Details

sample636.0ms

Algorithm

intervals

Results

416.0ms	3620×	body	80	nan
77.0ms	164×	body	640	valid
19.0ms	53×	body	320	valid
4.0ms	7×	body	1280	valid
3.0ms	11×	body	160	valid
3.0ms	21×	body	80	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: 6.2b

localize22.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(- (sqrt (+ y 1.0)) (sqrt y))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite99.0ms

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

series287.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune405.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite108.0ms

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 (+ y 1.0)) (sqrt y)))
23.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
26.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
24.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series361.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify65.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (54.0ms)

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

prune526.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite113.0ms

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:

25.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
25.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
23.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series434.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
148.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
68.0ms	(- (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	2763	1176
2	5001	1134

prune652.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.5b	(+ z (- 1.0 z))
3.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite97.0ms

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:

26.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
34.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms	(+ z (- 1.0 z))
23.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series370.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
150.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.0ms	(+ z (- 1.0 z))
75.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify67.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (55.0ms)

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

prune638.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

regimes432.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.0s	17149×	body	80	nan
370.0ms	773×	body	640	valid
85.0ms	235×	body	320	valid
14.0ms	55×	body	160	valid
14.0ms	23×	body	1280	valid
12.0ms	93×	body	80	valid