Details

sample139.0ms

Algorithm

intervals

Results

68.0ms	50×	body	2560	valid
42.0ms	87×	body	1280	valid
12.0ms	51×	body	640	valid
6.0ms	38×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	10×	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: 33.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.5b	(- 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))

series61.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify81.0ms

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

prune153.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/240 (pow x 5))
0.2b	(* 1/24 (pow x 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

9.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms	(* 1/240 (pow x 5))
9.0ms	(* 1/24 (pow x 3))

series151.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
52.0ms	(* 1/240 (pow x 5))
38.0ms	(* 1/24 (pow x 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5002	346

prune184.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.5b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

10.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series93.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
39.0ms	(/ (sin x) (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify66.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	510	1595
1	2396	1452
2	5002	1339

prune266.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin x))
0.1b	(/ 1 (- 1.0 (cos x)))
0.2b	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
2.5b	(- 1.0 (cos x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

705×	`times-frac`
396×	`add-sqr-sqrt` `*-un-lft-identity`
302×	`add-cube-cbrt`
52×	`add-exp-log`
47×	`distribute-lft-out--` `difference-of-squares`
39×	`div-inv`
36×	`div-exp`
31×	`associate-/r/`
29×	`associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-/l*`
16×	`flip3--` `flip--`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `diff-log` `associate-/l/`

Counts

4 → 425

Calls

4 calls:

2.0ms	(/ 1 (sin x))
6.0ms	(/ 1 (- 1.0 (cos x)))
18.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series99.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (sin x))
32.0ms	(/ 1 (- 1.0 (cos x)))
35.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
19.0ms	(- 1.0 (cos x))

simplify89.0ms

Algorithm

egg-herbie

Counts

437 → 437

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1640	5619
1	5002	4994

prune581.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes113.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.5b

bsearch81.0ms

Steps

Iters	Range		Point
10	7.712829756242493e-08	8770343.893451896	0.020393739459838457
9	-1827977.1926269082	-0.00043085380315138777	-0.022144219019054306

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1613×	body	2560	valid
1.2s	2670×	body	1280	valid
463.0ms	1933×	body	640	valid
148.0ms	941×	body	320	valid
53.0ms	478×	body	160	valid
24.0ms	363×	body	80	valid
11.0ms	2×	body	5120	valid