Details

sample117.0ms

Algorithm

intervals

Results

69.0ms	93×	body	1280	valid
20.0ms	51×	body	640	valid
7.0ms	77×	body	80	valid
5.0ms	18×	body	320	valid
3.0ms	17×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

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))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`add-exp-log` `associate-/r*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 117

Calls

4 calls:

18.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin ky) 2.0)
1.0ms	(pow (sin kx) 2.0)
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
99.0ms	(pow (sin ky) 2.0)
103.0ms	(pow (sin kx) 2.0)
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	341	1065
1	1159	981
2	5001	976

prune435.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.2b

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

0.2b

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

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:

0.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

8.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

3.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series935.0ms

Counts

3 → 9

Calls

3 calls:

243.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

327.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

365.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify38.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	295	1114
1	1091	988
2	5001	986

prune371.0ms

Filtered

82 candidates to 67 candidates (81.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.3b

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

0.3b

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite13.0ms

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:

0.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

3.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

8.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series896.0ms

Counts

3 → 9

Calls

3 calls:

232.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

317.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

347.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	291	1109
1	1164	984
2	5001	983

prune339.0ms

Filtered

82 candidates to 64 candidates (78.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.3b	(/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
0.3b	(* (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
0.3b	(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
84×	`times-frac`
61×	`add-cube-cbrt` `*-un-lft-identity`
51×	`sqrt-prod`
22×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 172

Calls

4 calls:

1.0ms	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
4.0ms	(/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
23.0ms	(* (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
4.0ms	(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

255.0ms	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
323.0ms	(/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
324.0ms	(* (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
316.0ms	(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	577	3695
1	2447	3364
2	5002	3221

prune600.0ms

Filtered

184 candidates to 124 candidates (67.4%)

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.2b

regimes663.0ms

Accuracy

0% (0.2b remaining)

Error of 8.7b against oracle of 8.5b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	11
1	15	11

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.0s	2739×	body	1280	valid
748.0ms	1832×	body	640	valid
385.0ms	785×	body	320	valid
206.0ms	2354×	body	80	valid
51.0ms	290×	body	160	valid