Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	51×	body	2560	valid
10.0ms	45×	body	1280	valid
5.0ms	36×	body	640	valid
3.0ms	86×	body	80	valid
2.0ms	22×	body	320	valid
2.0ms	16×	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: 31.1b

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
15.3b	(/ (- 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:

2.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

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

prune112.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

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))

rewrite25.0ms

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

series213.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (sqrt (- 1.0 (cos x))) x)
89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
17.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

simplify96.0ms

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

prune304.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.3b	(+ (cos x) 1.0)
1.5b	(- (pow 1.0 3) (pow (cos x) 3))
1.7b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
10×	`add-log-exp`
9×	`sqr-pow`
7×	`add-cube-cbrt`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `pow-pow` `flip3-+` `unpow3` `pow-exp` `sum-log` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 83

Calls

4 calls:

2.0ms	(pow (cos x) 3)
3.0ms	(+ (cos x) 1.0)
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))
3.0ms	(- 1.0 (cos x))

series103.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (cos x) 3)
9.0ms	(+ (cos x) 1.0)
49.0ms	(- (pow 1.0 3) (pow (cos x) 3))
18.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	305	520
1	1173	493
2	5002	473

prune269.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (pow (cos x) 3) 3))
0.4b	(pow (pow (cos x) 3) 3)
1.5b	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
1.7b	(- 1.0 (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
71×	`unpow-prod-down` `cube-prod`
70×	`cbrt-prod`
45×	`difference-of-squares`
29×	`sqr-pow`
22×	`*-un-lft-identity`
18×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`add-exp-log` `cube-mult` `unpow3`
5×	`add-cbrt-cube`
4×	`pow1` `pow-exp`
3×	`pow-unpow`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-pow` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 153

Calls

4 calls:

4.0ms	(cbrt (pow (pow (cos x) 3) 3))
4.0ms	(pow (pow (cos x) 3) 3)
35.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
3.0ms	(- 1.0 (cos x))

series148.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (pow (pow (cos x) 3) 3))
52.0ms	(pow (pow (cos x) 3) 3)
49.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
18.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	413	1106
1	1408	1052
2	5001	1041

prune308.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes69.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.6b

bsearch83.0ms

Steps

Iters	Range		Point
10	4.127477794865454e-14	0.2287861600326909	0.031178573100862143
7	-0.03925098124715615	-0.001787912586083248	-0.031199090863055844

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	55
1	51	55

end0.0ms

sample1.6s

Algorithm

intervals

Results

719.0ms	1562×	body	2560	valid
312.0ms	1318×	body	1280	valid
204.0ms	1405×	body	640	valid
94.0ms	918×	body	320	valid
74.0ms	2340×	body	80	valid
38.0ms	457×	body	160	valid