Details

sample86.0ms

Algorithm

intervals

Results

32.0ms	88×	body	1280	valid
16.0ms	70×	body	640	valid
15.0ms	280×	body	80	valid
5.0ms	31×	body	320	valid
2.0ms	14×	body	160	valid

simplify17.0ms

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.5b

Counts

2 → 1

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))

rewrite26.0ms

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:

7.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series293.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
208.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
58.0ms	(/ (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

prune271.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	7	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	7	108

Merged error: 0b

Counts

108 → 7

localize12.0ms

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))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite142.0ms

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))
54.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
218.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
63.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
99.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify126.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.6s

Filtered

729 candidates to 374 candidates (51.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	726	3	729
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	729	7	736

Merged error: 0b

Counts

736 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
0.4b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

1522×	`sqrt-prod`
1510×	`times-frac`
861×	`add-sqr-sqrt`
775×	`*-un-lft-identity`
763×	`add-cube-cbrt`
392×	`cbrt-prod` `associate-l`
82×	`add-exp-log`
52×	`add-cbrt-cube`
34×	`associate-/l*`
32×	`div-exp`
29×	`div-inv` `unswap-sqr`
27×	`prod-exp`
21×	`associate-/r*`
17×	`cbrt-undiv` `cbrt-unprod`
15×	`pow1`
11×	`frac-times` `associate-*r/`
7×	`pow-flip` `sqrt-pow1`
6×	`flip3-+` `flip-+`
5×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp`
4×	`associate-r` `pow-prod-down` `associate-*l/` `add-log-exp`
3×	`pow1/2`
2×	`frac-2neg` `pow1/3` `clear-num` `*-commutative` `pow-div`
1×	`associate-/l/` `inv-pow`

Counts

4 → 987

Calls

4 calls:

48.0ms	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
68.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))
19.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

series632.0ms

Counts

4 → 8

Calls

4 calls:

231.0ms	(* (/ (cos th) (sqrt (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))) (* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
401.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))

simplify179.0ms

Algorithm

egg-herbie

Counts

995 → 995

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2615	15493
1	5001	14498

prune2.7s

Filtered

995 candidates to 470 candidates (47.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	995	0	995
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	995	7	1002

Merged error: 0b

Counts

1002 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (pow a2 2))
0.1b	(* (pow a1 2) (cos th))
0.3b	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
0.3b	(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
30×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`times-frac` `prod-exp` `associate-/r*` `sqrt-prod`
11×	`associate-r` `associate-l`
8×	`unpow-prod-down` `div-exp` `unswap-sqr`
4×	`pow1` `cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod` `unpow2` `add-log-exp` `sqr-pow`
2×	`frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 112

Calls

4 calls:

6.0ms	(* (cos th) (pow a2 2))
6.0ms	(* (pow a1 2) (cos th))
6.0ms	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
6.0ms	(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

series299.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos th) (pow a2 2))
50.0ms	(* (pow a1 2) (cos th))
110.0ms	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
98.0ms	(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	404	742
1	2042	641
2	5001	641

prune296.0ms

Filtered

124 candidates to 77 candidates (62.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	124	7	131

Merged error: 0b

Counts

131 → 7

regimes231.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	20
1	25	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

867.0ms	2566×	body	1280	valid
471.0ms	2102×	body	640	valid
433.0ms	8126×	body	80	valid
166.0ms	1026×	body	320	valid
58.0ms	506×	body	160	valid