Details

sample73.0ms

Algorithm

intervals

Results

25.0ms	79×	body	1280	valid
13.0ms	257×	body	80	valid
12.0ms	57×	body	640	valid
5.0ms	36×	body	320	valid
2.0ms	14×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

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))

rewrite29.0ms

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))
19.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series299.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
208.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
63.0ms	(/ (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	5003	791

prune276.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

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))

rewrite90.0ms

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:

9.0ms	(+ (pow a2 2) (pow a1 2))
44.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
30.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series328.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (pow a2 2) (pow a1 2))
207.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
92.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (39.0ms)

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

prune281.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0)))
0.3b	(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0))))
7.1b	(sqrt (+ (pow a2 2) (pow a1 2)))
7.1b	(sqrt (+ (pow a2 2) (pow a1 2)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

187×	`*-un-lft-identity`
184×	`times-frac`
183×	`sqrt-prod`
161×	`add-sqr-sqrt`
114×	`cbrt-prod`
99×	`add-cube-cbrt`
76×	`associate-r`
44×	`unpow-prod-down` `distribute-lft-out`
27×	`add-exp-log`
21×	`unswap-sqr`
19×	`add-cbrt-cube`
12×	`associate-l`
9×	`associate-/r*`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`flip3-+` `flip-+` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 270

Calls

4 calls:

27.0ms	(/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0)))
113.0ms	(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0))))
15.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))
15.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0)))
100.0ms	(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0))))
41.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))
37.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))

simplify103.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	704	4665
1	3627	4261
2	5001	3931

prune660.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0)))))
0.3b	(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0))))))
7.1b	(sqrt (+ (pow a2 2) (pow a1 2)))
7.1b	(sqrt (+ (pow a2 2) (pow a1 2)))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

277×	`add-exp-log`
150×	`cbrt-prod`
149×	`times-frac`
140×	`prod-exp`
139×	`add-sqr-sqrt`
137×	`*-un-lft-identity`
117×	`sqrt-prod`
101×	`associate-r`
91×	`add-cbrt-cube`
90×	`div-exp`
68×	`add-cube-cbrt`
60×	`cbrt-unprod`
42×	`cbrt-undiv`
30×	`unpow-prod-down` `distribute-lft-out`
27×	`unswap-sqr`
19×	`associate-l`
16×	`rec-exp` `1-exp`
13×	`pow1`
6×	`frac-times` `associate-*r/`
4×	`sqrt-div` `pow-prod-down` `associate-*l/` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `*-commutative` `flip-+`

Counts

4 → 296

Calls

4 calls:

109.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0)))))
204.0ms	(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0))))))
17.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))
17.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0)))))
110.0ms	(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0))))))
36.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))
42.0ms	(sqrt (+ (pow a2 2) (pow a1 2)))

simplify77.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1336	7082
1	5002	5860

prune802.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes222.0ms

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	28	30
1	28	30

end0.0ms

sample2.2s

Algorithm

intervals

Results

813.0ms	2545×	body	1280	valid
454.0ms	2103×	body	640	valid
399.0ms	8016×	body	80	valid
155.0ms	1036×	body	320	valid
56.0ms	520×	body	160	valid