Details

sample113.0ms

Algorithm

intervals

Results

66.0ms	88×	body	1280	valid
18.0ms	46×	body	640	valid
7.0ms	25×	body	320	valid
7.0ms	83×	body	80	valid
2.0ms	14×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

47.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin ky) 2.0)
1.0ms	(pow (sin kx) 2.0)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
106.0ms	(pow (sin ky) 2.0)
107.0ms	(pow (sin kx) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	391	990
1	1382	928
2	5001	927

prune425.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.2b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

44.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
21.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin kx) 2.0)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
139.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
109.0ms	(pow (sin kx) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	412	1572
1	1672	1426
2	5002	1423

prune468.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
0.3b	(pow (sin kx) 2.0)
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
181×	`*-un-lft-identity`
114×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
85×	`sqrt-prod`
37×	`unpow-prod-down`
34×	`distribute-lft-out`
31×	`associate-/r*`
18×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/l*`
8×	`div-exp`
7×	`pow1`
6×	`div-inv`
4×	`cbrt-undiv` `sqrt-div` `add-log-exp`
3×	`pow-unpow`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `pow-flip` `pow-pow` `sqrt-pow1` `pow1/2` `pow-exp` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 219

Calls

4 calls:

25.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
26.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
1.0ms	(pow (sin kx) 2.0)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
152.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
106.0ms	(pow (sin kx) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	627	3215
1	2796	2908
2	5001	2759

prune557.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 10.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

114×	`sqrt-prod`
94×	`*-un-lft-identity`
66×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`associate-/r*`
20×	`unpow-prod-down` `distribute-lft-out`
12×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 156

Calls

4 calls:

20.0ms	(/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
22.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
148.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify135.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	381	2366
1	1146	2160
2	4717	2153
3	5001	2153

prune529.0ms

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 10.6b

regimes1.2s

Accuracy

0% (1.4b remaining)

Error of 12.7b against oracle of 11.2b and baseline of 12.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.0s	2684×	body	1280	valid
947.0ms	1906×	body	640	valid
204.0ms	767×	body	320	valid
204.0ms	2275×	body	80	valid
65.0ms	368×	body	160	valid