Details

sample393.0ms

Algorithm

intervals

Results

225.0ms	3717×	body	80	nan
43.0ms	170×	body	640	valid
9.0ms	48×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	4×	body	1280	valid
1.0ms	19×	body	80	valid

simplify30.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
3.3b	(- (sqrt (+ y 1.0)) (sqrt y))
3.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite130.0ms

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:

27.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
28.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
31.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
27.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series281.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify106.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (76.0ms)

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

prune991.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.5b

localize29.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
2.4b	(+ y (- 1.0 y))
3.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite106.0ms

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:

28.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
31.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(+ y (- 1.0 y))
27.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series216.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
1.0ms	(+ y (- 1.0 y))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify94.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (69.0ms)

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

prune841.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
3.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite123.0ms

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:

24.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
29.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
28.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
30.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series363.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify109.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (75.0ms)

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

prune995.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.2b	(+ x (- 1.0 x))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
3.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite99.0ms

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:

24.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
9.0ms	(+ x (- 1.0 x))
29.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
28.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series299.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.0ms	(+ x (- 1.0 x))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
75.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify95.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	864	2686
1	2984	1944
2	5002	1788

prune790.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.2b

regimes676.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample838.0ms

Algorithm

intervals

Results

494.0ms	8163×	body	80	nan
89.0ms	358×	body	640	valid
18.0ms	91×	body	320	valid
5.0ms	32×	body	160	valid
3.0ms	11×	body	1280	valid
3.0ms	46×	body	80	valid