Details

sample630.0ms

Algorithm

intervals

Results

359.0ms	3939×	body	80	nan
62.0ms	164×	body	640	valid
16.0ms	54×	body	320	valid
3.0ms	17×	body	160	valid
2.0ms	5×	body	1280	valid
1.0ms	16×	body	80	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5040	31

prune17.0ms

Filtered

1 candidates to 1 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: 5.4b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
3.8b	(- (sqrt (+ t 1.0)) (sqrt t))

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4985	1372
1	4985	1372

prune250.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	83	7	90

Merged error: 0.8b

Counts

90 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.7b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite43.0ms

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4993	1846
1	4993	1846

prune309.0ms

Filtered

78 candidates to 119 candidates (-52.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 0.5b

Counts

126 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))
1.7b	(- (sqrt (+ z 1.0)) (sqrt z))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite44.0ms

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
13.0ms	(/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify60.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5570	2134

prune378.0ms

Filtered

89 candidates to 141 candidates (-58.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	136	5	141
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Merged error: 0.0b

Counts

148 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
60×	`times-frac` `sqrt-prod` `distribute-lft-out`
46×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `difference-of-squares`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `distribute-lft-out--`
2×	`associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 151

Calls

4 calls:

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify63.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5812	2426

prune377.0ms

Filtered

101 candidates to 163 candidates (-61.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Merged error: 0.0b

Counts

172 → 9

regimes1.4s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	39
1	42	39

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	11447×	body	80	nan
195.0ms	505×	body	640	valid
40.0ms	145×	body	320	valid
8.0ms	42×	body	160	valid
7.0ms	16×	body	1280	valid
4.0ms	46×	body	80	valid

Details

sample630.0ms

simplify38.0ms

prune17.0ms

localize25.0ms

rewrite36.0ms

series42.0ms

simplify43.0ms

prune250.0ms

localize28.0ms

rewrite43.0ms

series44.0ms

simplify40.0ms

prune309.0ms

localize29.0ms

rewrite44.0ms

series42.0ms

simplify60.0ms

prune378.0ms

localize29.0ms

rewrite47.0ms

series44.0ms

simplify63.0ms

prune377.0ms

regimes1.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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