Details

sample276.0ms

Algorithm

intervals

Results

10.0ms	40×	body	1280	valid
6.0ms	41×	body	640	valid
5.0ms	142×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	12×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 1

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))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

140×	`add-sqr-sqrt`
132×	`*-un-lft-identity`
60×	`add-cube-cbrt`
50×	`times-frac`
45×	`prod-diff`
35×	`difference-of-squares`
33×	`associate-l`
22×	`swap-sqr` `distribute-lft-out`
18×	`pow1`
15×	`associate-r`
14×	`distribute-lft-out--`
12×	`*-commutative` `unswap-sqr`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`tan-quot`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 213

Calls

4 calls:

21.0ms	(- 1.0 (* (tan x) (tan x)))
21.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- 1.0 (* (tan x) (tan x)))
105.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

simplify85.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	559	2609
1	1880	2152
2	5001	2008

prune312.0ms

Filtered

225 candidates to 97 candidates (43.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	216	9	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	217	9	226

Merged error: 0.0b

Counts

226 → 9

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)

rewrite13.0ms

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×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
22.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)

simplify63.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	146	308
1	487	260
2	1671	260
3	5001	256

prune241.0ms

Filtered

92 candidates to 56 candidates (60.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	92	9	101

Merged error: 0.0b

Counts

101 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.5b	(pow (* (tan x) (tan x)) 3)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
33×	`pow1`
27×	`add-cube-cbrt` `*-un-lft-identity`
16×	`tan-quot`
15×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow-pow`
5×	`*-commutative` `unswap-sqr`
4×	`pow2` `expm1-log1p-u` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow3` `sqr-pow`

Counts

4 → 149

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
11.0ms	(pow (* (tan x) (tan x)) 3)

series172.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
37.0ms	(* (tan x) (tan x))
66.0ms	(pow (* (tan x) (tan x)) 3)

simplify68.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	311	619
1	1637	515
2	5001	500

prune323.0ms

Filtered

161 candidates to 75 candidates (46.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	161	9	170

Merged error: 0.0b

Counts

170 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

174×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
100×	`times-frac`
57×	`log-pow`
56×	`exp-prod`
55×	`difference-of-squares`
46×	`add-cube-cbrt`
42×	`distribute-lft-out`
38×	`associate-l`
22×	`distribute-lft-out--`
19×	`pow1`
17×	`swap-sqr`
13×	`*-commutative` `unswap-sqr`
11×	`add-exp-log`
10×	`add-cbrt-cube` `associate-/l*`
8×	`tan-quot`
6×	`associate-r`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`pow2` `frac-times` `flip3-+` `pow-plus` `div-sub` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `exp-diff` `div-exp` `clear-num` `flip--`

Counts

4 → 216

Calls

4 calls:

22.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))
28.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
39.0ms	(* (tan x) (tan x))
103.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	425	2103
1	1302	1982
2	5002	1954

prune390.0ms

Filtered

228 candidates to 114 candidates (50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	224	4	228
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	228	9	237

Merged error: 0.0b

Counts

237 → 9

regimes158.0ms

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

sample913.0ms

Algorithm

intervals

Results

351.0ms	1441×	body	1280	valid
208.0ms	1263×	body	640	valid
148.0ms	4380×	body	80	valid
66.0ms	595×	body	320	valid
25.0ms	321×	body	160	valid