Details

sample193.0ms

Algorithm

intervals

Results

117.0ms	121×	body	1280	valid
38.0ms	63×	body	640	valid
13.0ms	45×	body	80	valid
9.0ms	22×	body	320	valid
1.0ms	5×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

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)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
101.0ms	(pow (sin ky) 2.0)
101.0ms	(pow (sin kx) 2.0)
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune367.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin th) (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)))

rewrite39.0ms

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:

18.0ms	(/ (sin th) (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)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
106.0ms	(pow (sin ky) 2.0)
100.0ms	(pow (sin kx) 2.0)
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify122.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	329	1020
1	1058	944
2	4205	941
3	5001	941

prune330.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.3b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
127×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
89×	`associate-r`
84×	`add-cube-cbrt`
52×	`sqrt-prod`
26×	`unpow-prod-down`
25×	`add-exp-log`
20×	`distribute-lft-out`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp` `prod-exp` `unswap-sqr`
6×	`pow-unpow`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-l` `cbrt-unprod`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `associate-/r/` `un-div-inv` `-commutative` `flip-+`

Counts

4 → 171

Calls

4 calls:

68.0ms	(* (sin ky) (/ 1 (/ (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)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
101.0ms	(pow (sin ky) 2.0)
108.0ms	(pow (sin kx) 2.0)
71.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	836	1918
1	4320	1702
2	5001	1589

prune489.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.7b	(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
15×	`sqrt-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`unpow-prod-down`
11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`times-frac` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `distribute-lft-out`
4×	`sqrt-div` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `sin-mult` `associate-/l*`

Counts

4 → 85

Calls

4 calls:

1.0ms	(pow (sin ky) 2.0)
1.0ms	(pow (sin kx) 2.0)
19.0ms	(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sin ky) 2.0)
99.0ms	(pow (sin kx) 2.0)
137.0ms	(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	357	792
1	1385	720
2	5001	720

prune267.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.3b

regimes506.0ms

Accuracy

58.6% (0.6b remaining)

Error of 3.0b against oracle of 2.4b and baseline of 3.8b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	29
1	36	29

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.6s	3674×	body	1280	valid
1.5s	2082×	body	640	valid
311.0ms	700×	body	320	valid
160.0ms	1261×	body	80	valid
78.0ms	283×	body	160	valid