Details

sample666.0ms

Algorithm

intervals

Results

383.0ms	4093×	body	80	nan
65.0ms	169×	body	640	valid
15.0ms	49×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	16×	body	80	valid
1.0ms	3×	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 (100.0%)

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: 6.7b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
4.5b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite35.0ms

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

series37.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5003	824

prune264.0ms

Filtered

88 candidates to 60 candidates (31.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 5.4b

Counts

89 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.9b	(+ x (- 1.0 x))
4.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
15×	`add-log-exp`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 74

Calls

4 calls:

8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
5.0ms	(+ x (- 1.0 x))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series32.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify53.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	602	708
1	2429	673
2	5002	673

prune254.0ms

Filtered

86 candidates to 59 candidates (31.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 4.3b

Counts

95 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
4.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`sqrt-prod`
39×	`add-sqr-sqrt`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`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`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

17.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
15.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series69.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
16.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
16.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify93.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	816	1082
1	3586	1020
2	5002	1003

prune333.0ms

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Merged error: 4.2b

Counts

121 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))
3.4b	(+ y (- 1.0 y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
32×	`sqrt-prod`
31×	`add-sqr-sqrt`
20×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
13×	`add-log-exp`
8×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `diff-log` `associate-/l*`
2×	`associate-+r+` `flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 96

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
6.0ms	(+ y (- 1.0 y))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify70.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	728	926
1	3069	869
2	5001	852

prune233.0ms

Filtered

108 candidates to 70 candidates (35.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Merged error: 3.3b

Counts

121 → 11

regimes1.2s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	12746×	body	80	nan
207.0ms	545×	body	640	valid
42.0ms	156×	body	320	valid
8.0ms	18×	body	1280	valid
7.0ms	40×	body	160	valid
6.0ms	69×	body	80	valid

Details

sample666.0ms

simplify25.0ms

prune5.0ms

localize22.0ms

rewrite35.0ms

series37.0ms

simplify62.0ms

prune264.0ms

localize27.0ms

rewrite31.0ms

series32.0ms

simplify53.0ms

prune254.0ms

localize24.0ms

rewrite60.0ms

series69.0ms

simplify93.0ms

prune333.0ms

localize28.0ms

rewrite35.0ms

series29.0ms

simplify70.0ms

prune233.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

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