Details

sample396.0ms

Algorithm

intervals

Results

229.0ms	3510×	body	80	nan
48.0ms	182×	body	640	valid
8.0ms	44×	body	320	valid
2.0ms	6×	body	1280	valid
1.0ms	11×	body	160	valid
1.0ms	13×	body	80	valid

simplify28.0ms

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: 5.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
1.9b	(- (sqrt (+ z 1.0)) (sqrt z))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite88.0ms

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:

22.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
20.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
20.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
23.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series296.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune385.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite95.0ms

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:

28.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
20.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
23.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
20.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series378.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
78.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
77.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	627	1071
1	2344	979
2	5002	943

prune526.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite99.0ms

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:

28.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
22.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
21.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series440.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
146.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify68.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	721	1296
1	2733	1180
2	5001	1137

prune634.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
10.4b	(* (/ (+ 1.0 0) (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
87×	`distribute-lft-out`
80×	`sqrt-prod`
74×	`associate-l`
69×	`times-frac`
48×	`add-sqr-sqrt` `unpow-prod-down` `sqrt-div` `cube-prod`
34×	`frac-times`
32×	`frac-add`
27×	`add-cube-cbrt` `flip3-+` `flip-+`
26×	`associate-*r/`
19×	`flip3--` `flip--`
10×	`add-log-exp`
9×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
8×	`difference-of-squares`
6×	`pow1` `distribute-lft-out--`
4×	`sum-cubes`
3×	`sub-neg` `diff-log` `associate-r`
2×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `distribute-rgt-out--` `distribute-lft-in` `div-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 182

Calls

4 calls:

5.0ms	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
22.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
21.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
247.0ms	(* (/ (+ 1.0 0) (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
247.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
286.0ms	(* (/ (+ 1.0 0) (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1540	4460
1	5001	4215

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

regimes519.0ms

bsearch256.0ms

Steps

Iters	Range		Point
8	4.794520721250726e+70	3.902216421406529e+73	8.555820957645191e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	61
1	76	61
2	76	61

end0.0ms

sample1.0s

Algorithm

intervals

Results

613.0ms	9396×	body	80	nan
118.0ms	446×	body	640	valid
26.0ms	128×	body	320	valid
4.0ms	33×	body	160	valid
4.0ms	12×	body	1280	valid
2.0ms	32×	body	80	valid