Details

sample84.0ms

Algorithm

intervals

Results

43.0ms	141×	body	1280	valid
15.0ms	19×	body	2560	valid
11.0ms	57×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	4×	body	80	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: 38.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

19.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series72.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify110.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune88.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite111.0ms

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`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

12.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
70.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series321.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (cos eps))
87.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
52.0ms	(* (sin x) (sin eps))
138.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune253.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
1.8b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

10.0ms	(* (cos eps) (cos x))
12.0ms	(+ (* (sin x) (sin eps)) (cos x))
12.0ms	(* (sin x) (sin eps))
30.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos eps) (cos x))
61.0ms	(+ (* (sin x) (sin eps)) (cos x))
49.0ms	(* (sin x) (sin eps))
153.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	329	606
1	1247	575
2	5002	567

prune263.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
1.8b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
25.8b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

12.0ms	(* (sin x) (sin eps))
9.0ms	(pow (* (sin x) (sin eps)) 3)
87.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
4.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series316.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin x) (sin eps))
74.0ms	(pow (* (sin x) (sin eps)) 3)
141.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
52.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	293	634
1	1142	580
2	5001	565

prune243.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.0b

regimes222.0ms

Accuracy

86.5% (1.3b remaining)

Error of 15.4b against oracle of 14.1b and baseline of 24.0b

bsearch130.0ms

Steps

Iters	Range		Point
8	2.6312679778022526e-07	0.0004221944073348045	3.8682592957457557e-07
10	-4.57643111655563e-14	-8.576014553851025e-27	-4.51775150735862e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	53
1	49	53

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	4441×	body	1280	valid
512.0ms	615×	body	2560	valid
365.0ms	1907×	body	640	valid
97.0ms	669×	body	320	valid
26.0ms	290×	body	160	valid
4.0ms	78×	body	80	valid