Details

sample415.0ms

Algorithm

intervals

Results

337.0ms

3384×

body

valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune18.0ms

Filtered

1 candidates to 1 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: 1.2b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `times-frac`
63×	`add-cube-cbrt` `*-un-lft-identity`
26×	`unpow-prod-down` `cube-prod`
22×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `div-exp`
4×	`pow-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`sqrt-prod`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 172

Calls

4 calls:

11.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series109.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
43.0ms	(pow (/ 1.0 (fabs x)) 3)
40.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify127.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	584	1144
1	3655	959
2	5001	912

prune2.6s

Filtered

182 candidates to 100 candidates (45.1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	160	22	182
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	161	23	184

Merged error: 0.4b

Counts

184 → 23

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
98×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
13×	`unpow-prod-down` `cube-prod`
10×	`div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow3` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series99.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify112.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	535	1298
1	3321	1112
2	5001	972

prune3.1s

Filtered

203 candidates to 119 candidates (41.4%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	192	11	203
Fresh	10	12	22
Picked	0	1	1
Done	0	0	0
Total	202	24	226

Merged error: 0.3b

Counts

226 → 24

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-sqr-sqrt`
158×	`times-frac`
85×	`add-cube-cbrt` `*-un-lft-identity`
67×	`add-exp-log`
53×	`associate-r`
41×	`unpow-prod-down` `associate-l`
31×	`add-cbrt-cube`
29×	`div-exp` `unswap-sqr`
27×	`cube-prod`
20×	`prod-exp`
17×	`sqr-pow`
15×	`pow1`
13×	`swap-sqr`
10×	`pow-exp`
9×	`cbrt-undiv` `pow-to-exp`
8×	`cbrt-unprod` `div-inv` `unpow2`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `rem-cube-cbrt`
1×	`cube-div` `pow2` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 251

Calls

4 calls:

27.0ms	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)

series132.0ms

Counts

4 → 10

Calls

4 calls:

62.0ms	(* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (pow (fabs x) 3)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
44.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)

simplify50.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1131	2170
1	5001	1891

prune6.3s

Filtered

261 candidates to 157 candidates (39.8%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	245	16	261
Fresh	14	8	22
Picked	1	0	1
Done	1	0	1
Total	261	24	285

Merged error: 0.1b

Counts

285 → 24

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.7b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
58×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
13×	`unpow-prod-down` `cube-prod` `swap-sqr` `associate-r` `associate-l`
6×	`sqrt-prod` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 139

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series69.0ms

Counts

4 → 8

Calls

4 calls:

26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
43.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify104.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	535	845
1	3321	720
2	5001	646

prune1.7s

Filtered

147 candidates to 86 candidates (41.5%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	8	15	23
Picked	0	1	1
Done	0	0	0
Total	148	23	171

Merged error: 0.1b

Counts

171 → 23

regimes633.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	38
1	45	38

end0.0ms

sample7.7s

Algorithm

intervals

Results

6.6s

67791×

body

valid

Details

sample415.0ms

simplify67.0ms

prune18.0ms

localize28.0ms

rewrite28.0ms

series109.0ms

simplify127.0ms

prune2.6s

localize29.0ms

rewrite34.0ms

series99.0ms

simplify112.0ms

prune3.1s

localize32.0ms

rewrite56.0ms

series132.0ms

simplify50.0ms

prune6.3s

localize36.0ms

rewrite23.0ms

series69.0ms

simplify104.0ms

prune1.7s

regimes633.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.7s

Profiling