Details

sample104.0ms

Algorithm

intervals

Results

53.0ms	131×	body	1280	valid
21.0ms	24×	body	2560	valid
16.0ms	69×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	4×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 41.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite10.0ms

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune74.0ms

Filtered

30 candidates to 23 candidates (23.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	18	12	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	12	31

Merged error: 16.7b

Counts

31 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.9b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite23.0ms

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))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
11.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5001	567

prune142.0ms

Filtered

77 candidates to 53 candidates (31.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	63	14	77
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	70	19	89

Merged error: 16.4b

Counts

89 → 19

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

rewrite23.0ms

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)))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
11.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify112.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4487	582
3	5002	582

prune134.0ms

Filtered

82 candidates to 57 candidates (30.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	82	19	101

Merged error: 16.4b

Counts

101 → 19

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.9b	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
28.4b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `diff-log` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cos-mult` `frac-sub` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `flip3-+` `pow1/3` `sum-log` `*-commutative` `flip--` `rem-cbrt-cube` `flip-+` `associate--r+` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
6.0ms	(pow (* (sin x) (sin eps)) 3)
10.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
3.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series56.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin x) (sin eps))
15.0ms	(pow (* (sin x) (sin eps)) 3)
23.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
9.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	374	684
1	1626	609
2	5001	596

prune90.0ms

Filtered

88 candidates to 59 candidates (33.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	88	19	107

Merged error: 16.4b

Counts

107 → 19

regimes265.0ms

Accuracy

84.3% (1.6b remaining)

Error of 16.3b against oracle of 14.7b and baseline of 24.9b

bsearch61.0ms

Steps

Iters	Range		Point
3	3.067213227647497e-11	3.9322115533895686e-11	3.445649995159653e-11
10	-47.28095399221356	-5.329134551900152e-18	-2.7367017419380556e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	17
1	36	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4393×	body	1280	valid
533.0ms	622×	body	2560	valid
429.0ms	1919×	body	640	valid
106.0ms	669×	body	320	valid
32.0ms	308×	body	160	valid
5.0ms	89×	body	80	valid

Details

sample104.0ms

simplify6.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify112.0ms

prune74.0ms

localize17.0ms

rewrite23.0ms

series51.0ms

simplify42.0ms

prune142.0ms

localize15.0ms

rewrite23.0ms

series58.0ms

simplify112.0ms

prune134.0ms

localize17.0ms

rewrite26.0ms

series56.0ms

simplify50.0ms

prune90.0ms

regimes265.0ms

bsearch61.0ms

simplify2.0ms

end0.0ms

sample2.9s

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