Details

sample282.0ms

Algorithm

intervals

Results

10.0ms	40×	body	1280	valid
7.0ms	41×	body	640	valid
5.0ms	142×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	12×	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

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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
50×	`times-frac`
35×	`difference-of-squares`
29×	`add-cube-cbrt`
24×	`associate-l`
22×	`distribute-lft-out`
18×	`pow1`
14×	`distribute-lft-out--`
13×	`swap-sqr`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`*-commutative` `unswap-sqr`
8×	`tan-quot`
6×	`associate-r` `add-log-exp`
5×	`associate-/r*`
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 → 157

Calls

4 calls:

7.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 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:

35.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	354	1571
1	1198	1497
2	5002	1482

prune262.0ms

Filtered

169 candidates to 83 candidates (49.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Merged error: 0.0b

Counts

170 → 10

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)

rewrite12.0ms

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)

series77.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (55.0ms)

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

prune205.0ms

Filtered

84 candidates to 48 candidates (57.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

localize16.0ms

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)

rewrite27.0ms

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` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `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 → 141

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
8.0ms	(pow (* (tan x) (tan x)) 3)

series166.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
66.0ms	(pow (* (tan x) (tan x)) 3)

simplify69.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	305	589
1	1614	489
2	5001	474

prune293.0ms

Filtered

153 candidates to 67 candidates (43.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	153	10	163

Merged error: 0.0b

Counts

163 → 10

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))))))

rewrite65.0ms

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×	`associate-/r/` `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 → 208

Calls

4 calls:

17.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
26.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
97.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	414	2049
1	1253	1952
2	5002	1934

prune351.0ms

Filtered

220 candidates to 105 candidates (47.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	216	4	220
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	221	9	230

Merged error: 0.0b

Counts

230 → 9

regimes112.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	20	26

end0.0ms

sample934.0ms

Algorithm

intervals

Results

367.0ms	1441×	body	1280	valid
203.0ms	1263×	body	640	valid
159.0ms	4380×	body	80	valid
68.0ms	595×	body	320	valid
26.0ms	321×	body	160	valid