Details

sample151.0ms

Algorithm

intervals

Results

91.0ms	114×	body	1280	valid
33.0ms	67×	body	640	valid
5.0ms	51×	body	80	valid
5.0ms	14×	body	320	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

3.0ms	(pow (sin ky) 2.0)
16.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow (sin ky) 2.0)
158.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
111.0ms	(pow (sin kx) 2.0)
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

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

prune487.0ms

Filtered

130 candidates to 95 candidates (73.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

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

series545.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(hypot (sin ky) (sin kx))
183.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
237.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify140.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

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

prune273.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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

series547.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(hypot (sin ky) (sin kx))
223.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
205.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify35.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	258	719
1	1032	641
2	5001	641

prune267.0ms

Filtered

82 candidates to 64 candidates (78.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
0.2b	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-l`
36×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

1.0ms	(hypot (sin ky) (sin kx))
4.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
6.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
14.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))

series690.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(hypot (sin ky) (sin kx))
148.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
166.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
238.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))

simplify76.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	637	2121
1	2915	1881
2	5001	1782

prune549.0ms

Filtered

203 candidates to 137 candidates (67.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes294.0ms

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

sample5.0s

Algorithm

intervals

Results

3.2s	3726×	body	1280	valid
1.0s	2005×	body	640	valid
240.0ms	714×	body	320	valid
134.0ms	1287×	body	80	valid
74.0ms	268×	body	160	valid