Details

sample53.0ms

Algorithm

intervals

Results

25.0ms	57×	body	2560	valid
9.0ms	41×	body	1280	valid
5.0ms	37×	body	640	valid
3.0ms	26×	body	320	valid
3.0ms	84×	body	80	valid
1.0ms	11×	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: 31.4b

localize7.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
17.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

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))
18.0ms	(/ (- 1.0 (cos x)) (* x x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
40.0ms	(/ (- 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

prune104.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

20.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series96.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
17.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune254.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* -1 (/ (- (cos x) 1.0) x)) x)
0.1b	(/ (- (cos x) 1.0) x)
1.5b	(- (cos x) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

16.0ms	(/ (* -1 (/ (- (cos x) 1.0) x)) x)
18.0ms	(/ (- (cos x) 1.0) x)
7.0ms	(- (cos x) 1.0)

series114.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (* -1 (/ (- (cos x) 1.0) x)) x)
44.0ms	(/ (- (cos x) 1.0) x)
18.0ms	(- (cos x) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	383	529
1	1750	475
2	5001	472

prune153.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- 1.0 (cos x)))
0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
1.5b	(- 1.0 (cos x))
1.6b	(log (exp (- 1.0 (cos x))))

rewrite85.0ms

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:

15.0ms	(exp (- 1.0 (cos x)))
44.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
9.0ms	(- 1.0 (cos x))
14.0ms	(log (exp (- 1.0 (cos x))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(exp (- 1.0 (cos x)))
41.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
16.0ms	(- 1.0 (cos x))
17.0ms	(log (exp (- 1.0 (cos x))))

simplify119.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	304	679
1	935	604
2	3744	589
3	5001	587

prune194.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.8b

bsearch50.0ms

Steps

Iters	Range		Point
9	1.3330246063773173e-09	3.618674152218468	0.030875615092221424
7	-0.23317146499959118	-0.002309702793432406	-0.029930317430197608

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	11
1	37	11
2	37	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

726.0ms	1596×	body	2560	valid
299.0ms	1322×	body	1280	valid
213.0ms	1458×	body	640	valid
92.0ms	898×	body	320	valid
68.0ms	2255×	body	80	valid
33.0ms	471×	body	160	valid