Details

sample429.0ms

Algorithm

intervals

Results

225.0ms	3633×	body	80	nan
44.0ms	174×	body	640	valid
9.0ms	49×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	18×	body	80	valid
1.0ms	2×	body	1280	valid

simplify29.0ms

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: 4.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite225.0ms

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:

53.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
52.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
52.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
53.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series265.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
65.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
63.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify94.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (67.0ms)

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

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ y (- 1.0 y))
1.9b	(- (sqrt (+ t 1.0)) (sqrt t))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite187.0ms

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:

18.0ms	(+ y (- 1.0 y))
52.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
52.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
50.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(+ y (- 1.0 y))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify87.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (64.0ms)

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

prune821.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.9b	(- (sqrt (+ t 1.0)) (sqrt t))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite213.0ms

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:

46.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
50.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
52.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
52.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series347.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify104.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (73.0ms)

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

prune982.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite180.0ms

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:

45.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
53.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
17.0ms	(+ z (- 1.0 z))
54.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series278.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
72.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
1.0ms	(+ z (- 1.0 z))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify94.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	856	2684
1	2954	1944
2	5002	1788

prune788.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.6b

regimes824.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.8s	28063×	body	80	nan
323.0ms	1252×	body	640	valid
70.0ms	358×	body	320	valid
15.0ms	123×	body	160	valid
9.0ms	133×	body	80	valid
9.0ms	23×	body	1280	valid