Details

sample416.0ms

Algorithm

intervals

Results

238.0ms	3620×	body	80	nan
47.0ms	164×	body	640	valid
11.0ms	53×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	11×	body	160	valid
1.0ms	21×	body	80	valid

simplify37.0ms

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

prune6.0ms

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: 6.2b

Counts

2 → 1

localize30.0ms

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))

rewrite39.0ms

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:

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

series335.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
85.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
85.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
87.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify57.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

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

prune421.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 0.7b

Counts

89 → 7

localize26.0ms

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))

rewrite48.0ms

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:

18.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series410.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
82.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
85.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
79.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify79.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (65.0ms)

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

prune760.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 0.5b

Counts

126 → 6

localize28.0ms

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))

rewrite51.0ms

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:

15.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(/ (+ 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))

series486.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
163.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
84.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
79.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify91.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	728	1298
1	2760	1176
2	5001	1134

prune607.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	140	7	147

Merged error: 0.5b

Counts

147 → 7

localize30.0ms

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))

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:

10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
15.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
6.0ms	(+ z (- 1.0 z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series402.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
157.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.0ms	(+ z (- 1.0 z))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify90.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (75.0ms)

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

prune606.0ms

Filtered

139 candidates to 83 candidates (59.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	140	6	146

Merged error: 0.2b

Counts

146 → 6

regimes505.0ms

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	17149×	body	80	nan
219.0ms	773×	body	640	valid
50.0ms	235×	body	320	valid
9.0ms	55×	body	160	valid
8.0ms	23×	body	1280	valid
6.0ms	93×	body	80	valid