Details

sample101.0ms

Algorithm

intervals

Results

48.0ms	141×	body	1280	valid
16.0ms	19×	body	2560	valid
13.0ms	57×	body	640	valid
6.0ms	7×	body	160	valid
5.0ms	32×	body	320	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 39.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
4.0b	(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))

simplify106.0ms

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

prune80.0ms

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: 13.0b

Counts

31 → 12

localize14.0ms

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))
3.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite25.0ms

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)))
4.0ms	(* (cos x) (cos eps))
6.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series54.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
8.0ms	(* (cos x) (cos eps))
9.0ms	(* (sin x) (sin eps))
22.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify111.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4488	582
3	5001	582

prune143.0ms

Filtered

82 candidates to 56 candidates (31.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	78	16	94

Merged error: 12.9b

Counts

94 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
3.2b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
3.7b	(log (exp (* (sin x) (sin eps))))

rewrite21.0ms

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))
8.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.0ms	(log (exp (* (sin x) (sin eps))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
9.0ms	(* (sin x) (sin eps))
22.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
9.0ms	(log (exp (* (sin x) (sin eps))))

simplify86.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	264	602
1	857	523
2	3421	509
3	5001	509

prune133.0ms

Filtered

82 candidates to 54 candidates (34.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	81	17	98

Merged error: 12.9b

Counts

98 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
3.2b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
25.5b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (sin x) (sin eps))
4.0ms	(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))

series57.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin x) (sin eps))
17.0ms	(pow (* (sin x) (sin eps)) 3)
22.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
9.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	293	634
1	1142	580
2	5001	565

prune94.0ms

Filtered

90 candidates to 58 candidates (35.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	90	17	107

Merged error: 12.9b

Counts

107 → 17

regimes247.0ms

Accuracy

84.3% (1.5b remaining)

Error of 16.2b against oracle of 14.7b and baseline of 24.5b

bsearch56.0ms

Steps

Iters	Range		Point
6	1.1392916890431884e-14	1.5662135508538757e-13	1.5326915168128645e-13
7	-1.1374190914131416e-05	-4.610592636916848e-08	-8.994342410132382e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	50
1	47	50
2	47	50

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	4550×	body	1280	valid
512.0ms	594×	body	2560	valid
415.0ms	1834×	body	640	valid
103.0ms	682×	body	320	valid
28.0ms	269×	body	160	valid
4.0ms	71×	body	80	valid

Details

sample101.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series14.0ms

simplify106.0ms

prune80.0ms

localize14.0ms

rewrite25.0ms

series54.0ms

simplify111.0ms

prune143.0ms

localize17.0ms

rewrite21.0ms

series48.0ms

simplify86.0ms

prune133.0ms

localize17.0ms

rewrite23.0ms

series57.0ms

simplify40.0ms

prune94.0ms

regimes247.0ms

bsearch56.0ms

simplify2.0ms

end0.0ms

sample3.0s

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