Details

sample96.0ms

Algorithm

intervals

Results

44.0ms	108×	body	1280	valid
23.0ms	26×	body	2560	valid
12.0ms	52×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	8×	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: 35.9b

localize13.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (sin (+ x eps)) (sin x))
3.0b	(sin (+ x eps))

rewrite49.0ms

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:

39.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series56.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(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

prune79.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.2b	(+ (* (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:

14.0ms	(- (* (cos x) (sin eps)) (sin x))
11.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (cos eps))
29.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* (cos x) (sin eps)) (sin x))
43.0ms	(* (cos x) (sin eps))
39.0ms	(* (sin x) (cos eps))
104.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

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

prune227.0ms

Pruning

9 alts after pruning (9 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))
1.5b	(- (cos eps) 1)

rewrite68.0ms

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:

20.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
29.0ms	(* (sin x) (- (cos eps) 1))
7.0ms	(- (cos eps) 1)

series210.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
39.0ms	(* (cos x) (sin eps))
43.0ms	(* (sin x) (- (cos eps) 1))
21.0ms	(- (cos eps) 1)

simplify42.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune236.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos eps) (+ (cos eps) 1))
0.3b	(pow (cos eps) 3)
0.4b	(+ (cos eps) 1)
1.3b	(- (pow (cos eps) 3) 1)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-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` `associate-r` `sqr-pow`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

24.0ms	(* (cos eps) (+ (cos eps) 1))
3.0ms	(pow (cos eps) 3)
6.0ms	(+ (cos eps) 1)
17.0ms	(- (pow (cos eps) 3) 1)

series106.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (cos eps) (+ (cos eps) 1))
31.0ms	(pow (cos eps) 3)
9.0ms	(+ (cos eps) 1)
43.0ms	(- (pow (cos eps) 3) 1)

simplify60.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	307	461
1	1609	414
2	5001	414

prune262.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes99.0ms

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	25	15
1	25	15

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3274×	body	1280	valid
566.0ms	627×	body	2560	valid
450.0ms	1856×	body	640	valid
122.0ms	748×	body	320	valid
62.0ms	1143×	body	80	valid
37.0ms	352×	body	160	valid