Details

sample109.0ms

Algorithm

intervals

Results

37.0ms	87×	body	1280	valid
20.0ms	66×	body	640	valid
19.0ms	269×	body	80	valid
6.0ms	30×	body	320	valid
3.0ms	22×	body	160	valid

simplify14.0ms

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

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

localize10.0ms

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))

rewrite21.0ms

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:

3.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series48.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
37.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (43.0ms)

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

prune179.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	7	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 0b

Counts

108 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

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))
8.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series63.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
23.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
35.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (36.0ms)

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

prune104.0ms

Filtered

50 candidates to 71 candidates (-42.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	72	7	79

Merged error: 0b

Counts

79 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
0.7b	(/ (cos th) (sqrt 2.0))
6.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
6.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
35×	`sqrt-prod`
22×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `sqrt-div`
6×	`associate-r` `associate-/r*` `unswap-sqr`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 121

Calls

4 calls:

13.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
4.0ms	(/ (cos th) (sqrt 2.0))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify42.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	352	1093
1	1256	1042
2	5001	1028

prune167.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	133	7	140

Merged error: 0b

Counts

140 → 7

localize15.0ms

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

rewrite135.0ms

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:

3.0ms	(+ (* a1 a1) (* a2 a2))
53.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
15.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
35.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify120.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.4s

Filtered

373 candidates to 729 candidates (-95.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	728	1	729
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	730	6	736

Merged error: 0b

Counts

736 → 6

regimes394.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2595×	body	1280	valid
641.0ms	2082×	body	640	valid
587.0ms	8021×	body	80	valid
247.0ms	1080×	body	320	valid
78.0ms	508×	body	160	valid

Details

sample109.0ms

simplify14.0ms

prune8.0ms

localize10.0ms

rewrite21.0ms

series48.0ms

simplify52.0ms

prune179.0ms

localize10.0ms

rewrite21.0ms

series63.0ms

simplify43.0ms

prune104.0ms

localize13.0ms

rewrite28.0ms

series47.0ms

simplify42.0ms

prune167.0ms

localize15.0ms

rewrite135.0ms

series54.0ms

simplify120.0ms

prune1.4s

regimes394.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling