Details

sample64.0ms

Algorithm

intervals

Results

26.0ms	56×	body	2560	valid
12.0ms	49×	body	640	valid
10.0ms	43×	body	1280	valid
3.0ms	27×	body	320	valid
2.0ms	70×	body	80	valid
1.0ms	11×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

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: 33.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
16.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
6.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify58.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune91.0ms

Filtered

34 candidates to 48 candidates (-41.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	39	9	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	9	49

Merged error: 0.1b

Counts

49 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/720 (pow x 4)) 1/2)
0.1b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
12.0b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `flip--` `flip-+`

Counts

4 → 77

Calls

4 calls:

4.0ms	(+ (* 1/720 (pow x 4)) 1/2)
5.0ms	(* 1/720 (pow x 4))
5.0ms	(* 1/24 (pow x 2))
7.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* 1/720 (pow x 4)) 1/2)
4.0ms	(* 1/720 (pow x 4))
3.0ms	(* 1/24 (pow x 2))
5.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	312	408
1	1312	376
2	5001	369

prune144.0ms

Filtered

56 candidates to 89 candidates (-58.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	89	9	98

Merged error: 0.1b

Counts

98 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

13.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690

prune142.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	121	11	132

Merged error: 0.0b

Counts

132 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-sqr-sqrt`
156×	`times-frac`
143×	`*-un-lft-identity`
104×	`sqrt-prod`
89×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 206

Calls

4 calls:

6.0ms	(/ (sqrt (- 1.0 (cos x))) x)
24.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series20.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
5.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

simplify89.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	667	2403
1	3340	2087
2	5001	1922

prune265.0ms

Filtered

122 candidates to 218 candidates (-78.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	219	10	229

Merged error: 0.0b

Counts

229 → 10

regimes68.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch32.0ms

Steps

Iters	Range		Point
9	6.661366802070807e-05	306.28763118649994	0.034161151953311514
9	-3.853535794009	-4.644989184223309e-09	-0.030336872752258274

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

760.0ms	1590×	body	2560	valid
306.0ms	1272×	body	1280	valid
230.0ms	1447×	body	640	valid
115.0ms	1007×	body	320	valid
75.0ms	2208×	body	80	valid
41.0ms	476×	body	160	valid

Details

sample64.0ms

simplify6.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series9.0ms

simplify58.0ms

prune91.0ms

localize10.0ms

rewrite23.0ms

series20.0ms

simplify43.0ms

prune144.0ms

localize7.0ms

rewrite27.0ms

series13.0ms

simplify59.0ms

prune142.0ms

localize8.0ms

rewrite51.0ms

series20.0ms

simplify89.0ms

prune265.0ms

regimes68.0ms

bsearch32.0ms

simplify4.0ms

end0.0ms

sample1.7s

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