Details

sample97.0ms

Algorithm

intervals

Results

54.0ms	134×	body	1280	valid
16.0ms	67×	body	640	valid
12.0ms	13×	body	2560	valid
4.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	6×	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: 37.4b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify107.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune81.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.0b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite36.0ms

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`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
3.0ms	(* (cos x) (cos eps))
6.0ms	(* (sin x) (sin eps))
20.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series278.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
37.0ms	(* (cos x) (cos eps))
44.0ms	(* (sin x) (sin eps))
120.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify109.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4488	583
3	5001	583

prune227.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.0b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
3.1b	(log (exp (* (sin x) (sin eps))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`pow1` `add-cube-cbrt` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`log-prod` `diff-log` `log-pow`
2×	`sub-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `cos-mult` `flip--` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
4.0ms	(* (sin x) (sin eps))
29.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
1.0ms	(log (exp (* (sin x) (sin eps))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (cos eps))
42.0ms	(* (sin x) (sin eps))
126.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
43.0ms	(log (exp (* (sin x) (sin eps))))

simplify84.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	264	602
1	857	524
2	3421	510
3	5002	510

prune259.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.5b	(pow (* (cos x) (cos eps)) 3)
7.1b	(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
41×	`cos-mult`
40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`times-frac`
27×	`frac-add`
23×	`associate-/r/`
21×	`add-exp-log` `add-cbrt-cube`
20×	`sin-mult`
19×	`add-cube-cbrt`
18×	`pow-prod-down` `difference-of-squares`
17×	`frac-times` `associate-*r/` `sqr-pow`
11×	`associate-*l/`
9×	`prod-exp` `cbrt-unprod` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`cube-div` `distribute-lft-out--`
4×	`difference-cubes` `pow-sqr` `pow-prod-up` `associate-/l/`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `pow-pow` `pow-plus` `div-sub` `pow-exp` `flip--` `rem-cube-cbrt`
1×	`cbrt-undiv` `associate--l-` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `frac-2neg` `diff-log` `unpow3` `cube-prod` `swap-sqr` `div-exp` `associate-r` `associate-l` `clear-num` `*-commutative` `frac-sub` `div-inv` `sub-div`

Counts

4 → 155

Calls

4 calls:

50.0ms	(/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))
13.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
3.0ms	(pow (* (cos x) (cos eps)) 3)
263.0ms	(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

series1.1s

Counts

4 → 12

Calls

4 calls:

352.0ms	(/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))
52.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
61.0ms	(pow (* (cos x) (cos eps)) 3)
658.0ms	(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

simplify64.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1072	4866
1	5001	4706

prune594.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.1b

regimes196.0ms

Accuracy

83.4% (1.6b remaining)

Error of 16.5b against oracle of 14.9b and baseline of 24.7b

bsearch104.0ms

Steps

Iters	Range		Point
8	1.7085304078792323e-11	2.2698285208946172e-07	3.243542393555102e-08
6	-3.2357594850027844e-11	-7.532736069286782e-12	-3.188545179154075e-11

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	37
1	47	37

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4474×	body	1280	valid
610.0ms	663×	body	2560	valid
457.0ms	1831×	body	640	valid
114.0ms	667×	body	320	valid
33.0ms	277×	body	160	valid
6.0ms	88×	body	80	valid