Details

sample116.0ms

Algorithm

intervals

Results

48.0ms	96×	body	1280	valid
30.0ms	31×	body	2560	valid
20.0ms	64×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	31×	body	80	valid
2.0ms	13×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
4.8b	(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))

series13.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

simplify138.0ms

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

prune184.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.5b

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))
0.1b	(* (sin x) (cos eps))
2.3b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin 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`
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))
20.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series57.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
9.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (cos eps))
22.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune576.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

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))
2.0b	(- (cos eps) 1)

rewrite30.0ms

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
9.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (- (cos eps) 1))
3.0ms	(- (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

prune695.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
2.0b	(- (cos eps) 1)
3.0b	(log (exp (* (sin x) (- (cos eps) 1))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (- (cos eps) 1))
3.0ms	(- (cos eps) 1)
2.0ms	(log (exp (* (sin x) (- (cos eps) 1))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (- (cos eps) 1))
2.0ms	(- (cos eps) 1)
11.0ms	(log (exp (* (sin x) (- (cos eps) 1))))

simplify125.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	282	482
1	1029	426
2	4519	425
3	5001	423

prune645.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes321.0ms

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	21	10
1	23	10
2	23	10

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.7s	3358×	body	1280	valid
703.0ms	1804×	body	640	valid
661.0ms	667×	body	2560	valid
176.0ms	783×	body	320	valid
76.0ms	1039×	body	80	valid
50.0ms	349×	body	160	valid