Details

sample2.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 78.161621%

Results

20.0ms	40×	body	2560	valid
11.0ms	40×	body	1280	valid
9.0ms	50×	body	640	valid
4.0ms	34×	body	320	valid
3.0ms	73×	body	80	valid
2.0ms	19×	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: 29.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
14.1b	(/ (- 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))

simplify63.0ms

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

prune84.0ms

Filtered

34 candidates to 48 candidates (-41.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	41	7	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	7	49

Merged error: 0.1b

Counts

49 → 7

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)
2.6b	(- 1.0 (cos x))

rewrite30.0ms

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:

16.0ms	(* (/ 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:

6.0ms	(* (/ 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 (53.0ms)

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

prune143.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	118	12	130

Merged error: 0.1b

Counts

130 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.3b	(* (cos x) (cos x))
0.4b	(+ 1.0 (cos x))
2.7b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* 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)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
3.0ms	(* (cos x) (cos x))
2.0ms	(+ 1.0 (cos x))
5.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	425	655
1	2057	564
2	5001	548

prune129.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	95	10	105

Merged error: 0.1b

Counts

105 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ 1.0 (cos x)))
0.2b	(/ (- (- (* 1.0 1.0) 1/2) (* 1/2 (cos (* 2 x)))) (* x (+ 1.0 (cos x))))
0.4b	(+ 1.0 (cos x))
2.5b	(- (- (* 1.0 1.0) 1/2) (* 1/2 (cos (* 2 x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`pow1`
4×	`associate-r/` `associate-r*`
3×	`flip3-+` `times-frac` `diff-log` `associate-l` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `associate--l-` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

6.0ms	(* x (+ 1.0 (cos x)))
12.0ms	(/ (- (- (* 1.0 1.0) 1/2) (* 1/2 (cos (* 2 x)))) (* x (+ 1.0 (cos x))))
3.0ms	(+ 1.0 (cos x))
7.0ms	(- (- (* 1.0 1.0) 1/2) (* 1/2 (cos (* 2 x))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* x (+ 1.0 (cos x)))
13.0ms	(/ (- (- (* 1.0 1.0) 1/2) (* 1/2 (cos (* 2 x)))) (* x (+ 1.0 (cos x))))
2.0ms	(+ 1.0 (cos x))
5.0ms	(- (- (* 1.0 1.0) 1/2) (* 1/2 (cos (* 2 x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	422	746
1	1835	652
2	5001	652

prune137.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	88	11	99

Merged error: 0.1b

Counts

99 → 11

regimes74.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.4b

bsearch54.0ms

Steps

Iters	Range		Point
9	0.02530291237915767	15248.215659032794	0.034036281345763024
8	-0.24803134423807568	-0.0007152340593748159	-0.028220250504788404

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	32
1	55	32

end0.0ms

sample4.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 78.161621%

Results

799.0ms	1599×	body	2560	valid
341.0ms	1200×	body	1280	valid
247.0ms	1455×	body	640	valid
116.0ms	972×	body	320	valid
89.0ms	2304×	body	80	valid
44.0ms	470×	body	160	valid

Details

sample2.3s

simplify6.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series9.0ms

simplify63.0ms

prune84.0ms

localize7.0ms

rewrite30.0ms

series14.0ms

simplify62.0ms

prune143.0ms

localize13.0ms

rewrite22.0ms

series25.0ms

simplify53.0ms

prune129.0ms

localize16.0ms

rewrite30.0ms

series25.0ms

simplify53.0ms

prune137.0ms

regimes74.0ms

bsearch54.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling