Details

sample87.0ms

Algorithm

intervals

Results

30.0ms	94×	body	1280	valid
15.0ms	74×	body	640	valid
15.0ms	262×	body	80	valid
7.0ms	47×	body	320	valid
2.0ms	22×	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)

Merged error: 0.4b

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))

rewrite33.0ms

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))
22.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series299.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
217.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
56.0ms	(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

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

prune286.0ms

Filtered

107 candidates to 74 candidates (69.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (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:

3.0ms	(+ (* a1 a1) (* a2 a2))
9.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
7.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series340.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
104.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
210.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (38.0ms)

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

prune194.0ms

Filtered

71 candidates to 50 candidates (70.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
0.3b	(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`sqrt-div`
16×	`sqrt-prod`
15×	`add-exp-log` `add-cbrt-cube`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/`
9×	`flip3-+` `flip-+`
8×	`pow1` `associate-/l/`
6×	`times-frac` `associate-r` `associate-/r*`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 91

Calls

4 calls:

10.0ms	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
22.0ms	(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
212.0ms	(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
35.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
39.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	336	970
1	1658	827
2	5001	815

prune490.0ms

Filtered

103 candidates to 77 candidates (74.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
62×	`times-frac`
58×	`associate-r`
57×	`add-exp-log`
56×	`sqrt-prod`
44×	`add-cube-cbrt` `*-un-lft-identity`
40×	`cbrt-prod` `add-cbrt-cube`
22×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
8×	`pow1`
7×	`unswap-sqr`
6×	`sqrt-div`
5×	`associate-l`
4×	`add-log-exp`
3×	`flip3-+` `associate-*r/` `flip-+` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `associate-/l`

Counts

4 → 155

Calls

4 calls:

9.0ms	(/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
56.0ms	(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series837.0ms

Counts

4 → 12

Calls

4 calls:

552.0ms	(/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
211.0ms	(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
34.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
40.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify125.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	750	3162
1	4513	2674
2	5002	2505

prune430.0ms

Filtered

167 candidates to 99 candidates (59.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes189.0ms

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

sample2.2s

Algorithm

intervals

Results

797.0ms	2553×	body	1280	valid
442.0ms	2094×	body	640	valid
405.0ms	8064×	body	80	valid
153.0ms	1035×	body	320	valid
57.0ms	500×	body	160	valid