Details

sample105.0ms

Algorithm

intervals

Results

53.0ms	111×	body	1280	valid
17.0ms	19×	body	2560	valid
15.0ms	59×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	27×	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: 39.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ 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` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

simplify135.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	133	175
1	301	165
2	937	164
3	3445	164
4	5001	164

prune60.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 14.9b

Counts

31 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
2.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin 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`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

6.0ms	(* (cos x) (sin eps))
5.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms	(* (sin x) (cos eps))
8.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series54.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (sin eps))
16.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
8.0ms	(* (sin x) (cos eps))
21.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	554
2	5001	543

prune105.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 0.1b

Counts

83 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.8b	(- (cos eps) 1)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
8.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
7.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(- (cos eps) 1)

series42.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (sin eps))
20.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
10.0ms	(* (sin x) (- (cos eps) 1))
3.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	337	546
1	1279	498
2	5001	497

prune133.0ms

Filtered

55 candidates to 89 candidates (-61.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Merged error: 0.0b

Counts

97 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(pow (* (sin x) (- (cos eps) 1)) 3)
0.8b	(- (cos eps) 1)
9.9b	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

7.0ms	(* (sin x) (- (cos eps) 1))
6.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
4.0ms	(- (cos eps) 1)
6.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

series42.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin x) (- (cos eps) 1))
22.0ms	(pow (* (sin x) (- (cos eps) 1)) 3)
3.0ms	(- (cos eps) 1)
9.0ms	(cbrt (pow (* (sin x) (- (cos eps) 1)) 3))

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	308	549
1	1407	527
2	5002	525

prune106.0ms

Filtered

63 candidates to 99 candidates (-57.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	98	15	113

Merged error: 0.0b

Counts

113 → 15

regimes182.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3292×	body	1280	valid
589.0ms	642×	body	2560	valid
486.0ms	1867×	body	640	valid
132.0ms	736×	body	320	valid
62.0ms	1127×	body	80	valid
39.0ms	336×	body	160	valid

Details

sample105.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series12.0ms

simplify135.0ms

prune60.0ms

localize13.0ms

rewrite25.0ms

series54.0ms

simplify38.0ms

prune105.0ms

localize14.0ms

rewrite24.0ms

series42.0ms

simplify43.0ms

prune133.0ms

localize16.0ms

rewrite25.0ms

series42.0ms

simplify48.0ms

prune106.0ms

regimes182.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.1s

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