Details

sample73.0ms

Algorithm

intervals

Results

26.0ms	83×	body	1280	valid
12.0ms	242×	body	80	valid
11.0ms	54×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	19×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.5b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative`

Counts

3 → 98

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series302.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
218.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5003	791

prune292.0ms

Filtered

107 candidates to 74 candidates (69.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 0.0b

Counts

109 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
34×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `prod-exp` `cbrt-unprod` `flip-+`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `associate-/l/`

Counts

4 → 717

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
55.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
212.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
300.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
70.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify124.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.7s

Filtered

729 candidates to 373 candidates (51.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	724	5	729
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	730	7	737

Merged error: 0b

Counts

737 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

867×	`sqrt-prod`
750×	`times-frac`
403×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
102×	`cbrt-prod`
34×	`associate-/l*`
21×	`associate-/r*`
17×	`add-exp-log`
15×	`div-inv`
11×	`sqrt-pow1` `add-cbrt-cube`
8×	`pow1` `div-exp`
7×	`pow-flip`
4×	`cbrt-undiv` `pow1/3` `add-log-exp`
3×	`pow1/2`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `pow-div`
1×	`associate-/l/` `inv-pow`

Counts

4 → 515

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
5.0ms	(/ 1 (sqrt (sqrt 2.0)))
20.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

simplify96.0ms

Algorithm

egg-herbie

Counts

519 → 519

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1075	7915
1	5001	7242

prune1.2s

Filtered

519 candidates to 185 candidates (35.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	519	0	519
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	519	7	526

Merged error: 0b

Counts

526 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))
0.3b	(* (/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0)))))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

66843×	`times-frac`
49162×	`sqrt-prod`
28388×	`add-sqr-sqrt`
27898×	`*-un-lft-identity`
27820×	`add-cube-cbrt`
8809×	`associate-l`
1213×	`div-inv`
324×	`associate-/r*`
118×	`unswap-sqr`
103×	`add-exp-log`
66×	`associate-/r/`
64×	`div-exp`
61×	`add-cbrt-cube`
43×	`associate-/l*`
34×	`cbrt-undiv`
13×	`prod-exp`
7×	`cbrt-unprod`
6×	`pow1` `rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 18500

Calls

4 calls:

15.0ms	(/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))
1.3s	(* (/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
238.0ms	(/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0)))))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))
217.0ms	(* (/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0))))) (+ (* a1 a1) (* a2 a2)))
59.0ms	(/ (/ 1 (sqrt (sqrt 1))) (/ (sqrt (sqrt 2.0)) (/ (cos th) (sqrt (sqrt 2.0)))))
106.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify4.2s

Algorithm

egg-herbie

Counts

18512 → 18512

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	8108	449013

prune1.0m

Filtered

18512 candidates to 9201 candidates (49.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	18510	2	18512
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	18512	7	18519

Merged error: 0b

Counts

18519 → 7

regimes249.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	19
1	27	19

end0.0ms

sample2.2s

Algorithm

intervals

Results

800.0ms	2477×	body	1280	valid
456.0ms	2118×	body	640	valid
415.0ms	7983×	body	80	valid
166.0ms	1072×	body	320	valid
55.0ms	524×	body	160	valid