Details

sample117.0ms

Algorithm

intervals

Results

67.0ms	96×	body	1280	valid
22.0ms	55×	body	640	valid
6.0ms	23×	body	320	valid
6.0ms	68×	body	80	valid
2.0ms	14×	body	160	valid

simplify58.0ms

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: 11.4b

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)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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:

46.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
110.0ms	(pow (sin ky) 2.0)
104.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (36.0ms)

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

prune429.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.1b

localize17.0ms

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)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite71.0ms

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:

49.0ms	(* (/ (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)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
105.0ms	(pow (sin ky) 2.0)
107.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (36.0ms)

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

prune442.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.1b

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	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin kx) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite89.0ms

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:

19.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
48.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (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)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
145.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
113.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	412	1572
1	1672	1426
2	5001	1423

prune463.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.1b

localize16.0ms

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	(* (sin ky) (/ (- (sin th)) (- (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.3b	(pow (sin kx) 2.0)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

409×	`*-un-lft-identity`
401×	`times-frac`
291×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
243×	`add-sqr-sqrt`
237×	`add-cube-cbrt`
215×	`sqrt-prod`
206×	`associate-r`
89×	`unpow-prod-down`
86×	`distribute-lft-out`
62×	`neg-mul-1`
20×	`associate-/r*`
12×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`associate-/l*`
8×	`pow1`
6×	`sqrt-div`
4×	`associate-/r/` `distribute-neg-frac` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+`
2×	`cbrt-undiv` `distribute-frac-neg` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-rgt-neg-out` `sqr-pow`

Counts

4 → 506

Calls

4 calls:

41.0ms	(/ (- (sin th)) (- (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
127.0ms	(* (sin ky) (/ (- (sin th)) (- (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (- (sin th)) (- (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
146.0ms	(* (sin ky) (/ (- (sin th)) (- (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
105.0ms	(pow (sin kx) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

518 → 518

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1202	7445
1	5001	7022

prune1.3s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.1b

regimes1.1s

Accuracy

74.3% (0.3b remaining)

Error of 11.4b against oracle of 11.1b and baseline of 12.3b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	31
1	45	31
2	48	31
3	48	31

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.0s	2782×	body	1280	valid
737.0ms	1765×	body	640	valid
215.0ms	2351×	body	80	valid
209.0ms	734×	body	320	valid
64.0ms	368×	body	160	valid