Details

sample385.0ms

Algorithm

intervals

Results

222.0ms	3910×	body	80	nan
39.0ms	157×	body	640	valid
10.0ms	58×	body	320	valid
2.0ms	21×	body	160	valid
1.0ms	18×	body	80	valid
1.0ms	2×	body	1280	valid

simplify25.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite55.0ms

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 (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series302.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
89.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
81.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify98.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (64.0ms)

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

prune1.0s

Filtered

292 candidates to 132 candidates (45.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.8b

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(+ x (- 1.0 x))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite50.0ms

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:

12.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
7.0ms	(+ x (- 1.0 x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series203.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify90.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	856	3329
1	2715	2292
2	5001	2082

prune816.0ms

Filtered

253 candidates to 105 candidates (41.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite56.0ms

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 (+ x 1.0)) (sqrt x)))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series358.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify100.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	956	3619
1	3178	2584
2	5001	2530

prune982.0ms

Filtered

265 candidates to 131 candidates (49.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
3.2b	(+ y (- 1.0 y))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite50.0ms

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

series289.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ y (- 1.0 y))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify103.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	864	2686
1	2985	1944
2	5003	1788

prune985.0ms

Filtered

226 candidates to 106 candidates (46.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.0b

regimes713.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample607.0ms

Algorithm

intervals

Results

358.0ms	6228×	body	80	nan
63.0ms	249×	body	640	valid
15.0ms	83×	body	320	valid
4.0ms	32×	body	160	valid
2.0ms	26×	body	80	valid
1.0ms	3×	body	1280	valid