Details

sample594.0ms

Algorithm

intervals

Results

381.0ms	3777×	body	80	nan
76.0ms	180×	body	640	valid
12.0ms	41×	body	320	valid
3.0ms	4×	body	1280	valid
3.0ms	14×	body	160	valid
2.0ms	17×	body	80	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 (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: 5.9b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.6b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite33.0ms

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 (+ z 1.0)) (sqrt z))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series756.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
180.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
218.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
177.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify65.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5002	824

prune660.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	13	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Merged error: 4.7b

Counts

89 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.7b	(+ y (- 1.0 y))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))

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

series539.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
180.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(+ y (- 1.0 y))
180.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify56.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	604	708
1	2432	673
2	5001	673

prune442.0ms

Filtered

86 candidates to 59 candidates (68.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	86	13	99

Merged error: 3.0b

Counts

99 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.3b	(- (sqrt (+ x 1.0)) (sqrt x))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite38.0ms

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:

9.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series741.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
173.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
184.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
185.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify78.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	813	1083
1	3571	1022
2	5003	1005

prune529.0ms

Filtered

110 candidates to 72 candidates (65.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 3.0b

Counts

123 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.3b	(- (sqrt (+ x 1.0)) (sqrt x))
2.4b	(+ t (- 1.0 t))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite36.0ms

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

series552.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
175.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(+ t (- 1.0 t))
177.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify94.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	722	927
1	3053	871
2	5001	854

prune462.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 1.6b

Counts

122 → 13

regimes1.1s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.9s	22131×	body	80	nan
349.0ms	975×	body	640	valid
77.0ms	292×	body	320	valid
16.0ms	89×	body	160	valid
11.0ms	25×	body	1280	valid
9.0ms	104×	body	80	valid

Details

sample594.0ms

simplify25.0ms

prune5.0ms

localize21.0ms

rewrite33.0ms

series756.0ms

simplify65.0ms

prune660.0ms

localize28.0ms

rewrite31.0ms

series539.0ms

simplify56.0ms

prune442.0ms

localize22.0ms

rewrite38.0ms

series741.0ms

simplify78.0ms

prune529.0ms

localize25.0ms

rewrite36.0ms

series552.0ms

simplify94.0ms

prune462.0ms

regimes1.1s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.9s

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