Details

sample134.0ms

Algorithm

intervals

Results

68.0ms	58×	body	2560	valid
37.0ms	86×	body	1280	valid
15.0ms	67×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	9×	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: 31.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 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:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify79.0ms

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

prune161.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `flip3-+` `unpow3` `sum-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

4.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series225.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(+ (* 1/240 (pow x 5)) (* 1/2 x))
48.0ms	(* 1/240 (pow x 5))
41.0ms	(* 1/24 (pow x 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	282	301
1	1180	277
2	5002	276

prune187.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b	(- 1.0 (cos x))

rewrite31.0ms

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:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
11.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series135.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify87.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

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

prune316.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.3b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.4b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.9b	(- 1.0 (cos x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

231×	`times-frac`
159×	`add-sqr-sqrt` `*-un-lft-identity`
136×	`exp-prod`
113×	`add-cube-cbrt`
69×	`log-pow`
23×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r/`
9×	`div-inv`
8×	`flip3--` `flip--`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
3×	`log-prod` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 207

Calls

4 calls:

6.0ms	(/ (sin x) (- 1.0 (cos x)))
13.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
20.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
4.0ms	(- 1.0 (cos x))

series148.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sin x) (- 1.0 (cos x)))
42.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
44.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
20.0ms	(- 1.0 (cos x))

simplify57.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	526	1686
1	1918	1532
2	5001	1387

prune578.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

regimes155.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.4b

bsearch84.0ms

Steps

Iters	Range		Point
9	1.2358748968334836e-07	0.22405535791780642	0.026425734950010618
9	-0.11986014733990268	-1.6789357321840064e-10	-0.02298531208321491

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	1670×	body	2560	valid
1.2s	2817×	body	1280	valid
413.0ms	1829×	body	640	valid
126.0ms	851×	body	320	valid
58.0ms	480×	body	160	valid
22.0ms	352×	body	80	valid
3.0ms	1×	body	5120	valid