Details

sample522.0ms

Algorithm

intervals

Results

331.0ms	3668×	body	80	nan
58.0ms	163×	body	640	valid
15.0ms	55×	body	320	valid
2.0ms	12×	body	160	valid
2.0ms	22×	body	80	valid
2.0ms	4×	body	1280	valid

simplify25.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.2b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (+ z 1.0)) (sqrt z))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite33.0ms

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))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series278.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune343.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.7b

Counts

89 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.4b	(- (sqrt (+ z 1.0)) (sqrt z))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite39.0ms

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:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
68.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify65.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (49.0ms)

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

prune490.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Merged error: 0.1b

Counts

123 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite55.0ms

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:

19.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series434.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
136.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
83.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify70.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (55.0ms)

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

prune580.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Merged error: 0.1b

Counts

148 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

241×	`*-un-lft-identity`
238×	`sqrt-prod`
120×	`times-frac`
111×	`add-sqr-sqrt`
90×	`distribute-lft-out`
67×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
19×	`pow1`
10×	`associate-/r/`
9×	`unswap-sqr`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
6×	`associate-/r*` `distribute-lft-out--`
5×	`flip3-+` `pow-prod-up` `flip-+` `div-inv`
4×	`sqrt-div`
3×	`pow-prod-down` `pow-sqr` `associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 211

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
34.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series449.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
166.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (sqrt (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify104.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	738	2298
1	3375	2060
2	5002	2032

prune789.0ms

Filtered

223 candidates to 115 candidates (51.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	223	8	231

Merged error: 0.1b

Counts

231 → 8

regimes680.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	22
1	48	22
2	48	22

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s	32165×	body	80	nan
520.0ms	1416×	body	640	valid
128.0ms	470×	body	320	valid
24.0ms	126×	body	160	valid
18.0ms	39×	body	1280	valid
16.0ms	176×	body	80	valid