Details

sample96.0ms

Algorithm

intervals

Results

32.0ms	75×	body	1280	valid
15.0ms	61×	body	640	valid
15.0ms	252×	body	80	valid
8.0ms	45×	body	320	valid
2.0ms	16×	body	160	valid

simplify15.0ms

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

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite25.0ms

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:

6.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series362.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* a1 a1) (* a2 a2))
254.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
76.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5001	791

prune396.0ms

Filtered

107 candidates to 74 candidates (30.8%)

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.3b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
9.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series424.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* a1 a1) (* a2 a2))
130.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
260.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	309	564
1	1642	490
2	5001	481

prune234.0ms

Filtered

71 candidates to 49 candidates (31.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	71	8	79

Merged error: 0b

Counts

79 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow a2 2) (pow a1 2))
0.2b	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.4b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
62×	`times-frac`
48×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
34×	`associate-r` `sqrt-prod`
28×	`unpow-prod-down` `distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `associate-/l*` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 122

Calls

3 calls:

11.0ms	(+ (pow a2 2) (pow a1 2))
20.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
11.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series427.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (pow a2 2) (pow a1 2))
264.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
124.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	344	1118
1	1557	1023
2	5001	1018

prune314.0ms

Filtered

131 candidates to 69 candidates (47.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	131	8	139

Merged error: 0b

Counts

139 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (/ (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)))

rewrite150.0ms

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))
60.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
17.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a1 a1) (* a2 a2))
271.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
80.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
123.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify125.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune6.9s

Filtered

729 candidates to 374 candidates (48.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	729	0	729
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	729	8	737

Merged error: 0b

Counts

737 → 8

regimes511.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

end0.0ms

sample2.7s

Algorithm

intervals

Results

887.0ms	2425×	body	1280	valid
516.0ms	2052×	body	640	valid
471.0ms	8146×	body	80	valid
181.0ms	1011×	body	320	valid
64.0ms	531×	body	160	valid

Details

sample96.0ms

simplify15.0ms

prune14.0ms

localize10.0ms

rewrite25.0ms

series362.0ms

simplify54.0ms

prune396.0ms

localize11.0ms

rewrite20.0ms

series424.0ms

simplify45.0ms

prune234.0ms

localize12.0ms

rewrite48.0ms

series427.0ms

simplify49.0ms

prune314.0ms

localize15.0ms

rewrite150.0ms

series507.0ms

simplify125.0ms

prune6.9s

regimes511.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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