Details

sample90.0ms

Algorithm

intervals

Results

48.0ms	113×	body	1280	valid
13.0ms	59×	body	640	valid
12.0ms	13×	body	2560	valid
3.0ms	22×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	14×	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: 36.4b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite54.0ms

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:

43.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series52.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- (sin (+ x eps)) (sin x))
17.0ms	(sin (+ x eps))

simplify140.0ms

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

prune81.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(- (* (cos x) (sin eps)) (sin x))
0.2b	(* (sin x) (cos eps))
2.8b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite66.0ms

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×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 66

Calls

4 calls:

11.0ms	(* (cos x) (sin eps))
12.0ms	(- (* (cos x) (sin eps)) (sin x))
13.0ms	(* (sin x) (cos eps))
29.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (sin eps))
54.0ms	(- (* (cos x) (sin eps)) (sin x))
42.0ms	(* (sin x) (cos eps))
100.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565

prune230.0ms

Pruning

13 alts after pruning (13 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	(* (cos x) (sin eps))
0.1b	(* (sin x) (- (cos eps) 1))
1.3b	(- (cos eps) 1)

rewrite67.0ms

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:

21.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
13.0ms	(* (cos x) (sin eps))
25.0ms	(* (sin x) (- (cos eps) 1))
7.0ms	(- (cos eps) 1)

series202.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
40.0ms	(* (cos x) (sin eps))
44.0ms	(* (sin x) (- (cos eps) 1))
18.0ms	(- (cos eps) 1)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune253.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (log (exp (- (cos eps) 1))))
1.3b	(- (cos eps) 1)
1.3b	(log (exp (- (cos eps) 1)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`log-pow`
15×	`log-prod`
14×	`exp-prod` `associate-r`
13×	`add-cube-cbrt`
10×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `exp-sum` `add-log-exp` `difference-of-squares`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sub-neg`
3×	`difference-of-sqr-1` `distribute-lft-out--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 92

Calls

4 calls:

11.0ms	(* (cos x) (sin eps))
57.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
7.0ms	(- (cos eps) 1)
15.0ms	(log (exp (- (cos eps) 1)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (sin eps))
41.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
19.0ms	(- (cos eps) 1)
18.0ms	(log (exp (- (cos eps) 1)))

simplify132.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	287	592
1	1044	493
2	4516	482
3	5002	482

prune270.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes137.0ms

Accuracy

0% (0.3b 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	15	10
1	15	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3434×	body	1280	valid
566.0ms	648×	body	2560	valid
435.0ms	1746×	body	640	valid
124.0ms	748×	body	320	valid
53.0ms	1086×	body	80	valid
35.0ms	338×	body	160	valid