Details

sample101.0ms

Algorithm

intervals

Results

41.0ms	92×	body	1280	valid
23.0ms	23×	body	2560	valid
20.0ms	73×	body	640	valid
4.0ms	20×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	12×	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: 39.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite30.0ms

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:

25.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series56.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify136.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

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

prune82.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.1b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite32.0ms

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

series281.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin x) (cos eps))
44.0ms	(* (cos x) (sin eps))
87.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
108.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune210.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
1.4b	(- (cos eps) 1)

rewrite28.0ms

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

series216.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
48.0ms	(* (sin x) (- (cos eps) 1))
41.0ms	(* (cos x) (sin eps))
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

prune229.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.2b	(* (cos eps) (cos eps))
0.4b	(+ (cos eps) 1)
1.6b	(- (* (cos eps) (cos eps)) 1)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`pow1` `*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-r` `associate-l`
3×	`swap-sqr`
2×	`sqr-cos` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `pow2` `sub-neg` `flip3--` `flip3-+` `pow-plus` `diff-log` `difference-of-sqr-1` `associate--l+` `sum-log` `sub-1-cos` `pow-sqr` `cos-mult` `pow-prod-up` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
4.0ms	(* (cos eps) (cos eps))
3.0ms	(+ (cos eps) 1)
6.0ms	(- (* (cos eps) (cos eps)) 1)

series103.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (sin eps))
16.0ms	(* (cos eps) (cos eps))
9.0ms	(+ (cos eps) 1)
32.0ms	(- (* (cos eps) (cos eps)) 1)

simplify40.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	310	375
1	1267	322
2	5001	317

prune229.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	31	13
2	32	13
3	32	13

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	3263×	body	1280	valid
631.0ms	660×	body	2560	valid
535.0ms	1800×	body	640	valid
166.0ms	793×	body	320	valid
80.0ms	1128×	body	80	valid
54.0ms	356×	body	160	valid