Details

sample183.0ms

Algorithm

intervals

Results

116.0ms	118×	body	1280	valid
39.0ms	67×	body	640	valid
8.0ms	21×	body	320	valid
4.0ms	40×	body	80	valid
2.0ms	10×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.0b

Counts

2 → 1

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)
4.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite39.0ms

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:

23.0ms	(* (/ (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)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin kx) 2.0)
106.0ms	(pow (sin ky) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune386.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	13	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Merged error: 3.3b

Counts

114 → 13

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	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

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:

11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
21.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
104.0ms	(pow (sin ky) 2.0)
143.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	412	1572
1	1810	1426
2	5002	1423

prune378.0ms

Filtered

145 candidates to 86 candidates (59.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	145	13	158

Merged error: 3.3b

Counts

158 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

4.6b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
17.5b	(cbrt (pow (sin kx) 2.0))
17.5b	(cbrt (pow (sin kx) 2.0))
17.5b	(cbrt (pow (sin kx) 2.0))

rewrite23.0ms

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:

14.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
2.0ms	(cbrt (pow (sin kx) 2.0))
2.0ms	(cbrt (pow (sin kx) 2.0))
2.0ms	(cbrt (pow (sin kx) 2.0))

series689.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(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))
200.0ms	(cbrt (pow (sin kx) 2.0))
204.0ms	(cbrt (pow (sin kx) 2.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (53.0ms)

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

prune291.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	72	13	85

Merged error: 3.3b

Counts

85 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
1.0b	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.4b	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
8.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
9.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow (sin ky) 2.0)
94.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
81.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	250	773
1	692	728
2	2182	712
3	5001	706

prune258.0ms

Filtered

91 candidates to 58 candidates (63.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	90	14	104

Merged error: 3.3b

Counts

104 → 14

regimes600.0ms

Accuracy

68.4% (0.4b remaining)

Error of 2.9b against oracle of 2.5b and baseline of 3.9b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	29
1	37	29

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.8s	3765×	body	1280	valid
1.2s	1998×	body	640	valid
273.0ms	697×	body	320	valid
146.0ms	1272×	body	80	valid
67.0ms	268×	body	160	valid