Details

sample56.0ms

Algorithm

intervals

Results

24.0ms	51×	body	2560	valid
9.0ms	39×	body	1280	valid
7.0ms	41×	body	640	valid
5.0ms	40×	body	320	valid
3.0ms	69×	body	80	valid
1.0ms	16×	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: 31.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
15.6b	(/ (- 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))

series14.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
11.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

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

prune102.0ms

Filtered

34 candidates to 48 candidates (-41.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	35	13	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	13	49

Merged error: 0.1b

Counts

49 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 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))

series14.0ms

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))

simplify62.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (52.0ms)

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

prune137.0ms

Filtered

79 candidates to 123 candidates (-55.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	125	11	136

Merged error: 0.1b

Counts

136 → 11

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `times-frac`
23×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-l`
12×	`associate-r`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`div-inv`
5×	`pow1` `add-log-exp`
4×	`frac-times` `associate-*r/` `prod-exp`
3×	`sub-neg` `flip3--` `div-exp` `associate-/r` `frac-sub` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-rgt-out--` `distribute-lft-in` `cbrt-unprod`
1×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 106

Calls

3 calls:

20.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
4.0ms	(/ (cos x) x)
13.0ms	(- (/ 1.0 x) (/ (cos x) x))

series21.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
5.0ms	(/ (cos x) x)
6.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify59.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	478	762
1	2181	681
2	5001	665

prune127.0ms

Filtered

87 candidates to 115 candidates (-32.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	117	9	126

Merged error: 0.1b

Counts

126 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
0.2b	(* (cos x) (cos x))
0.3b	(+ 1.0 (cos x))
2.0b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`distribute-lft-out` `difference-of-squares`
4×	`associate-/r` `associate-/l`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `associate--r+` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

7.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
4.0ms	(* (cos x) (cos x))
3.0ms	(+ 1.0 (cos x))
4.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
3.0ms	(* (cos x) (cos x))
2.0ms	(+ 1.0 (cos x))
7.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	380	812
1	1751	741
2	5002	723

prune121.0ms

Filtered

75 candidates to 106 candidates (-41.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	105	10	115

Merged error: 0.0b

Counts

115 → 10

regimes116.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch30.0ms

Steps

Iters	Range		Point
8	2.4879688186424768e-05	0.3609580473631881	0.027307667834710694
10	-522.1368722912733	-5.949899967025005e-16	-0.034991262613253825

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	35
1	51	35

end0.0ms

sample1.7s

Algorithm

intervals

Results

770.0ms	1605×	body	2560	valid
305.0ms	1224×	body	1280	valid
260.0ms	1500×	body	640	valid
111.0ms	926×	body	320	valid
81.0ms	2302×	body	80	valid
36.0ms	443×	body	160	valid

Details

sample56.0ms

simplify6.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series14.0ms

simplify60.0ms

prune102.0ms

localize9.0ms

rewrite27.0ms

series14.0ms

simplify62.0ms

prune137.0ms

localize8.0ms

rewrite40.0ms

series21.0ms

simplify59.0ms

prune127.0ms

localize11.0ms

rewrite21.0ms

series24.0ms

simplify55.0ms

prune121.0ms

regimes116.0ms

bsearch30.0ms

simplify1.0ms

end0.0ms

sample1.7s

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