Details

sample95.0ms

Algorithm

intervals

Results

45.0ms	108×	body	1280	valid
22.0ms	25×	body	2560	valid
12.0ms	54×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	11×	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: 34.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
2.2b	(sin (+ x eps))

rewrite25.0ms

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:

20.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series67.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify142.0ms

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

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

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))
0.2b	(* (sin x) (cos eps))
3.5b	(- (+ (* (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))

series290.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
42.0ms	(* (cos x) (sin eps))
47.0ms	(* (sin x) (cos eps))
111.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

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

prune227.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

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))
1.0b	(- (cos eps) 1)

rewrite31.0ms

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)))
4.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (- (cos eps) 1))
3.0ms	(- (cos eps) 1)

series222.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
44.0ms	(* (sin x) (- (cos eps) 1))
19.0ms	(- (cos eps) 1)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	333	552
1	1271	503
2	5001	501

prune260.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos eps) (cos eps))
0.4b	(+ (* 1 1) (* (cos eps) 1))
0.4b	(pow (cos eps) 3)
0.8b	(- (pow (cos eps) 3) (pow 1 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
24×	`difference-of-squares`
21×	`unpow-prod-down` `cube-prod`
12×	`pow1`
11×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-lft-out--`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`cube-mult`
1×	`difference-cubes` `+-commutative` `pow2` `pow-to-exp` `sub-neg` `sqr-cos` `distribute-rgt-out` `flip3--` `pow-pow` `flip3-+` `pow-plus` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos eps) (cos eps))
3.0ms	(+ (* 1 1) (* (cos eps) 1))
1.0ms	(pow (cos eps) 3)
16.0ms	(- (pow (cos eps) 3) (pow 1 3))

series109.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (cos eps) (cos eps))
11.0ms	(+ (* 1 1) (* (cos eps) 1))
28.0ms	(pow (cos eps) 3)
53.0ms	(- (pow (cos eps) 3) (pow 1 3))

simplify73.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	387	551
1	1757	480
2	5002	447

prune328.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes103.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	37	17
2	37	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3314×	body	1280	valid
547.0ms	618×	body	2560	valid
453.0ms	1849×	body	640	valid
113.0ms	704×	body	320	valid
68.0ms	1116×	body	80	valid
43.0ms	399×	body	160	valid