Details

sample418.0ms

Algorithm

intervals

Results

241.0ms	3828×	body	80	nan
40.0ms	146×	body	640	valid
11.0ms	60×	body	320	valid
3.0ms	21×	body	160	valid
2.0ms	25×	body	80	valid
1.0ms	4×	body	1280	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

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: 4.6b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ z 1.0)) (sqrt z))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite38.0ms

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

series268.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
63.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune358.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 0.6b

Counts

89 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite40.0ms

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

series345.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
66.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify66.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (54.0ms)

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

prune489.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 0.5b

Counts

127 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

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:

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

series412.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify75.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	721	1296
1	2731	1177
2	5002	1135

prune560.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	140	9	149

Merged error: 0.4b

Counts

149 → 9

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.7b	(+ x (- 1.0 x))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite45.0ms

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:

9.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
6.0ms	(+ x (- 1.0 x))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series339.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.0ms	(+ x (- 1.0 x))
64.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify66.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	683	1181
1	2593	1073
2	5003	1005

prune564.0ms

Filtered

139 candidates to 83 candidates (59.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	141	7	148

Merged error: 0.2b

Counts

148 → 7

regimes677.0ms

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

sample515.0ms

Algorithm

intervals

Results

303.0ms	5290×	body	80	nan
49.0ms	202×	body	640	valid
11.0ms	62×	body	320	valid
4.0ms	34×	body	80	valid
2.0ms	8×	body	1280	valid
2.0ms	14×	body	160	valid