Details

sample156.0ms

Algorithm

intervals

Results

88.0ms	117×	body	1280	valid
34.0ms	74×	body	640	valid
12.0ms	19×	body	320	valid
3.0ms	15×	body	160	valid
3.0ms	31×	body	80	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

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: 2.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (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)
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite27.0ms

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:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
103.0ms	(pow (sin ky) 2.0)
102.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5002	943

prune354.0ms

Filtered

112 candidates to 70 candidates (62.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 1.9b

Counts

113 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
0.3b	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
30×	`associate-r`
28×	`add-cube-cbrt` `times-frac`
27×	`sqrt-prod`
16×	`unpow-prod-down`
15×	`add-exp-log`
14×	`associate-*r/`
10×	`distribute-lft-out`
9×	`pow1` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `associate-/l*` `add-log-exp`
3×	`associate-l` `un-div-inv`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `clear-num` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 121

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
20.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (sin ky) 2.0)
102.0ms	(pow (sin kx) 2.0)
130.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
72.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	457	997
1	2203	908
2	5002	863

prune384.0ms

Filtered

133 candidates to 75 candidates (56.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Merged error: 1.9b

Counts

144 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

62×	`sqrt-prod`
56×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`times-frac`
32×	`add-cube-cbrt`
15×	`unpow-prod-down`
12×	`distribute-lft-out`
11×	`associate-/r*`
8×	`sqrt-div`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `div-inv` `sqr-pow`

Counts

4 → 112

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
13.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (sin kx) 2.0)
150.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify135.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	341	1434
1	1086	1322
2	4447	1318
3	5001	1318

prune437.0ms

Filtered

124 candidates to 75 candidates (60.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	124	10	134

Merged error: 1.9b

Counts

134 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin ky) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.3b	(* (sin ky) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

444×	`sqrt-div`
405×	`sqrt-prod`
348×	`*-un-lft-identity`
326×	`add-sqr-sqrt`
248×	`associate-/r*`
238×	`associate-*r/`
196×	`frac-times`
150×	`add-cube-cbrt`
132×	`times-frac`
99×	`associate-r`
93×	`associate-/l*`
90×	`unswap-sqr`
84×	`unpow-prod-down` `distribute-lft-out`
53×	`associate-l`
31×	`frac-2neg` `clear-num`
14×	`associate-*l/`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r/`
5×	`flip3-+` `flip-+`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`*-commutative` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 461

Calls

4 calls:

71.0ms	(* (* (sin ky) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
23.0ms	(* (sin ky) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
12.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (* (sin ky) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
150.0ms	(* (sin ky) (sqrt (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify131.0ms

Algorithm

egg-herbie

Counts

473 → 473

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	1115	10396
1	3378	8390
2	5001	8251

prune895.0ms

Filtered

473 candidates to 159 candidates (33.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	471	2	473
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	474	9	483

Merged error: 1.9b

Counts

483 → 9

regimes473.0ms

Accuracy

0% (1.8b remaining)

Error of 4.3b against oracle of 2.5b and baseline of 4.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.1s	3571×	body	1280	valid
1.0s	2074×	body	640	valid
235.0ms	715×	body	320	valid
135.0ms	1324×	body	80	valid
64.0ms	316×	body	160	valid