Details

sample411.0ms

Algorithm

intervals

Results

214.0ms	3633×	body	80	nan
42.0ms	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

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: 4.7b

localize22.0ms

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))

rewrite166.0ms

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:

41.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
41.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
39.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
42.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series271.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune383.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 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))

rewrite181.0ms

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:

55.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
40.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
43.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
39.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series340.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
68.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
66.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	634	1073
1	2368	978
2	5001	942

prune524.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.9b	(- (sqrt (+ t 1.0)) (sqrt t))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite185.0ms

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:

56.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
42.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
42.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series414.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
133.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify72.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	728	1298
1	2763	1179
2	5001	1136

prune628.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.9b	(- (sqrt (+ t 1.0)) (sqrt t))
1.9b	(log (exp (- (sqrt (+ z 1.0)) (sqrt z))))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`sqrt-prod`
19×	`distribute-lft-out`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`log-pow`
10×	`exp-prod`
9×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `log-prod`
3×	`sub-neg` `associate-/l*`
2×	`flip3--` `diff-log` `exp-sum` `associate-/r/` `flip--`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
88.0ms	(log (exp (- (sqrt (+ z 1.0)) (sqrt z))))
43.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series334.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(log (exp (- (sqrt (+ z 1.0)) (sqrt z))))
65.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify56.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	518	949
1	1806	852
2	5002	820

prune566.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

regimes554.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	52	35
2	52	35

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	28063×	body	80	nan
314.0ms	1252×	body	640	valid
65.0ms	358×	body	320	valid
15.0ms	123×	body	160	valid
8.0ms	133×	body	80	valid
7.0ms	23×	body	1280	valid