Details

sample146.0ms

Algorithm

intervals

Results

90.0ms	114×	body	1280	valid
31.0ms	67×	body	640	valid
5.0ms	51×	body	80	valid
4.0ms	14×	body	320	valid
2.0ms	10×	body	160	valid

simplify52.0ms

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: 4.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin kx) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite37.0ms

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:

2.0ms	(pow (sin ky) 2.0)
16.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin kx) 2.0)
12.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sin ky) 2.0)
147.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune393.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize14.0ms

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))))
0.2b	(pow (sin kx) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite42.0ms

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:

17.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
133.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
101.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (40.0ms)

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

prune413.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
0.3b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

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:

3.0ms	(pow (sin kx) 2.0)
10.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
13.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(pow (sin kx) 2.0)
142.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
149.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (51.0ms)

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

prune479.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

localize18.0ms

Local error

Found 4 expressions with local error:

4.1b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
15.8b	(cbrt (pow (sin kx) 2.0))
15.8b	(cbrt (pow (sin kx) 2.0))
15.8b	(cbrt (pow (sin kx) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

14.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
2.0ms	(cbrt (pow (sin kx) 2.0))
2.0ms	(cbrt (pow (sin kx) 2.0))
2.0ms	(cbrt (pow (sin kx) 2.0))

series673.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
197.0ms	(cbrt (pow (sin kx) 2.0))
193.0ms	(cbrt (pow (sin kx) 2.0))
202.0ms	(cbrt (pow (sin kx) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	204	682
1	478	640
2	1705	640
3	5001	634

prune294.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.2b

regimes430.0ms

Accuracy

0% (1.4b remaining)

Error of 4.1b against oracle of 2.7b and baseline of 4.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.1s	3726×	body	1280	valid
975.0ms	2005×	body	640	valid
245.0ms	714×	body	320	valid
137.0ms	1287×	body	80	valid
62.0ms	268×	body	160	valid