Details

analyze264.0ms

Algorithm: search

sample137.0ms

Algorithm

intervals

Results

63.0ms	165×	body	640	valid
32.0ms	346×	body	80	nan
15.0ms	54×	body	320	valid
3.0ms	13×	body	160	valid
2.0ms	20×	body	80	valid
2.0ms	4×	body	1280	valid

simplify26.0ms

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

prune7.0ms

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: 5.4b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (sqrt (+ z 1.0)) (sqrt z))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ y 1.0)) (sqrt y))
4.1b	(- (sqrt (+ x 1.0)) (sqrt x))

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:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify64.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (14.0ms)

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

prune239.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 4.4b

Counts

89 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (sqrt (+ z 1.0)) (sqrt z))
2.4b	(+ y (- 1.0 y))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite30.0ms

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:

7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
5.0ms	(+ y (- 1.0 y))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series33.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

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

prune219.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 3.0b

Counts

92 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.0b	(- (sqrt (+ z 1.0)) (sqrt z))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ x 1.0)) (sqrt x))

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)))
7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series37.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify78.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (64.0ms)

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

prune315.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Merged error: 3.0b

Counts

116 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (+ (sqrt (+ y 1.0)) (sqrt y))))
2.0b	(- (sqrt (+ z 1.0)) (sqrt z))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite94.0ms

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ y 1.0)) (sqrt y)))) (sqrt (+ (sqrt (+ y 1.0)) (sqrt y))))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
17.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify99.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1404	8413
1	5002	7359

prune725.0ms

Filtered

134 candidates to 425 candidates (-217.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	421	4	425
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	424	13	437

Merged error: 3.0b

Counts

437 → 13

regimes1.4s

Accuracy

0% (1.1b remaining)

Error of 4.2b against oracle of 3.2b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	36
1	41	36

end0.0ms

analyze257.0ms

Algorithm: search

sample4.0s

Algorithm

intervals

Results

2.0s	5223×	body	640	valid
925.0ms	9616×	body	80	nan
443.0ms	1540×	body	320	valid
85.0ms	451×	body	160	valid
69.0ms	146×	body	1280	valid
64.0ms	640×	body	80	valid

Details

analyze264.0ms

sample137.0ms

simplify26.0ms

prune7.0ms

localize22.0ms

rewrite33.0ms

series40.0ms

simplify64.0ms

prune239.0ms

localize26.0ms

rewrite30.0ms

series33.0ms

simplify56.0ms

prune219.0ms

localize23.0ms

rewrite38.0ms

series37.0ms

simplify78.0ms

prune315.0ms

localize24.0ms

rewrite94.0ms

series44.0ms

simplify99.0ms

prune725.0ms

regimes1.4s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze257.0ms

sample4.0s

Profiling