Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 88.876343%

Guaranteed chance to sample good point: 28.230453%

Results

59.0ms	159×	body	640	valid
20.0ms	217×	body	80	nan
16.0ms	50×	body	320	valid
4.0ms	21×	body	160	valid
3.0ms	6×	body	1280	valid
2.0ms	20×	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

prune6.0ms

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: 6.4b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ y 1.0)) (sqrt y))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite37.0ms

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))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify68.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (17.0ms)

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

prune279.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 5.0b

Counts

89 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ y 1.0)) (sqrt y))
2.7b	(+ x (- 1.0 x))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite33.0ms

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (12.0ms)

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

prune257.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	86	11	97

Merged error: 3.6b

Counts

97 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ y 1.0)) (sqrt y))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite39.0ms

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:

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify78.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (66.0ms)

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

prune324.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	107	14	121

Merged error: 3.6b

Counts

121 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
2.5b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ y 1.0)) (sqrt y))
3.7b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

701×	`*-un-lft-identity`
664×	`sqrt-prod`
567×	`times-frac`
259×	`distribute-lft-out`
256×	`add-sqr-sqrt`
232×	`add-cube-cbrt`
33×	`associate-/l*`
22×	`sqrt-div` `associate-/r/`
12×	`difference-of-squares`
11×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
9×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out--`
4×	`pow1`
3×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `flip--`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 413

Calls

4 calls:

28.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify99.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1407	8412
1	5001	7358

prune720.0ms

Filtered

135 candidates to 425 candidates (-214.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	422	3	425
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	424	15	439

Merged error: 3.6b

Counts

439 → 15

regimes1.6s

Accuracy

0% (1.2b remaining)

Error of 4.2b against oracle of 3.1b and baseline of 4.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample4.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 88.876343%

Guaranteed chance to sample good point: 28.230453%

Results

2.0s	5136×	body	640	valid
589.0ms	6091×	body	80	nan
436.0ms	1564×	body	320	valid
88.0ms	466×	body	160	valid
76.0ms	156×	body	1280	valid
66.0ms	678×	body	80	valid

Details

sample1.1s

simplify25.0ms

prune6.0ms

localize22.0ms

rewrite37.0ms

series39.0ms

simplify68.0ms

prune279.0ms

localize25.0ms

rewrite33.0ms

series29.0ms

simplify54.0ms

prune257.0ms

localize23.0ms

rewrite39.0ms

series39.0ms

simplify78.0ms

prune324.0ms

localize30.0ms

rewrite90.0ms

series39.0ms

simplify99.0ms

prune720.0ms

regimes1.6s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.9s

Profiling