Details

sample405.0ms

Algorithm

intervals

Results

232.0ms	3885×	body	80	nan
43.0ms	175×	body	640	valid
9.0ms	47×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	4×	body	1280	valid
1.0ms	19×	body	80	valid

simplify26.0ms

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: 6.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.8b	(- (sqrt (+ y 1.0)) (sqrt y))

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 (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series266.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
63.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

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

prune351.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 0.8b

Counts

89 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite42.0ms

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

series338.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify63.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

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

prune443.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	120	5	125

Merged error: 0.2b

Counts

125 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
3.6b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite45.0ms

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:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series399.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
133.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
64.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify73.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (60.0ms)

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

prune556.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	140	6	146

Merged error: 0.1b

Counts

146 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.7b	(+ t (- 1.0 t))

rewrite43.0ms

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:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
6.0ms	(+ t (- 1.0 t))

series344.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
140.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
64.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ t (- 1.0 t))

simplify66.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	690	1183
1	2621	1075
2	5002	1006

prune543.0ms

Filtered

139 candidates to 83 candidates (59.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	140	5	145

Merged error: 0.0b

Counts

145 → 5

regimes541.0ms

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

sample617.0ms

Algorithm

intervals

Results

357.0ms	6101×	body	80	nan
68.0ms	273×	body	640	valid
12.0ms	64×	body	320	valid
2.0ms	7×	body	1280	valid
2.0ms	18×	body	160	valid
2.0ms	33×	body	80	valid

Details

sample405.0ms

simplify26.0ms

prune5.0ms

localize23.0ms

rewrite36.0ms

series266.0ms

simplify42.0ms

prune351.0ms

localize30.0ms

rewrite42.0ms

series338.0ms

simplify63.0ms

prune443.0ms

localize27.0ms

rewrite45.0ms

series399.0ms

simplify73.0ms

prune556.0ms

localize30.0ms

rewrite43.0ms

series344.0ms

simplify66.0ms

prune543.0ms

regimes541.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample617.0ms

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