Details

analyze2.0ms

Algorithm: search

sample99.0ms

Algorithm

intervals

Results

51.0ms	140×	body	1280	valid
21.0ms	23×	body	2560	valid
12.0ms	49×	body	640	valid
5.0ms	29×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	3×	body	80	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

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: 35.1b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite18.0ms

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))
10.0ms	(cos (+ x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify110.0ms

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	5001	164

prune74.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	19	11	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	11	31

Merged error: 12.0b

Counts

31 → 11

localize14.0ms

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))
2.1b	(- (- (* (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))
4.0ms	(- (* (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)))
9.0ms	(* (sin x) (sin eps))
25.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify113.0ms

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

prune136.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	75	18	93

Merged error: 12.0b

Counts

93 → 18

localize14.0ms

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))
2.1b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite24.0ms

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
10.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	574
2	5002	565

prune127.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	7	10	17
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Merged error: 11.9b

Counts

95 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
0.2b	(* (sin x) (sin eps))
2.1b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.6b	(log (exp (* (sin x) (sin eps))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin 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))))

simplify82.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	266	688
1	792	625
2	3018	609
3	5001	609

prune71.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	79	15	94

Merged error: 11.9b

Counts

94 → 15

regimes223.0ms

Accuracy

77.9% (2.1b remaining)

Error of 16.7b against oracle of 14.5b and baseline of 24.3b

bsearch114.0ms

Steps

Iters	Range		Point
8	2.6929718420220114e-44	8.888680649181726e-41	8.783440420268414e-41
10	-172119.39769644174	-1.0972913478401585e-07	-1.5914380768193874e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

analyze1.0ms

Algorithm: search

sample3.1s

Algorithm

intervals

Results

1.8s	4511×	body	1280	valid
606.0ms	649×	body	2560	valid
426.0ms	1753×	body	640	valid
111.0ms	685×	body	320	valid
35.0ms	312×	body	160	valid
5.0ms	90×	body	80	valid

Details

analyze2.0ms

sample99.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite18.0ms

series14.0ms

simplify110.0ms

prune74.0ms

localize14.0ms

rewrite23.0ms

series58.0ms

simplify113.0ms

prune136.0ms

localize14.0ms

rewrite24.0ms

series49.0ms

simplify41.0ms

prune127.0ms

localize17.0ms

rewrite23.0ms

series56.0ms

simplify82.0ms

prune71.0ms

regimes223.0ms

bsearch114.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample3.1s

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