Details

sample177.0ms

Algorithm

intervals

Results

90.0ms	87×	body	1280	valid
41.0ms	53×	body	640	valid
11.0ms	81×	body	80	valid
10.0ms	22×	body	320	valid
4.0ms	13×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	74	30
1	193	27
2	704	27
3	2994	27
4	5001	27

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
123×	`prod-diff`
119×	`*-un-lft-identity`
109×	`add-cube-cbrt`
56×	`times-frac`
52×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
12×	`associate-r` `associate-l`
9×	`flip3--` `flip--`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
6×	`sub-neg` `fma-neg` `div-inv`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u`
3×	`unswap-sqr`
2×	`diff-log` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 234

Calls

4 calls:

14.0ms	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series242.0ms

Counts

4 → 10

Calls

4 calls:

98.0ms	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
87.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
57.0ms	(- (cos x) (cos y))

simplify123.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1079	4683
1	4343	3463
2	5001	3456

prune821.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.3b	(- (cos x) (cos y))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`cbrt-prod` `prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt 16.0)
1.0ms	(cbrt 16.0)
1.0ms	(cbrt 16.0)
5.0ms	(- (cos x) (cos y))

series51.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
51.0ms	(- (cos x) (cos y))

simplify128.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	257	567
1	748	462
2	3823	444
3	5001	434

prune562.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.5b	(+ (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`prod-diff`
95×	`*-un-lft-identity`
89×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `div-inv`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `fma-neg` `cos-mult` `log1p-expm1-u`
3×	`flip3--` `fma-def` `flip--`
2×	`sqr-cos` `diff-log` `associate-*r/` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-cos` `pow-prod-down` `prod-exp` `associate--l+` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r+` `sub-div`

Counts

4 → 188

Calls

4 calls:

14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms	(+ (cos x) (cos y))
5.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

series243.0ms

Counts

4 → 10

Calls

4 calls:

92.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
39.0ms	(+ (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))
111.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

simplify101.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	949	3669
1	3508	2700
2	5001	2436

prune759.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))
1.3b	(- (cos x) (cos y))
1.3b	(- (cos x) (cos y))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
45×	`prod-diff`
38×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
10×	`sqrt-prod`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`diff-cos`

Counts

4 → 125

Calls

4 calls:

5.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))
5.0ms	(- (cos x) (cos y))
5.0ms	(- (cos x) (cos y))

series164.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
52.0ms	(- (cos x) (cos y))
59.0ms	(- (cos x) (cos y))
53.0ms	(- (cos x) (cos y))

simplify143.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	312	1276
1	887	853
2	4559	798
3	5001	752

prune869.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes208.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	56
1	60	56
2	60	56

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.0s	2722×	body	1280	valid
1.3s	1861×	body	640	valid
352.0ms	2355×	body	80	valid
338.0ms	707×	body	320	valid
108.0ms	355×	body	160	valid