Details

analyze261.0ms

Algorithm: search

sample136.0ms

Algorithm

intervals

Results

66.0ms	167×	body	640	valid
29.0ms	310×	body	80	nan
14.0ms	50×	body	320	valid
3.0ms	19×	body	160	valid
3.0ms	6×	body	1280	valid
1.0ms	14×	body	80	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

prune5.0ms

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: 5.5b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (sqrt (+ x 1.0)) (sqrt x))
3.9b	(- (sqrt (+ z 1.0)) (sqrt z))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (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 (+ 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))

series38.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify65.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5001	824

prune241.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 4.4b

Counts

89 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b	(+ z (- 1.0 z))
3.3b	(- (sqrt (+ x 1.0)) (sqrt x))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite32.0ms

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:

5.0ms	(+ z (- 1.0 z))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series29.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(+ z (- 1.0 z))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
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	601	708
1	2432	673
2	5001	673

prune227.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 2.9b

Counts

93 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
3.3b	(- (sqrt (+ x 1.0)) (sqrt x))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (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 (+ z 1.0)) (sqrt z)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (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	813	1082
1	3573	1020
2	5002	1003

prune307.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 2.9b

Counts

118 → 11

localize39.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (sqrt (+ x 1.0)) (sqrt x))
4.1b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (sqrt (+ t 1.0)) (sqrt t))
9.8b	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
72×	`sqrt-prod`
57×	`associate-l`
55×	`add-sqr-sqrt`
54×	`distribute-lft-out`
52×	`times-frac`
48×	`sqrt-div`
36×	`unpow-prod-down` `cube-prod`
34×	`frac-times`
32×	`frac-add`
27×	`flip3-+` `flip-+`
26×	`add-cube-cbrt` `associate-*r/`
19×	`flip3--` `flip--`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`add-exp-log` `associate-*l/` `add-cbrt-cube` `distribute-lft-out--`
6×	`pow1`
3×	`sub-neg` `diff-log` `associate-r` `sum-cubes`
2×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 171

Calls

4 calls:

8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
48.0ms	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
19.0ms	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1847	4272
1	5002	4054

prune769.0ms

Filtered

114 candidates to 183 candidates (-60.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	182	12	194

Merged error: 2.9b

Counts

194 → 12

regimes1.3s

Accuracy

0% (1.3b remaining)

Error of 4.2b against oracle of 2.9b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	37
1	45	37

end0.0ms

analyze262.0ms

Algorithm: search

sample4.1s

Algorithm

intervals

Results

2.1s	5228×	body	640	valid
948.0ms	9701×	body	80	nan
455.0ms	1571×	body	320	valid
88.0ms	459×	body	160	valid
76.0ms	150×	body	1280	valid
57.0ms	592×	body	80	valid

Details

analyze261.0ms

sample136.0ms

simplify26.0ms

prune5.0ms

localize23.0ms

rewrite36.0ms

series38.0ms

simplify65.0ms

prune241.0ms

localize25.0ms

rewrite32.0ms

series29.0ms

simplify54.0ms

prune227.0ms

localize24.0ms

rewrite38.0ms

series37.0ms

simplify78.0ms

prune307.0ms

localize39.0ms

rewrite85.0ms

series51.0ms

simplify73.0ms

prune769.0ms

regimes1.3s

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze262.0ms

sample4.1s

Profiling