Details

sample104.0ms

Algorithm

intervals

Results

47.0ms	118×	body	1280	valid
28.0ms	28×	body	2560	valid
13.0ms	51×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	25×	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: 40.5b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.5b	(sin (+ x eps))

rewrite26.0ms

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:

21.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify139.0ms

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

prune80.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.2b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
3.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite36.0ms

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))
5.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
22.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series286.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin x) (cos eps))
86.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
43.0ms	(* (cos x) (sin eps))
111.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

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

prune221.0ms

Pruning

8 alts after pruning (8 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	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
1.8b	(- (cos eps) 1)

rewrite29.0ms

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:

8.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
12.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
3.0ms	(- (cos eps) 1)

series225.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
46.0ms	(* (sin x) (- (cos eps) 1))
46.0ms	(* (cos x) (sin eps))
19.0ms	(- (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

prune249.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.3b	(pow (cos eps) 3)
0.5b	(+ (cos eps) 1)
1.7b	(- (pow (cos eps) 3) 1)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
2.0ms	(pow (cos eps) 3)
3.0ms	(+ (cos eps) 1)
10.0ms	(- (pow (cos eps) 3) 1)

series135.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos x) (sin eps))
28.0ms	(pow (cos eps) 3)
9.0ms	(+ (cos eps) 1)
50.0ms	(- (pow (cos eps) 3) 1)

simplify49.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	317	420
1	1377	378
2	5001	362

prune255.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes150.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	17
1	27	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3196×	body	1280	valid
605.0ms	668×	body	2560	valid
452.0ms	1857×	body	640	valid
140.0ms	772×	body	320	valid
70.0ms	1132×	body	80	valid
41.0ms	375×	body	160	valid