Details

sample406.0ms

Algorithm

intervals

Results

233.0ms	3808×	body	80	nan
46.0ms	172×	body	640	valid
8.0ms	40×	body	320	valid
3.0ms	4×	body	1280	valid
2.0ms	19×	body	160	valid
1.0ms	21×	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: 3.9b

localize30.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
3.0b	(- (sqrt (+ t 1.0)) (sqrt t))
3.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite36.0ms

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:

8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series297.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (41.0ms)

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

prune405.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
3.0b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite44.0ms

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:

13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series365.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify68.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	634	1073
1	2370	978
2	5001	942

prune523.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
3.0b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite58.0ms

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:

10.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
20.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series461.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
145.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
77.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
78.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify71.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	728	1298
1	2760	1176
2	5001	1134

prune644.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(+ z (- 1.0 z))
3.0b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite42.0ms

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:

10.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
6.0ms	(+ z (- 1.0 z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series372.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
150.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(+ z (- 1.0 z))
77.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify69.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	683	1181
1	2593	1073
2	5001	1005

prune651.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes452.0ms

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

sample1.1s

Algorithm

intervals

Results

654.0ms	10718×	body	80	nan
124.0ms	496×	body	640	valid
29.0ms	154×	body	320	valid
5.0ms	42×	body	160	valid
3.0ms	11×	body	1280	valid
3.0ms	50×	body	80	valid