Details

sample149.0ms

Algorithm

intervals

Results

94.0ms	117×	body	1280	valid
28.0ms	63×	body	640	valid
7.0ms	24×	body	320	valid
4.0ms	44×	body	80	valid
2.0ms	8×	body	160	valid

simplify50.0ms

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: 4.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

22.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin ky) 2.0)
1.0ms	(pow (sin kx) 2.0)
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin ky) 2.0)
110.0ms	(pow (sin kx) 2.0)
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify138.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	329	1022
1	1104	946
2	4889	943
3	5002	943

prune364.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2)
0.3b	(pow (sin kx) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
3.7b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-l`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

1.0ms	(pow (sin ky) 2)
1.0ms	(pow (sin kx) 2)
51.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
20.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin ky) 2)
22.0ms	(pow (sin kx) 2)
118.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
105.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify45.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	369	1076
1	1262	985
2	5002	948

prune394.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
14.8b	(cbrt (pow (sin kx) 2.0))
14.8b	(cbrt (pow (sin kx) 2.0))
14.8b	(cbrt (pow (sin kx) 2.0))

rewrite50.0ms

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:

42.0ms	(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))

series674.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
204.0ms	(cbrt (pow (sin kx) 2.0))
199.0ms	(cbrt (pow (sin kx) 2.0))
198.0ms	(cbrt (pow (sin kx) 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (50.0ms)

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

prune331.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.4b

localize20.0ms

Local error

Found 4 expressions with local error:

3.7b	(sqrt (/ 1 (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2))))
14.8b	(cbrt (pow (sin kx) 2))
14.8b	(cbrt (pow (sin kx) 2))
14.8b	(cbrt (pow (sin kx) 2))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
21×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`sqrt-prod`
11×	`times-frac`
9×	`unpow-prod-down`
6×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/3` `unpow2` `sqr-pow`
2×	`associate-/r/`
1×	`pow-flip` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv` `inv-pow`

Counts

4 → 78

Calls

4 calls:

53.0ms	(sqrt (/ 1 (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2))))
1.0ms	(cbrt (pow (sin kx) 2))
1.0ms	(cbrt (pow (sin kx) 2))
1.0ms	(cbrt (pow (sin kx) 2))

series446.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (/ 1 (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2))))
112.0ms	(cbrt (pow (sin kx) 2))
117.0ms	(cbrt (pow (sin kx) 2))
112.0ms	(cbrt (pow (sin kx) 2))

simplify104.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	254	1055
1	749	931
2	3514	866
3	5002	852

prune320.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.4b

regimes521.0ms

Accuracy

60.8% (0.7b remaining)

Error of 3.4b against oracle of 2.7b and baseline of 4.4b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	24
1	37	24

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.2s	3779×	body	1280	valid
911.0ms	1976×	body	640	valid
226.0ms	675×	body	320	valid
121.0ms	1284×	body	80	valid
57.0ms	286×	body	160	valid