Details

sample694.0ms

Algorithm

intervals

Results

443.0ms	3668×	body	80	nan
79.0ms	163×	body	640	valid
19.0ms	55×	body	320	valid
3.0ms	12×	body	160	valid
3.0ms	4×	body	1280	valid
3.0ms	22×	body	80	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

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: 5.2b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (+ z 1.0)) (sqrt z))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

228×	`sqrt-prod`
200×	`*-un-lft-identity`
168×	`prod-diff`
148×	`add-sqr-sqrt`
116×	`add-cube-cbrt`
32×	`distribute-lft-out`
28×	`fma-neg`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 280

Calls

4 calls:

13.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series298.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
79.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify109.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	945	4262
1	2912	2932
2	5002	2860

prune1.1s

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	277	15	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	278	15	293

Merged error: 4.4b

Counts

293 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (+ z 1.0)) (sqrt z))
1.7b	(+ y (- 1.0 y))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

171×	`sqrt-prod`
163×	`*-un-lft-identity`
135×	`prod-diff`
119×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
26×	`distribute-lft-out`
21×	`fma-neg`
15×	`add-log-exp`
12×	`difference-of-squares`
11×	`associate-+r+`
10×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `diff-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `fma-def` `flip--`
2×	`sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 241

Calls

4 calls:

10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
7.0ms	(+ y (- 1.0 y))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series242.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ y (- 1.0 y))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify121.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	855	3329
1	2715	2292
2	5002	2082

prune767.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	256	12	268

Merged error: 2.8b

Counts

268 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.4b	(- (sqrt (+ z 1.0)) (sqrt z))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

190×	`*-un-lft-identity`
187×	`sqrt-prod`
126×	`prod-diff`
123×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
40×	`distribute-lft-out`
21×	`fma-neg`
18×	`times-frac`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 253

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
12.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series348.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify111.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	955	3619
1	3176	2584
2	5002	2530

prune886.0ms

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	261	4	265
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	262	15	277

Merged error: 2.8b

Counts

277 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))))
1.4b	(- (sqrt (+ z 1.0)) (sqrt z))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

377×	`sqrt-prod`
335×	`*-un-lft-identity`
192×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
126×	`prod-diff`
102×	`times-frac`
96×	`distribute-lft-out`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
21×	`fma-neg`
19×	`pow1`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--` `unswap-sqr`
8×	`sqrt-pow1` `pow1/2` `associate-/r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u` `div-inv`
3×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `flip--`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 344

Calls

4 calls:

39.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series386.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))))
73.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify141.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1079	4786
1	4230	3470
2	5001	3416

prune1.0s

Filtered

356 candidates to 145 candidates (40.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	354	2	356
Fresh	0	14	14
Picked	1	0	1
Done	0	0	0
Total	355	16	371

Merged error: 2.8b

Counts

371 → 16

regimes1.3s

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	48
1	42	48

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.2s	32165×	body	80	nan
577.0ms	1416×	body	640	valid
139.0ms	470×	body	320	valid
25.0ms	126×	body	160	valid
20.0ms	39×	body	1280	valid
19.0ms	176×	body	80	valid