Details

sample95.0ms

Algorithm

intervals

Results

49.0ms	139×	body	1280	valid
18.0ms	20×	body	2560	valid
16.0ms	72×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	1×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.2b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (cos (+ x eps)) (cos x))
3.8b	(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:

6.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify115.0ms

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

prune294.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	20	10	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	10	31

Merged error: 15.2b

Counts

31 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite29.0ms

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:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
13.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series287.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
79.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
123.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify119.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune230.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	67	15	82
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	73	19	92

Merged error: 15.0b

Counts

92 → 19

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.4b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite26.0ms

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

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
6.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos x) (cos eps))
53.0ms	(+ (* (sin x) (sin eps)) (cos x))
43.0ms	(* (sin x) (sin eps))
127.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune225.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	77	19	96

Merged error: 14.9b

Counts

96 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.3b	(* (cos x) (cos x))
2.9b	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-sqr` `pow-prod-up` `sin-mult`
4×	`swap-sqr`
3×	`pow-plus` `*-commutative`
2×	`pow2` `cos-mult` `unswap-sqr`
1×	`frac-times` `sub-neg` `sqr-cos` `flip3--` `diff-log` `div-sub` `associate-r/` `associate-l/` `frac-sub` `flip--` `associate--r-`

Counts

4 → 97

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
9.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
5.0ms	(* (cos x) (cos x))
15.0ms	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin x) (sin eps))
50.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
20.0ms	(* (cos x) (cos x))
289.0ms	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	397	967
1	1718	824
2	5001	771

prune215.0ms

Filtered

109 candidates to 60 candidates (55.0%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	108	20	128

Merged error: 14.9b

Counts

128 → 20

regimes210.0ms

Accuracy

70.3% (2.9b remaining)

Error of 17.8b against oracle of 14.8b and baseline of 24.7b

bsearch127.0ms

Steps

Iters	Range		Point
7	1.649892455878812e-57	3.6571079890251755e-55	3.557363453189356e-55
9	-8.961399793617711e-18	-7.949661431150896e-23	-8.847627512437046e-18

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	53
1	47	53

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4479×	body	1280	valid
557.0ms	637×	body	2560	valid
416.0ms	1851×	body	640	valid
118.0ms	681×	body	320	valid
34.0ms	277×	body	160	valid
4.0ms	75×	body	80	valid