Details

sample109.0ms

Algorithm

intervals

Results

50.0ms	105×	body	1280	valid
28.0ms	30×	body	2560	valid
12.0ms	44×	body	640	valid
6.0ms	32×	body	320	valid
2.0ms	14×	body	160	valid
2.0ms	31×	body	80	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: 40.8b

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
4.2b	(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))
5.0ms	(sin (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(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

prune78.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.0b

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))
3.1b	(- (+ (* (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))
21.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series286.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
43.0ms	(* (sin x) (cos eps))
109.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

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

prune224.0ms

Pruning

12 alts after pruning (12 fresh and 0 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	(* (sin x) (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
0.9b	(- (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)))
11.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
3.0ms	(- (cos eps) 1)

series230.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
45.0ms	(* (sin x) (- (cos eps) 1))
47.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (39.0ms)

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

prune245.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
48×	`times-frac`
40×	`difference-of-squares`
28×	`add-cube-cbrt`
20×	`difference-of-sqr-1`
18×	`unpow-prod-down` `cube-prod`
16×	`associate-/l*` `sqr-pow`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 144

Calls

4 calls:

34.0ms	(/ (- (pow (cos eps) 3) 1) (+ (* (cos eps) (+ (cos eps) 1)) 1))
3.0ms	(+ (cos eps) 1)
1.0ms	(pow (cos eps) 3)
10.0ms	(- (pow (cos eps) 3) 1)

series193.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (pow (cos eps) 3) 1) (+ (* (cos eps) (+ (cos eps) 1)) 1))
10.0ms	(+ (cos eps) 1)
28.0ms	(pow (cos eps) 3)
52.0ms	(- (pow (cos eps) 3) 1)

simplify87.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	485	1779
1	2276	1691
2	5002	1632

prune378.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

regimes134.0ms

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

sample3.1s

Algorithm

intervals

Results

1.5s	3335×	body	1280	valid
603.0ms	627×	body	2560	valid
523.0ms	1811×	body	640	valid
145.0ms	768×	body	320	valid
66.0ms	1119×	body	80	valid
47.0ms	340×	body	160	valid