Details

sample63.0ms

Algorithm

intervals

Results

24.0ms	47×	body	2560	valid
15.0ms	52×	body	1280	valid
9.0ms	46×	body	640	valid
4.0ms	29×	body	320	valid
3.0ms	69×	body	80	valid
1.0ms	13×	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: 31.7b

localize10.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
16.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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:

3.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify64.0ms

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

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 1/24 (pow x 2))
0.3b	(* 1/720 (pow x 4))
11.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite37.0ms

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:

6.0ms	(* 1/24 (pow x 2))
5.0ms	(* 1/720 (pow x 4))
24.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series105.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* 1/24 (pow x 2))
35.0ms	(* 1/720 (pow x 4))
46.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify39.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (33.0ms)

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

prune155.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
40×	`sqrt-prod`
38×	`add-cube-cbrt`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
4×	`pow1` `flip3--` `sqrt-div` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
10.0ms	(/ (sqrt (- 1.0 (cos x))) x)
2.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (sqrt (- 1.0 (cos x))) x)
90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
17.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify98.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	242	1020
1	706	972
2	2968	960
3	5002	960

prune297.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x))))) (/ (sqrt (- 1.0 (cos x))) x))
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
1.7b	(- 1.0 (cos x))
1.7b	(- 1.0 (cos x))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

437×	`times-frac`
357×	`add-sqr-sqrt`
252×	`sqrt-prod`
250×	`*-un-lft-identity`
187×	`add-cube-cbrt`
185×	`associate-l`
30×	`unswap-sqr`
28×	`associate-r`
27×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
14×	`sqrt-div`
13×	`associate-/r/`
10×	`cbrt-undiv` `div-exp`
9×	`flip3--` `flip--` `div-inv`
8×	`associate-/l*` `add-log-exp`
6×	`pow1` `prod-exp` `cbrt-unprod`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 344

Calls

4 calls:

140.0ms	(* (/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x))))) (/ (sqrt (- 1.0 (cos x))) x))
8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series173.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ (sqrt 1) (/ x (sqrt (- 1.0 (cos x))))) (/ (sqrt (- 1.0 (cos x))) x))
89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify141.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	1138	4617
1	4827	4386
2	5001	4358

prune811.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes52.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.5b

bsearch78.0ms

Steps

Iters	Range		Point
9	0.0012055448239290207	14520.350903362307	0.025388615584991975
9	-1078.7327260164275	-0.0019174381104543623	-0.03385827954078283

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	23
1	38	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

844.0ms	1596×	body	2560	valid
360.0ms	1257×	body	1280	valid
287.0ms	1453×	body	640	valid
143.0ms	954×	body	320	valid
117.0ms	2259×	body	80	valid
49.0ms	481×	body	160	valid