Details

sample143.0ms

Algorithm

intervals

Results

82.0ms	103×	body	1280	valid
25.0ms	52×	body	640	valid
10.0ms	17×	body	320	valid
10.0ms	75×	body	80	valid
2.0ms	9×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

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)
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite69.0ms

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:

48.0ms	(* (/ (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)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
106.0ms	(pow (sin ky) 2.0)
103.0ms	(pow (sin kx) 2.0)
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune429.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin kx) 2.0)
2.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-r`
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-l` `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` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

1.0ms	(pow (sin ky) 2.0)
44.0ms	(* (sin ky) (/ (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)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (sin ky) 2.0)
139.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
106.0ms	(pow (sin kx) 2.0)
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	437	948
1	1864	870
2	5002	870

prune381.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
14.1b	(cbrt (pow (sin kx) 2.0))
14.1b	(cbrt (pow (sin kx) 2.0))
14.1b	(cbrt (pow (sin kx) 2.0))

rewrite51.0ms

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:

45.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))

series665.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
199.0ms	(cbrt (pow (sin kx) 2.0))
193.0ms	(cbrt (pow (sin kx) 2.0))
194.0ms	(cbrt (pow (sin kx) 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (51.0ms)

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

prune370.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 9.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
2.2b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
13.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (sin kx))
97.0ms	(cbrt (sin kx))
97.0ms	(cbrt (sin kx))
77.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	183	511
1	496	483
2	2171	477
3	5002	476

prune264.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 9.0b

regimes1.0s

Accuracy

0% (1.3b remaining)

Error of 12.6b against oracle of 11.3b and baseline of 12.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.3s	2755×	body	1280	valid
915.0ms	1804×	body	640	valid
397.0ms	727×	body	320	valid
323.0ms	2362×	body	80	valid
83.0ms	352×	body	160	valid