Details

sample133.0ms

Algorithm

intervals

Results

58.0ms	46×	body	2560	valid
45.0ms	90×	body	1280	valid
15.0ms	66×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	8×	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: 29.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 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))

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

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

prune152.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

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))))
1.9b	(- 1.0 (cos x))

rewrite43.0ms

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))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
16.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series140.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
42.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
40.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify88.0ms

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

prune309.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
2.0b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite27.0ms

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:

2.0ms	(/ 1.0 (sin x))
3.0ms	(/ (cos x) (sin x))
19.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series129.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1.0 (sin x))
19.0ms	(/ (cos x) (sin x))
86.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (52.0ms)

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

prune210.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin x))
0.1b	(/ 1.0 (sin x))
0.2b	(* (cos x) (/ 1 (sin x)))
2.0b	(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`associate-r` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`div-exp`
4×	`prod-exp` `div-inv`
3×	`cbrt-undiv` `associate-r/` `associate-l*` `un-div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub` `cbrt-unprod` `sub-div`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `flip--` `inv-pow`

Counts

4 → 111

Calls

4 calls:

2.0ms	(/ 1 (sin x))
2.0ms	(/ 1.0 (sin x))
9.0ms	(* (cos x) (/ 1 (sin x)))
13.0ms	(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

series136.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (sin x))
18.0ms	(/ 1.0 (sin x))
19.0ms	(* (cos x) (/ 1 (sin x)))
85.0ms	(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

simplify99.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	391	701
1	1433	627
2	4833	581
3	5002	577

prune213.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes64.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.2b

bsearch100.0ms

Steps

Iters	Range		Point
10	4.8244160186105205e-08	257763.20554958374	0.02016717054387116
10	-772.3369502403921	-4.163765984402517e-10	-0.022146274038337438

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	23
1	43	23

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1584×	body	2560	valid
1.3s	2805×	body	1280	valid
445.0ms	1880×	body	640	valid
165.0ms	961×	body	320	valid
53.0ms	434×	body	160	valid
37.0ms	332×	body	80	valid
11.0ms	4×	body	5120	valid