Details

sample410.0ms

Algorithm

intervals

Results

239.0ms	3717×	body	80	nan
46.0ms	170×	body	640	valid
10.0ms	48×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	4×	body	1280	valid
1.0ms	19×	body	80	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize22.0ms

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))

rewrite95.0ms

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:

23.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
22.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
22.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
25.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series289.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
75.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

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

prune389.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))
3.3b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite104.0ms

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:

31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
25.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
22.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series355.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
67.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (50.0ms)

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

prune498.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite108.0ms

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:

32.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
24.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
25.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series434.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
142.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify84.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	721	1296
1	2731	1180
2	5001	1137

prune630.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

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 (+ y 1.0)) (sqrt y)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.7b	(+ t (- 1.0 t))

rewrite91.0ms

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:

32.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
23.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(+ t (- 1.0 t))

series530.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
137.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ t (- 1.0 t))

simplify67.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	683	1181
1	2592	1076
2	5001	1007

prune604.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes574.0ms

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

sample871.0ms

Algorithm

intervals

Results

523.0ms	8163×	body	80	nan
96.0ms	358×	body	640	valid
18.0ms	91×	body	320	valid
4.0ms	32×	body	160	valid
4.0ms	11×	body	1280	valid
3.0ms	46×	body	80	valid