Details

sample598.0ms

Algorithm

intervals

Results

392.0ms	4095×	body	80	nan
65.0ms	170×	body	640	valid
11.0ms	37×	body	320	valid
4.0ms	19×	body	160	valid
2.0ms	5×	body	1280	valid
2.0ms	25×	body	80	valid

simplify31.0ms

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: 5.8b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))
3.7b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite54.0ms

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:

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

series286.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
76.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify103.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (70.0ms)

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

prune935.0ms

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: 4.5b

Counts

293 → 18

localize27.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(+ z (- 1.0 z))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.7b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite47.0ms

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 (+ x 1.0)) (sqrt x))
7.0ms	(+ z (- 1.0 z))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series214.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ z (- 1.0 z))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify93.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	848	3327
1	2686	2292
2	5002	2082

prune754.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	258	13	271

Merged error: 3.1b

Counts

271 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.7b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite50.0ms

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:

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

series357.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify100.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	948	3617
1	3148	2584
2	5001	2530

prune868.0ms

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	260	5	265
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	265	13	278

Merged error: 3.1b

Counts

278 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.7b	(+ t (- 1.0 t))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))
3.7b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
130×	`sqrt-prod`
94×	`add-sqr-sqrt`
93×	`prod-diff`
78×	`add-cube-cbrt`
34×	`distribute-lft-out`
18×	`times-frac`
14×	`fma-neg`
13×	`add-log-exp`
11×	`associate-+r+`
8×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-def` `diff-log` `associate-/l*`
2×	`flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 214

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
6.0ms	(+ t (- 1.0 t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
13.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series291.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.0ms	(+ t (- 1.0 t))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify99.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	857	2684
1	2953	1944
2	5001	1788

prune681.0ms

Filtered

226 candidates to 106 candidates (46.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	229	10	239

Merged error: 2.4b

Counts

239 → 10

regimes761.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.9s	20226×	body	80	nan
330.0ms	850×	body	640	valid
71.0ms	245×	body	320	valid
20.0ms	99×	body	160	valid
13.0ms	25×	body	1280	valid
9.0ms	100×	body	80	valid