Details

sample54.0ms

Algorithm

intervals

Results

23.0ms	49×	body	2560	valid
10.0ms	49×	body	1280	valid
7.0ms	52×	body	640	valid
2.0ms	24×	body	320	valid
2.0ms	62×	body	80	valid
1.0ms	20×	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: 33.1b

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
14.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite30.0ms

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))
23.0ms	(/ (- 1.0 (cos x)) (* x x))

series67.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

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

prune106.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
10.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`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×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

11.0ms	(* 1/720 (pow x 4))
12.0ms	(* 1/24 (pow x 2))
52.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 1/720 (pow x 4))
29.0ms	(* 1/24 (pow x 2))
44.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	268	347
1	1132	316
2	5001	310

prune150.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
10.2b	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`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×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `associate-+r+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

11.0ms	(* 1/720 (pow x 4))
14.0ms	(* 1/24 (pow x 2))
15.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series111.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 1/720 (pow x 4))
30.0ms	(* 1/24 (pow x 2))
44.0ms	(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify37.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	274	345
1	1103	314
2	5001	314

prune155.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

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)
1.8b	(- 1.0 (cos x))

rewrite51.0ms

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:

23.0ms	(/ (/ (- 1.0 (cos x)) x) x)
15.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series112.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (/ (- 1.0 (cos x)) x) x)
49.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (38.0ms)

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

prune256.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch55.0ms

Steps

Iters	Range		Point
8	1.317141247235427e-05	0.43775957865898985	0.03384107969428519
9	-3096.4512561506854	-0.0006592480666379122	-0.033917851243536225

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	42	16
2	42	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

701.0ms	1569×	body	2560	valid
273.0ms	1248×	body	1280	valid
216.0ms	1497×	body	640	valid
101.0ms	967×	body	320	valid
73.0ms	2257×	body	80	valid
37.0ms	462×	body	160	valid