Details

sample163.0ms

Algorithm

intervals

Results

103.0ms	120×	body	1280	valid
31.0ms	62×	body	640	valid
10.0ms	26×	body	320	valid
4.0ms	38×	body	80	valid
2.0ms	10×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	39	10
2	67	10
3	153	10
4	439	10
5	1830	10
6	5001	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: 3.2b

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
20×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `hypot-def`
8×	`distribute-lft-out` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 118

Calls

4 calls:

15.0ms	(* (/ (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)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
104.0ms	(pow (sin kx) 2.0)
107.0ms	(pow (sin ky) 2.0)
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	403	1038
1	1435	967
2	5002	965

prune459.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	10	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	10	131

Merged error: 0.0b

Counts

131 → 10

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
6.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series506.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(hypot (sin ky) (sin kx))
167.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
223.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify147.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	287	725
1	1045	645
2	4965	644
3	5001	644

prune264.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 0b

Counts

92 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
0.3b	(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
4.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
4.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
1.0ms	(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

series808.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
170.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
215.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
215.0ms	(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify127.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	253	765
1	833	670
2	3899	669
3	5001	668

prune305.0ms

Filtered

83 candidates to 67 candidates (80.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Merged error: 0b

Counts

92 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin th) (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
4.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
7.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series542.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(hypot (sin ky) (sin kx))
202.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
221.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify38.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	258	719
1	1032	641
2	5002	641

prune232.0ms

Filtered

82 candidates to 64 candidates (78.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	83	8	91

Merged error: 0b

Counts

91 → 8

regimes287.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.3s	3781×	body	1280	valid
1.0s	2014×	body	640	valid
256.0ms	686×	body	320	valid
148.0ms	1252×	body	80	valid
59.0ms	267×	body	160	valid