Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
31.2%	68.7%	0.1%	7
34.3%	65.6%	0.1%	8
37.5%	59.3%	3.2%	9
42.9%	53.5%	3.6%	10
44.5%	50%	5.6%	11
47.8%	45.8%	6.4%	12
48.7%	43.7%	7.6%	13
50.5%	41.3%	8.2%	14

sample142.0ms

Algorithm

intervals

Results

46.0ms	201×	body	80	invalid
46.0ms	215×	body	80	valid
18.0ms	19×	body	640	valid
9.0ms	15×	body	320	valid
2.0ms	5×	body	160	valid
2.0ms	2×	body	1280	valid

simplify427.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5054	109

prune25.0ms

Filtered

1 candidates to 1 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: 0.5b

Counts

2 → 2

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 6.0 (* x1 x1))
0.2b	(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
3.3b	(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* 6.0 (* x1 x1)))
3.4b	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`associate-l`
15×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
13×	`add-cube-cbrt`
11×	`pow1` `times-frac`
8×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`associate-r` `pow-prod-down`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `associate-r/` `associate--l+` `associate-/r/` `-commutative` `flip--` `difference-of-squares`
1×	`cbrt-undiv` `associate--l-` `associate-+r-` `div-sub` `div-exp` `associate-*l/` `div-inv` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

5.0ms	(* 6.0 (* x1 x1))
35.0ms	(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
37.0ms	(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* 6.0 (* x1 x1)))
19.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

series130.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* 6.0 (* x1 x1))
31.0ms	(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
70.0ms	(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* 6.0 (* x1 x1)))
23.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5383	3593

prune563.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	91	10	101

Merged error: 0.3b

Counts

101 → 10

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 6.0 (* x1 x1))
0.2b	(* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0)))
3.3b	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* 6.0 (* x1 x1)))
3.4b	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
11×	`pow1`
10×	`-un-lft-identity` `associate-r*`
8×	`add-cube-cbrt` `add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l`
4×	`times-frac` `pow-prod-down`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `diff-log` `div-exp` `associate-l/` `associate-/r/` `-commutative` `flip--` `difference-of-squares` `unswap-sqr`
1×	`associate--l-` `associate-+r-` `div-sub` `associate-*r/` `div-inv` `distribute-lft-out--`

Counts

4 → 78

Calls

4 calls:

7.0ms	(* 6.0 (* x1 x1))
33.0ms	(* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0)))
32.0ms	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* 6.0 (* x1 x1)))
17.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

series115.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 6.0 (* x1 x1))
32.0ms	(* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0)))
65.0ms	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* 6.0 (* x1 x1)))
14.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4985	2989
1	4985	2989

prune418.0ms

Filtered

70 candidates to 90 candidates (-28.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 0.3b

Counts

100 → 9

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x1 (* x1 (+ (* 3.0 (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0))) x1)))
0.2b	(* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0)))
3.3b	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* (* x1 6.0) x1))
3.4b	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
11×	`pow1`
10×	`-un-lft-identity` `associate-r*`
8×	`add-cube-cbrt` `add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`associate-*r/`
4×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `frac-times` `sub-neg` `flip3--` `diff-log` `div-exp` `associate-l/` `associate-/r/` `-commutative` `flip--` `difference-of-squares`
1×	`associate--l-` `associate-+r-` `div-sub` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

19.0ms	(* x1 (* x1 (+ (* 3.0 (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0))) x1)))
33.0ms	(* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0)))
32.0ms	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* (* x1 6.0) x1))
19.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

series129.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* x1 (* x1 (+ (* 3.0 (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0))) x1)))
32.0ms	(* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0)))
64.0ms	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* (* x1 6.0) x1))
16.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4977	3525
1	4977	3525

prune430.0ms

Filtered

73 candidates to 95 candidates (-30.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 0.3b

Counts

104 → 10

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 6.0) (* x1 (* x1 (sqrt 6.0))))
0.5b	(* x1 (sqrt 6.0))
3.4b	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
5.1b	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* (sqrt 6.0) (* x1 (* x1 (sqrt 6.0)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `associate-l`
8×	`add-log-exp`
7×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`sub-neg` `flip3--` `diff-log` `*-commutative` `flip--` `difference-of-squares` `unswap-sqr`
1×	`associate--l-` `associate-+r-` `times-frac` `div-sub` `distribute-lft-out--`

Counts

4 → 72

Calls

4 calls:

9.0ms	(* (sqrt 6.0) (* x1 (* x1 (sqrt 6.0))))
5.0ms	(* x1 (sqrt 6.0))
17.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
36.0ms	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* (sqrt 6.0) (* x1 (* x1 (sqrt 6.0)))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sqrt 6.0) (* x1 (* x1 (sqrt 6.0))))
4.0ms	(* x1 (sqrt 6.0))
14.0ms	(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
72.0ms	(- (* (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (/ (* x1 (+ (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)) (* x1 4.0))) (+ (* x1 x1) 1.0))) (* (sqrt 6.0) (* x1 (* x1 (sqrt 6.0)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5181	1591

prune288.0ms

Filtered

57 candidates to 84 candidates (-47.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	84	10	94

Merged error: 0.3b

Counts

94 → 10

regimes376.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	141	107
1	141	107

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	6884×	body	80	valid
1.2s	5678×	body	80	invalid
423.0ms	492×	body	640	valid
197.0ms	314×	body	320	valid
152.0ms	144×	body	1280	valid
70.0ms	166×	body	160	valid

Details

analyze2.0s

sample142.0ms

simplify427.0ms

prune25.0ms

localize40.0ms

rewrite100.0ms

series130.0ms

simplify44.0ms

prune563.0ms

localize40.0ms

rewrite91.0ms

series115.0ms

simplify53.0ms

prune418.0ms

localize39.0ms

rewrite105.0ms

series129.0ms

simplify43.0ms

prune430.0ms

localize42.0ms

rewrite69.0ms

series97.0ms

simplify42.0ms

prune288.0ms

regimes376.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample3.8s

Profiling