Details

sample92.0ms

Algorithm

intervals

Results

50.0ms	144×	body	1280	valid
16.0ms	19×	body	2560	valid
11.0ms	51×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 41.1b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
5.1b	(cos (+ x eps))

rewrite11.0ms

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))

series72.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify114.0ms

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

prune100.0ms

Filtered

30 candidates to 23 candidates (76.7%)

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: 14.3b

Counts

31 → 11

localize15.0ms

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

rewrite25.0ms

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))
6.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
54.0ms	(+ (* (sin x) (sin eps)) (cos x))
48.0ms	(* (sin x) (sin eps))
131.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567

prune273.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	61	16	77
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	66	22	88

Merged error: 14.1b

Counts

88 → 22

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))
3.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite26.0ms

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))
6.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
9.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series307.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
87.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
135.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify122.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583

prune266.0ms

Filtered

82 candidates to 57 candidates (69.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	7	14	21
Picked	1	0	1
Done	0	0	0
Total	82	22	104

Merged error: 14.1b

Counts

104 → 22

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(pow (cos x) 3)
0.6b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
2.7b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
11×	`add-log-exp`
10×	`add-cube-cbrt` `sqr-pow`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`cube-div`
2×	`cube-mult` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-exp` `sum-log` `cos-mult` `flip--` `sin-mult` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `associate-+l-` `flip3-+` `frac-sub` `flip-+` `distribute-lft-out` `sub-div`

Counts

4 → 100

Calls

4 calls:

9.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
3.0ms	(pow (cos x) 3)
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
20.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series867.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
29.0ms	(pow (cos x) 3)
117.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
619.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify100.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	599	1456
1	2881	1337
2	5001	1328

prune356.0ms

Filtered

112 candidates to 63 candidates (56.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	11	10	21
Picked	1	0	1
Done	0	0	0
Total	112	22	134

Merged error: 13.9b

Counts

134 → 22

regimes306.0ms

Accuracy

78.8% (2.1b remaining)

Error of 16.6b against oracle of 14.4b and baseline of 24.6b

bsearch156.0ms

Steps

Iters	Range		Point
8	6.3780966821006384e-18	1.0989223242724141e-13	1.0832738602013395e-13
7	-9.683097938158369e-25	-1.113797997846539e-26	-9.474781037984798e-25

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	107
1	84	107
2	84	107

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4498×	body	1280	valid
532.0ms	613×	body	2560	valid
401.0ms	1825×	body	640	valid
116.0ms	679×	body	320	valid
37.0ms	295×	body	160	valid
5.0ms	90×	body	80	valid

Details

sample92.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite11.0ms

series72.0ms

simplify114.0ms

prune100.0ms

localize15.0ms

rewrite25.0ms

series274.0ms

simplify44.0ms

prune273.0ms

localize15.0ms

rewrite26.0ms

series307.0ms

simplify122.0ms

prune266.0ms

localize26.0ms

rewrite41.0ms

series867.0ms

simplify100.0ms

prune356.0ms

regimes306.0ms

bsearch156.0ms

simplify3.0ms

end0.0ms

sample2.9s

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