Details

sample94.0ms

Algorithm

intervals

Results

46.0ms	111×	body	1280	valid
19.0ms	21×	body	2560	valid
13.0ms	55×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	9×	body	160	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: 36.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.4b	(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))

series18.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

simplify136.0ms

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

prune55.0ms

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: 14.1b

Counts

31 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
8.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (cos eps))
21.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune110.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 0.2b

Counts

83 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
2.3b	(- (cos eps) 1)

rewrite25.0ms

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:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
9.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (- (cos eps) 1))
3.0ms	(- (cos eps) 1)

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	337	546
1	1279	498
2	5002	497

prune132.0ms

Filtered

54 candidates to 89 candidates (-64.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	86	13	99

Merged error: 0.0b

Counts

99 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (- (* (cos eps) (cos eps)) 1) (+ (cos eps) 1)))
0.2b	(* (cos eps) (cos eps))
0.3b	(+ (cos eps) 1)
2.3b	(- (* (cos eps) (cos eps)) 1)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
33×	`associate-r`
32×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`distribute-lft-out`
6×	`associate-l`
5×	`difference-of-sqr-1`
3×	`swap-sqr` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`sqr-cos` `flip3-+` `pow-prod-down` `sub-1-cos` `associate-/r/` `*-commutative` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `associate-*r/` `distribute-frac-neg` `div-exp` `associate--l+` `sum-log` `pow-sqr` `cos-mult` `pow-prod-up` `distribute-rgt-neg-out` `flip--` `div-inv`

Counts

4 → 106

Calls

4 calls:

14.0ms	(* (sin x) (/ (- (* (cos eps) (cos eps)) 1) (+ (cos eps) 1)))
4.0ms	(* (cos eps) (cos eps))
4.0ms	(+ (cos eps) 1)
5.0ms	(- (* (cos eps) (cos eps)) 1)

series37.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (sin x) (/ (- (* (cos eps) (cos eps)) 1) (+ (cos eps) 1)))
3.0ms	(* (cos eps) (cos eps))
2.0ms	(+ (cos eps) 1)
5.0ms	(- (* (cos eps) (cos eps)) 1)

simplify67.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	467	833
1	2375	717
2	5001	711

prune125.0ms

Filtered

81 candidates to 118 candidates (-45.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	119	12	131

Merged error: 0.0b

Counts

131 → 12

regimes151.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	34	11
2	36	11
3	36	11

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3342×	body	1280	valid
595.0ms	658×	body	2560	valid
460.0ms	1787×	body	640	valid
123.0ms	763×	body	320	valid
59.0ms	1084×	body	80	valid
41.0ms	366×	body	160	valid

Details

sample94.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series18.0ms

simplify136.0ms

prune55.0ms

localize14.0ms

rewrite23.0ms

series57.0ms

simplify40.0ms

prune110.0ms

localize14.0ms

rewrite25.0ms

series40.0ms

simplify46.0ms

prune132.0ms

localize17.0ms

rewrite30.0ms

series37.0ms

simplify67.0ms

prune125.0ms

regimes151.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.9s

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