Details

sample157.0ms

Algorithm

intervals

Results

94.0ms	120×	body	1280	valid
26.0ms	56×	body	640	valid
8.0ms	27×	body	320	valid
4.0ms	44×	body	80	valid
2.0ms	9×	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	1785	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: 4.5b

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 ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
30×	`associate-l`
28×	`add-cube-cbrt`
26×	`times-frac` `sqrt-prod`
16×	`unpow-prod-down`
14×	`associate-*l/`
11×	`add-exp-log`
10×	`distribute-lft-out`
9×	`pow1` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-/l*` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `clear-num` `*-commutative` `div-inv`

Counts

4 → 114

Calls

4 calls:

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

series452.0ms

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 ky) 2.0)
109.0ms	(pow (sin kx) 2.0)
84.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	420	1076
1	1771	1008
2	5002	1008

prune349.0ms

Filtered

126 candidates to 85 candidates (67.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	11	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	11	127

Merged error: 3.1b

Counts

127 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (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)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

18.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
6.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
104.0ms	(pow (sin ky) 2.0)
110.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	470	1035
1	2087	951
2	5001	951

prune313.0ms

Filtered

128 candidates to 76 candidates (59.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	127	12	139

Merged error: 3.1b

Counts

139 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
157×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
70×	`sqrt-prod`
34×	`unpow-prod-down`
31×	`associate-/r*`
28×	`distribute-lft-out`
16×	`associate-/r/`
11×	`add-exp-log` `associate-/l*`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`pow-unpow`
5×	`div-inv`
4×	`sqrt-div` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `associate-/l/` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 196

Calls

4 calls:

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

series449.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
106.0ms	(pow (sin ky) 2.0)
105.0ms	(pow (sin kx) 2.0)
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	697	2926
1	2988	2743
2	5002	2743

prune482.0ms

Filtered

208 candidates to 122 candidates (58.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	202	6	208
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	209	11	220

Merged error: 3.1b

Counts

220 → 11

localize15.0ms

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) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
157×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
70×	`sqrt-prod`
34×	`unpow-prod-down`
31×	`associate-/r*`
28×	`distribute-lft-out`
16×	`associate-/r/`
11×	`add-exp-log` `associate-/l*`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`pow-unpow`
5×	`div-inv`
4×	`sqrt-div` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `associate-/l/` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 196

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
16.0ms	(/ (sin ky) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sin ky) 2.0)
106.0ms	(pow (sin kx) 2.0)
157.0ms	(/ (sin ky) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	697	2925
1	3025	2743
2	5001	2743

prune452.0ms

Filtered

208 candidates to 120 candidates (57.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	208	11	219

Merged error: 3.1b

Counts

219 → 11

regimes361.0ms

Accuracy

0% (1.6b remaining)

Error of 4.3b against oracle of 2.7b and baseline of 4.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.1s	3723×	body	1280	valid
1.1s	1983×	body	640	valid
242.0ms	714×	body	320	valid
122.0ms	1279×	body	80	valid
61.0ms	301×	body	160	valid