Details

sample59.0ms

Algorithm

intervals

Results

29.0ms	56×	body	2560	valid
10.0ms	44×	body	1280	valid
6.0ms	42×	body	640	valid
3.0ms	29×	body	320	valid
2.0ms	65×	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: 30.6b

localize6.0ms

Local error

Found 2 expressions with local error:

1.6b	(- 1.0 (cos x))
17.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

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))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

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

prune111.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) x)
0.3b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.6b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

6.0ms	(/ (- 1.0 (cos x)) x)
13.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
4.0ms	(- 1.0 (cos x))

series103.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (- 1.0 (cos x)) x)
45.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
18.0ms	(- 1.0 (cos x))

simplify62.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5003	690

prune218.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 x) (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) x))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.5b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

492×	`times-frac`
453×	`add-sqr-sqrt`
288×	`*-un-lft-identity`
247×	`associate-r`
183×	`add-cube-cbrt`
160×	`difference-of-squares`
123×	`unpow-prod-down` `cube-prod`
81×	`sqr-pow`
50×	`distribute-lft-out--`
44×	`add-exp-log`
26×	`add-cbrt-cube`
18×	`div-exp`
13×	`associate-l`
12×	`prod-exp`
10×	`difference-cubes`
9×	`cbrt-undiv` `unswap-sqr`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-/r/` `cbrt-unprod`
5×	`div-inv`
4×	`flip3-+` `flip-+`
3×	`rec-exp` `pow-unpow` `1-exp`
1×	`+-commutative` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `sum-log` `*-commutative` `flip--` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 368

Calls

4 calls:

102.0ms	(* (/ 1 x) (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) x))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
12.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series245.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (/ 1 x) (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) x))
27.0ms	(pow (cos x) 3)
9.0ms	(+ (cos x) 1.0)
53.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify87.0ms

Algorithm

egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1951	5626
1	5002	5410

prune953.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.0b	(log (exp (pow (cos x) 3)))
1.5b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`log-pow`
12×	`add-cube-cbrt` `exp-prod`
7×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp`
6×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `unpow3` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

3.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
4.0ms	(log (exp (pow (cos x) 3)))
15.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos x) 3)
9.0ms	(+ (cos x) 1.0)
28.0ms	(log (exp (pow (cos x) 3)))
52.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	296	446
1	1109	381
2	5001	373

prune255.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes74.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch90.0ms

Steps

Iters	Range		Point
10	1.4316099847845607e-10	21.660028671588154	0.03040407886584754
9	-8.718619127186496	-1.4100946153605287e-08	-0.035460081688607266

simplify9.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	42
1	62	42
2	62	42

end0.0ms

sample1.6s

Algorithm

intervals

Results

741.0ms	1581×	body	2560	valid
284.0ms	1257×	body	1280	valid
222.0ms	1468×	body	640	valid
106.0ms	916×	body	320	valid
72.0ms	2298×	body	80	valid
34.0ms	480×	body	160	valid