Details

sample47.0ms

Algorithm

intervals

Results

20.0ms	47×	body	2560	valid
8.0ms	61×	body	640	valid
6.0ms	28×	body	1280	valid
3.0ms	86×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

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: 28.7b

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
14.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite25.0ms

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:

6.0ms	(- 1.0 (cos x))
19.0ms	(/ (- 1.0 (cos x)) (* x x))

series69.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
50.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify61.0ms

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

prune113.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
63.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series180.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (sqrt (- 1.0 (cos x))) x)
49.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
19.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify88.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	667	2403
1	3340	2087
2	5001	1922

prune387.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (sqrt (- 1.0 (cos x))))
0.2b	(/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x)))))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

372×	`times-frac`
242×	`add-sqr-sqrt` `*-un-lft-identity`
218×	`sqrt-prod`
188×	`add-cube-cbrt`
38×	`associate-/r*`
27×	`distribute-lft-out--` `difference-of-squares`
17×	`associate-/r/`
16×	`sqrt-div`
11×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--`
9×	`div-inv` `associate-/l*`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`sub-neg` `frac-2neg` `diff-log` `clear-num`

Counts

4 → 308

Calls

4 calls:

14.0ms	(/ x (sqrt (- 1.0 (cos x))))
22.0ms	(/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x)))))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series247.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ x (sqrt (- 1.0 (cos x))))
94.0ms	(/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x)))))
19.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	779	3921
1	3503	3253
2	5002	2856

prune389.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.1b	(/ (- 1.0 (cos x)) x)
1.8b	(- 1.0 (cos x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-l`
17×	`add-cbrt-cube`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

3 → 115

Calls

3 calls:

37.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
15.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series112.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
43.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	537	819
1	2228	734
2	5001	700

prune207.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch57.0ms

Steps

Iters	Range		Point
8	0.002806896206153352	41.96612619086958	0.027659643589273242
7	-0.5149414008252181	-0.002950799818357885	-0.020329540819315716

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	41	24

end0.0ms

sample1.6s

Algorithm

intervals

Results

735.0ms	1644×	body	2560	valid
287.0ms	1276×	body	1280	valid
194.0ms	1428×	body	640	valid
94.0ms	916×	body	320	valid
77.0ms	2254×	body	80	valid
33.0ms	482×	body	160	valid