Details

sample143.0ms

Algorithm

intervals

Results

75.0ms	49×	body	2560	valid
39.0ms	88×	body	1280	valid
13.0ms	62×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	20×	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: 31.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite24.0ms

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:

16.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 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

prune150.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

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	(* 1/24 (pow x 3))
0.3b	(* 1/240 (pow x 5))

rewrite46.0ms

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:

20.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
12.0ms	(* 1/24 (pow x 3))
11.0ms	(* 1/240 (pow x 5))

series149.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
36.0ms	(* 1/24 (pow x 3))
51.0ms	(* 1/240 (pow x 5))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	375
1	1301	346
2	5001	346

prune184.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 1/24 (pow x 3))
0.3b	(* 1/240 (pow x 5))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`associate-r`
12×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-cbrt-cube`
4×	`cube-prod` `sqr-pow`
2×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
1×	`cube-mult` `unpow3`

Counts

2 → 56

Calls

2 calls:

12.0ms	(* 1/24 (pow x 3))
14.0ms	(* 1/240 (pow x 5))

series89.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* 1/24 (pow x 3))
48.0ms	(* 1/240 (pow x 5))

simplify187.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	208	209
1	871	193
2	4634	193
3	5001	193

prune148.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

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)))
1.8b	(- 1.0 (cos x))

rewrite45.0ms

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:

17.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
15.0ms	(/ (sin x) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series96.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
37.0ms	(/ (sin x) (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify63.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (46.0ms)

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

prune222.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

regimes125.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	33
1	48	33

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1566×	body	2560	valid
1.2s	2753×	body	1280	valid
432.0ms	1901×	body	640	valid
149.0ms	963×	body	320	valid
51.0ms	464×	body	160	valid
24.0ms	351×	body	80	valid
5.0ms	2×	body	5120	valid