Details

sample435.0ms

Algorithm

intervals

Results

227.0ms	3848×	body	80	nan
40.0ms	169×	body	640	valid
9.0ms	53×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	19×	body	80	valid
1.0ms	3×	body	1280	valid

simplify27.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
3.7b	(- (sqrt (+ z 1.0)) (sqrt z))
4.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

43.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
42.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
44.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
44.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series260.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
62.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
66.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
66.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	472	702
1	1521	635
2	5001	620

prune425.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
44×	`sqrt-prod`
40×	`add-sqr-sqrt`
30×	`distribute-lft-out`
24×	`times-frac`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `associate-/l*`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 107

Calls

4 calls:

58.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
42.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
43.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
45.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series327.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
64.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	627	1071
1	2341	979
2	5001	943

prune591.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))
2.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
52×	`sqrt-prod`
45×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`times-frac`
27×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

58.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
45.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
42.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
44.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series411.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
133.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	721	1296
1	2731	1180
2	5002	1137

prune745.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.5b	(+ y (- 1.0 y))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
46×	`distribute-lft-out`
44×	`sqrt-prod`
42×	`times-frac`
35×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
12×	`associate-/r*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
4×	`pow1` `flip3-+` `associate-/r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--`

Counts

4 → 127

Calls

4 calls:

57.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
45.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
15.0ms	(+ y (- 1.0 y))
46.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series335.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
138.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
1.0ms	(+ y (- 1.0 y))
64.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify71.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	683	1181
1	2592	1076
2	5002	1007

prune674.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

regimes1.2s

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	26
1	55	26
2	55	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

592.0ms	10124×	body	80	nan
100.0ms	420×	body	640	valid
23.0ms	130×	body	320	valid
5.0ms	42×	body	160	valid
3.0ms	11×	body	1280	valid
3.0ms	53×	body	80	valid