Details

sample143.0ms

Algorithm

intervals

Results

69.0ms	47×	body	2560	valid
45.0ms	98×	body	1280	valid
13.0ms	56×	body	640	valid
5.0ms	29×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	13×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune144.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
14.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
13.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series131.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
46.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify93.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune297.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`exp-prod`
31×	`log-pow`
28×	`log-prod`
24×	`times-frac`
23×	`add-cube-cbrt`
20×	`exp-sum`
7×	`pow1`
6×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`add-exp-log`
4×	`log-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`exp-diff` `rem-log-exp`
1×	`sub-neg` `diff-log` `div-inv` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

4.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
21.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
3.0ms	(- 1.0 (cos x))

series151.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(exp (log (- 1.0 (cos x))))
73.0ms	(log (- 1.0 (cos x)))
35.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify64.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	302	619
1	710	559
2	2016	547
3	5001	531

prune281.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
1.7b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

5.0ms	(/ 1.0 (sin x))
3.0ms	(/ (cos x) (sin x))
20.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series121.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ 1.0 (sin x))
18.0ms	(/ (cos x) (sin x))
85.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	287	581
1	772	552
2	2229	552
3	5002	551

prune175.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

regimes149.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 30.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	30
1	42	30

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1593×	body	2560	valid
1.2s	2747×	body	1280	valid
466.0ms	1853×	body	640	valid
168.0ms	952×	body	320	valid
58.0ms	477×	body	160	valid
39.0ms	375×	body	80	valid
13.0ms	3×	body	5120	valid