqr` `associate-r` `associate-l`
3×	`cube-div` `pow-unpow`
2×	`pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3--` `distribute-rgt-out--` `diff-log` `unpow3` `cube-prod` `flip--` `sqr-pow`

Counts

4 → 207

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
39.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
23.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
7.0ms	(pow (* (tan x) (tan x)) 3)

series245.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
98.0ms	(- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1.0 (* (tan x) (tan x))))
49.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
65.0ms	(pow (* (tan x) (tan x)) 3)

simplify98.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	805	1700
1	3060	1367
2	5001	1356

prune335.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes130.0ms

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	20	26
1	20	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

736.0ms	1559×	body	1280	valid
381.0ms	4274×	body	80	valid
366.0ms	1242×	body	640	valid
138.0ms	641×	body	320	valid
43.0ms	284×	body	160	valid