Details

sample234.0ms

Algorithm

intervals

Results

13.0ms	26×	body	2560	valid
7.0ms	45×	body	640	valid
6.0ms	25×	body	1280	valid
5.0ms	35×	body	320	valid
4.0ms	105×	body	80	valid
2.0ms	20×	body	160	valid

simplify248.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 16.6b

Counts

2 → 1

localize26.0ms

Local error

Found 2 expressions with local error:

0.7b	(- 1.0 (cos x))
8.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

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:

4.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series17.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
14.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify67.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (7.0ms)

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

prune100.0ms

Filtered

48 candidates to 34 candidates (29.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	38	10	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	10	49

Merged error: 0.2b

Counts

49 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.2b	(/ (- 1.0 (cos x)) x)
0.7b	(- 1.0 (cos x))

rewrite27.0ms

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-r`
17×	`add-cbrt-cube`
13×	`associate-l`
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` `*-commutative`

Counts

3 → 114

Calls

3 calls:

14.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify63.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690

prune147.0ms

Filtered

123 candidates to 80 candidates (35.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	122	11	133

Merged error: 0.2b

Counts

133 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (- 1.0 (cos x)))
0.2b	(/ (log (exp (- 1.0 (cos x)))) x)
0.7b	(- 1.0 (cos x))
0.9b	(log (exp (- 1.0 (cos x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`exp-prod` `log-pow`
27×	`times-frac`
25×	`add-cube-cbrt`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod`
4×	`exp-sum`
3×	`sub-neg` `exp-diff` `associate-/r*`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 103

Calls

4 calls:

5.0ms	(exp (- 1.0 (cos x)))
8.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (- 1.0 (cos x)))
5.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
3.0ms	(- 1.0 (cos x))
3.0ms	(log (exp (- 1.0 (cos x))))

simplify125.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	304	679
1	935	604
2	3744	589
3	5002	587

prune161.0ms

Filtered

115 candidates to 77 candidates (33.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Merged error: 0.2b

Counts

126 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ x (sqrt (- 1.0 (cos x)))))
0.7b	(- 1.0 (cos x))
0.7b	(- 1.0 (cos x))
0.9b	(log (exp (- 1.0 (cos x))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

672×	`times-frac`
474×	`sqrt-prod`
440×	`add-sqr-sqrt` `*-un-lft-identity`
294×	`add-cube-cbrt`
192×	`log-pow`
160×	`exp-prod`
73×	`distribute-lft-out--` `difference-of-squares`
36×	`pow1`
30×	`associate-/r*`
27×	`associate-/r/`
26×	`sqrt-div`
15×	`flip3--` `flip--`
14×	`div-inv`
12×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`log-prod`
3×	`cbrt-undiv` `sub-neg` `div-exp`
2×	`diff-log` `exp-sum`
1×	`log-div` `frac-2neg` `exp-diff` `rem-log-exp` `clear-num`

Counts

4 → 465

Calls

4 calls:

21.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ x (sqrt (- 1.0 (cos x)))))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
5.0ms	(log (exp (- 1.0 (cos x))))

series15.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) (/ x (sqrt (- 1.0 (cos x)))))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(log (exp (- 1.0 (cos x))))

simplify95.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1178	8750
1	5001	7099

prune628.0ms

Filtered

477 candidates to 213 candidates (55.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	473	4	477
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	476	14	490

Merged error: 0.1b

Counts

490 → 14

regimes193.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 15.3b

bsearch57.0ms

Steps

Iters	Range		Point
11	9.244429547692074e-24	0.06968268467981475	0.030085075980491694
15	-163.36048396326007	3.867226923396042e-305	-0.03479137856505966

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	28
1	41	28

end0.0ms

sample1.3s

Algorithm

intervals

Results

370.0ms	770×	body	2560	valid
255.0ms	1561×	body	640	valid
154.0ms	630×	body	1280	valid
130.0ms	1087×	body	320	valid
128.0ms	3382×	body	80	valid
50.0ms	570×	body	160	valid

Details

sample234.0ms

simplify248.0ms

prune4.0ms

localize26.0ms

rewrite15.0ms

series17.0ms

simplify67.0ms

prune100.0ms

localize8.0ms

rewrite27.0ms

series13.0ms

simplify63.0ms

prune147.0ms

localize12.0ms

rewrite24.0ms

series22.0ms

simplify125.0ms

prune161.0ms

localize15.0ms

rewrite75.0ms

series15.0ms

simplify95.0ms

prune628.0ms

regimes193.0ms

bsearch57.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling