Details

sample164.0ms

Algorithm

intervals

Results

106.0ms	135×	body	1280	valid
33.0ms	55×	body	640	valid
6.0ms	19×	body	320	valid
4.0ms	42×	body	80	valid
1.0ms	5×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

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 kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

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:

16.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
104.0ms	(pow (sin kx) 2.0)
111.0ms	(pow (sin ky) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune394.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.3b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
3.4b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

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-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 103

Calls

4 calls:

20.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
3.0ms	(pow (sin kx) 2)
3.0ms	(pow (sin ky) 2)
8.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
19.0ms	(pow (sin kx) 2)
19.0ms	(pow (sin ky) 2)
80.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify45.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	982
1	1374	902
2	5001	899

prune360.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
0.3b	(pow (sin ky) 2)
3.4b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite46.0ms

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` `unpow2` `sqr-pow`

Counts

4 → 134

Calls

4 calls:

18.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
12.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
3.0ms	(pow (sin ky) 2)
8.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
136.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
18.0ms	(pow (sin ky) 2)
78.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	407	1568
1	1778	1413
2	5002	1410

prune392.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2)
1.5b	(exp (log (pow (sin kx) 2)))
3.4b	(sqrt (+ (exp (log (pow (sin kx) 2))) (pow (sin ky) 2)))
15.2b	(log (pow (sin kx) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`unpow-prod-down`
8×	`exp-sum`
7×	`add-exp-log`
6×	`pow1`
4×	`exp-prod` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `rem-log-exp` `unpow2` `sqr-pow`
2×	`pow-to-exp` `sqrt-div` `pow-exp` `log-pow`
1×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 73

Calls

4 calls:

3.0ms	(pow (sin ky) 2)
8.0ms	(exp (log (pow (sin kx) 2)))
11.0ms	(sqrt (+ (exp (log (pow (sin kx) 2))) (pow (sin ky) 2)))
3.0ms	(log (pow (sin kx) 2))

series191.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (sin ky) 2)
19.0ms	(exp (log (pow (sin kx) 2)))
79.0ms	(sqrt (+ (exp (log (pow (sin kx) 2))) (pow (sin ky) 2)))
70.0ms	(log (pow (sin kx) 2))

simplify108.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	284	481
1	891	428
2	3291	416
3	5001	412

prune250.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.6b

regimes264.0ms

Accuracy

0% (1.4b remaining)

Error of 3.9b against oracle of 2.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.1s	3693×	body	1280	valid
1.2s	2058×	body	640	valid
231.0ms	714×	body	320	valid
122.0ms	1225×	body	80	valid
65.0ms	310×	body	160	valid