Details

sample93.0ms

Algorithm

intervals

Results

44.0ms	110×	body	1280	valid
21.0ms	24×	body	2560	valid
13.0ms	56×	body	640	valid
5.0ms	32×	body	320	valid
1.0ms	27×	body	80	valid
1.0ms	7×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.9b	(sin (+ x eps))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

26.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series58.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify137.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune87.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.8b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

4.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
18.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (cos x) (sin eps))
49.0ms	(* (sin x) (cos eps))
114.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify45.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543

prune218.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
1.3b	(- (cos eps) 1)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

7.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
7.0ms	(* (cos x) (sin eps))
12.0ms	(* (sin x) (- (cos eps) 1))
3.0ms	(- (cos eps) 1)

series229.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
49.0ms	(* (cos x) (sin eps))
47.0ms	(* (sin x) (- (cos eps) 1))
20.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune239.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (- (cos eps) 1))
0.3b	(pow (* (sin x) (- (cos eps) 1)) 3)
1.3b	(- (cos eps) 1)
9.2b	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
7×	`associate-r`
6×	`associate-*r/` `add-log-exp`
4×	`cube-div` `flip3--` `flip--` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `associate-l`
2×	`distribute-rgt-in` `cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `distribute-lft-in` `unpow3` `difference-of-sqr-1` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `diff-log` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

12.0ms	(* (sin x) (- (cos eps) 1))
6.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
3.0ms	(- (cos eps) 1)
3.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

series253.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin x) (- (cos eps) 1))
131.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
24.0ms	(- (cos eps) 1)
47.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	307	551
1	1406	529
2	5001	527

prune281.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes101.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3333×	body	1280	valid
594.0ms	666×	body	2560	valid
428.0ms	1791×	body	640	valid
131.0ms	779×	body	320	valid
54.0ms	1083×	body	80	valid
36.0ms	348×	body	160	valid