Details

sample92.0ms

Algorithm

intervals

Results

52.0ms	147×	body	1280	valid
14.0ms	64×	body	640	valid
13.0ms	15×	body	2560	valid
3.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	3×	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: 37.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite11.0ms

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:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series69.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

simplify112.0ms

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

prune95.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.5b

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))
1.5b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite34.0ms

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:

3.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
20.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series302.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
82.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
132.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify115.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (32.0ms)

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

prune245.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* 1 (* (cos x) (cos eps))) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.5b	(- (- (* 1 (* (cos x) (cos eps))) (* (sin x) (sin eps))) (cos x))

rewrite67.0ms

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--` `associate-r/` `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:

3.0ms	(* (cos x) (cos eps))
9.0ms	(- (* 1 (* (cos x) (cos eps))) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
46.0ms	(- (- (* 1 (* (cos x) (cos eps))) (* (sin x) (sin eps))) (cos x))

series295.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos eps))
77.0ms	(- (* 1 (* (cos x) (cos eps))) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
127.0ms	(- (- (* 1 (* (cos x) (cos eps))) (* (sin x) (sin eps))) (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	328	666
1	1177	621
2	5001	600

prune255.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
1.5b	(- (- (* 1 (* (cos x) (cos eps))) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
28.9b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-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` `distribute-lft-out--`
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` `difference-of-squares` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

4.0ms	(* (sin x) (sin eps))
3.0ms	(pow (* (sin x) (sin eps)) 3)
69.0ms	(- (- (* 1 (* (cos x) (cos eps))) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
2.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series293.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin x) (sin eps))
67.0ms	(pow (* (sin x) (sin eps)) 3)
128.0ms	(- (- (* 1 (* (cos x) (cos eps))) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
48.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	303	664
1	1197	602
2	5001	584

prune252.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.4b

regimes144.0ms

Accuracy

72.4% (2.7b remaining)

Error of 17.0b against oracle of 14.3b and baseline of 24.2b

bsearch141.0ms

Steps

Iters	Range		Point
9	3.3093313890471513e-56	3.6463009244439584e-50	3.6043668904446245e-50
8	-1.495443386135692e-28	-3.1745033099698537e-31	-1.4779477312146429e-28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	20
1	44	20
2	44	20

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4459×	body	1280	valid
564.0ms	656×	body	2560	valid
437.0ms	1856×	body	640	valid
110.0ms	691×	body	320	valid
32.0ms	263×	body	160	valid
5.0ms	75×	body	80	valid