Details

sample370.0ms

Algorithm

intervals

Results

208.0ms	3620×	body	80	nan
41.0ms	164×	body	640	valid
11.0ms	53×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	11×	body	160	valid
1.0ms	21×	body	80	valid

simplify26.0ms

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: 6.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(- (sqrt (+ y 1.0)) (sqrt y))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite52.0ms

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:

11.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series268.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
64.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify103.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (67.0ms)

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

prune933.0ms

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	273	19	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	274	19	293

Merged error: 4.6b

Counts

293 → 19

localize29.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(+ t (- 1.0 t))
3.4b	(- (sqrt (+ y 1.0)) (sqrt y))
4.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite46.0ms

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:

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

series209.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ t (- 1.0 t))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify91.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	856	3329
1	2712	2292
2	5001	2082

prune705.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	8	10	18
Picked	1	0	1
Done	0	0	0
Total	259	13	272

Merged error: 3.7b

Counts

272 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(- (sqrt (+ y 1.0)) (sqrt y))
4.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite49.0ms

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

series342.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify104.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	956	3619
1	3174	2584
2	5002	2530

prune877.0ms

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	258	7	265
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	262	16	278

Merged error: 3.7b

Counts

278 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.5b	(+ z (- 1.0 z))
3.4b	(- (sqrt (+ y 1.0)) (sqrt y))
4.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite47.0ms

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 (+ t 1.0)) (sqrt t)))
7.0ms	(+ z (- 1.0 z))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
13.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series274.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.0ms	(+ z (- 1.0 z))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify93.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	857	2684
1	2952	1944
2	5002	1788

prune661.0ms

Filtered

226 candidates to 106 candidates (46.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	229	13	242

Merged error: 3.0b

Counts

242 → 13

regimes1.1s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	17149×	body	80	nan
200.0ms	773×	body	640	valid
46.0ms	235×	body	320	valid
8.0ms	23×	body	1280	valid
7.0ms	55×	body	160	valid
6.0ms	93×	body	80	valid