Details

sample124.0ms

Algorithm

intervals

Results

67.0ms	91×	body	1280	valid
28.0ms	56×	body	640	valid
6.0ms	75×	body	80	valid
5.0ms	19×	body	320	valid
3.0ms	15×	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: 10.2b

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)
0.2b	(pow (sin kx) 2.0)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite121.0ms

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:

81.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
98.0ms	(pow (sin ky) 2.0)
100.0ms	(pow (sin kx) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune425.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.0b

localize19.0ms

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)
0.2b	(pow (sin kx) 2.0)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite122.0ms

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:

84.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
4.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
99.0ms	(pow (sin ky) 2.0)
98.0ms	(pow (sin kx) 2.0)
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

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

prune472.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.2b	(/ (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)))))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite154.0ms

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:

4.0ms	(pow (sin kx) 2.0)
36.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
79.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
29.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(pow (sin kx) 2.0)
120.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
136.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (39.0ms)

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

prune532.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`sqrt-prod`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`unpow-prod-down` `sqrt-div` `distribute-lft-out`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (sin ky))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (sin ky))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
68.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	171	583
1	424	554
2	1478	552
3	5002	551

prune363.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.0b

regimes1.3s

Accuracy

0% (1.6b remaining)

Error of 12.7b against oracle of 11.1b and baseline of 12.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	37
1	29	37

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.0s	2727×	body	1280	valid
932.0ms	1864×	body	640	valid
206.0ms	2300×	body	80	valid
203.0ms	754×	body	320	valid
69.0ms	355×	body	160	valid