Details

sample418.0ms

Algorithm

intervals

Results

241.0ms	3946×	body	80	nan
46.0ms	178×	body	640	valid
8.0ms	44×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	10×	body	160	valid
1.0ms	17×	body	80	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 6.3b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
3.4b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ z 1.0)) (sqrt z))

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:

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

series303.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
77.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify115.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	936	4262
1	2794	2932
2	5001	2652

prune744.0ms

Filtered

292 candidates to 108 candidates (63.0%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	275	17	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	276	17	293

Merged error: 5.3b

Counts

293 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
3.4b	(+ z (- 1.0 z))
3.4b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite54.0ms

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))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
7.0ms	(+ z (- 1.0 z))
13.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series236.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
78.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(+ z (- 1.0 z))
80.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify95.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	839	3327
1	2583	2292
2	5001	2082

prune754.0ms

Filtered

253 candidates to 105 candidates (58.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	244	9	253
Fresh	14	2	16
Picked	1	0	1
Done	0	0	0
Total	259	11	270

Merged error: 4.3b

Counts

270 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
3.4b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite58.0ms

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

series392.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
80.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
77.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
81.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify109.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	939	3617
1	3034	2584
2	5001	2358

prune758.0ms

Filtered

265 candidates to 109 candidates (58.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	252	13	265
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	262	14	276

Merged error: 4.2b

Counts

276 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(+ t (- 1.0 t))

rewrite52.0ms

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:

10.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
13.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
7.0ms	(+ t (- 1.0 t))

series304.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
78.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(+ t (- 1.0 t))

simplify93.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	848	2684
1	2854	1944
2	5001	1788

prune709.0ms

Filtered

226 candidates to 106 candidates (53.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	216	10	226
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	228	12	240

Merged error: 2.2b

Counts

240 → 12

regimes885.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	17402×	body	80	nan
200.0ms	770×	body	640	valid
46.0ms	238×	body	320	valid
8.0ms	52×	body	160	valid
8.0ms	24×	body	1280	valid
5.0ms	82×	body	80	valid