Details

sample181.0ms

Algorithm

intervals

Results

109.0ms	118×	body	1280	valid
41.0ms	61×	body	640	valid
9.0ms	24×	body	320	valid
5.0ms	43×	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	39	10
2	67	10
3	153	10
4	439	10
5	1830	10
6	5001	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: 5.4b

Counts

2 → 1

localize22.0ms

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)
0.3b	(pow (sin kx) 2.0)
5.0b	(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 ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
105.0ms	(pow (sin ky) 2.0)
102.0ms	(pow (sin kx) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

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

prune448.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	121	9	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	9	131

Merged error: 0.0b

Counts

131 → 9

localize11.0ms

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))

series503.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(hypot (sin ky) (sin kx))
166.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
223.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify142.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

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

prune249.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	81	10	91

Merged error: 0b

Counts

91 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

12.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
2.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series893.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
224.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
215.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
218.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify50.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	291	2447
1	993	2341
2	5001	2212

prune565.0ms

Filtered

164 candidates to 130 candidates (79.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	164	10	174

Merged error: 0b

Counts

174 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin ky)) (cbrt (sin ky)))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (sin ky)) (cbrt (sin ky)))
1.0ms	(cbrt (sin ky))
1.0ms	(cbrt (sin ky))
2.0ms	(cbrt (sin ky))

series410.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (cbrt (sin ky)) (cbrt (sin ky)))
102.0ms	(cbrt (sin ky))
98.0ms	(cbrt (sin ky))
97.0ms	(cbrt (sin ky))

simplify94.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	160	483
1	568	430
2	3134	398
3	5001	392

prune256.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	93	10	103

Merged error: 0b

Counts

103 → 10

regimes377.0ms

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	10	7
1	10	7

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.8s	3760×	body	1280	valid
1.2s	2008×	body	640	valid
294.0ms	730×	body	320	valid
141.0ms	1219×	body	80	valid
79.0ms	283×	body	160	valid