Details

sample405.0ms

Algorithm

intervals

Results

233.0ms	3885×	body	80	nan
43.0ms	175×	body	640	valid
9.0ms	47×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	4×	body	1280	valid
1.0ms	19×	body	80	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 6.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.8b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite53.0ms

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:

9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series293.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify102.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (71.0ms)

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

prune954.0ms

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	274	18	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	275	18	293

Merged error: 4.6b

Counts

293 → 18

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.7b	(+ y (- 1.0 y))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite52.0ms

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

series220.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify95.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (69.0ms)

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

prune729.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	7	10	17
Picked	1	0	1
Done	0	0	0
Total	260	11	271

Merged error: 3.8b

Counts

271 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite54.0ms

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:

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

series365.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify104.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (76.0ms)

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

prune913.0ms

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	261	4	265
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	261	15	276

Merged error: 3.8b

Counts

276 → 15

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

242×	`sqrt-prod`
231×	`*-un-lft-identity`
190×	`add-sqr-sqrt`
126×	`prod-diff`
120×	`add-cube-cbrt`
76×	`times-frac`
48×	`distribute-lft-out`
33×	`associate-r` `associate-l`
26×	`add-exp-log`
21×	`fma-neg`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
8×	`div-exp` `prod-exp`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `associate-/r/` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 317

Calls

4 calls:

47.0ms	(* (/ 1 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series369.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (/ 1 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))))
75.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
78.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify73.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1288	5064
1	5001	3623

prune963.0ms

Filtered

329 candidates to 137 candidates (41.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	325	4	329
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	328	16	344

Merged error: 3.8b

Counts

344 → 16

regimes1.3s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample613.0ms

Algorithm

intervals

Results

360.0ms	6101×	body	80	nan
67.0ms	273×	body	640	valid
12.0ms	64×	body	320	valid
2.0ms	33×	body	80	valid
2.0ms	7×	body	1280	valid
2.0ms	18×	body	160	valid

Details

sample405.0ms

simplify27.0ms

prune5.0ms

localize25.0ms

rewrite53.0ms

series293.0ms

simplify102.0ms

prune954.0ms

localize26.0ms

rewrite52.0ms

series220.0ms

simplify95.0ms

prune729.0ms

localize23.0ms

rewrite54.0ms

series365.0ms

simplify104.0ms

prune913.0ms

localize32.0ms

rewrite93.0ms

series369.0ms

simplify73.0ms

prune963.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample613.0ms

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