Details

sample64.0ms

Algorithm

intervals

Results

28.0ms	53×	body	2560	valid
12.0ms	40×	body	1280	valid
8.0ms	44×	body	640	valid
4.0ms	30×	body	320	valid
3.0ms	74×	body	80	valid
2.0ms	15×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
15.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune109.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.2b	(* 1/24 (pow x 2))
12.4b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 1/720 (pow x 4))
6.0ms	(* 1/24 (pow x 2))
27.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series104.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 1/720 (pow x 4))
29.0ms	(* 1/24 (pow x 2))
41.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	268	347
1	1132	316
2	5001	310

prune157.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
28×	`cbrt-prod`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
10×	`swap-sqr` `add-log-exp`
9×	`flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

20.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series194.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

simplify100.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	224	813
1	704	769
2	3166	698
3	5001	681

prune247.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
15.0b	(/ (exp (log (- 1.0 (cos x)))) (* x x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`log-prod`
15×	`exp-sum`
11×	`add-cube-cbrt`
9×	`add-cbrt-cube`
8×	`add-exp-log` `times-frac` `associate-/l*`
6×	`pow1` `log-div` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
2×	`cbrt-undiv` `div-exp` `log-pow` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

3.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))
12.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

series154.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(exp (log (- 1.0 (cos x))))
74.0ms	(log (- 1.0 (cos x)))
17.0ms	(- 1.0 (cos x))
46.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	271	595
1	865	494
2	2746	485
3	5001	479

prune182.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch72.0ms

Steps

Iters	Range		Point
10	2.1112891761060846e-05	363928.4733812492	0.0331222017964037
8	-0.10438916540540782	-0.00034188071245303247	-0.03145496023122399

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	11
1	34	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

869.0ms	1594×	body	2560	valid
382.0ms	1255×	body	1280	valid
298.0ms	1447×	body	640	valid
136.0ms	927×	body	320	valid
121.0ms	2293×	body	80	valid
51.0ms	484×	body	160	valid