Details

analyze132.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample40.0ms

Algorithm

intervals

Results

13.0ms	216×	body	80	valid
8.0ms	256×	pre	80	true
5.0ms	16×	body	1280	valid
3.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4904	27
1	4904	27

prune11.0ms

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: 9.4b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
0.1b	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
1.3b	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
1.4b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

7.0ms	(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
18.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
29.0ms	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
20.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
28.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))
94.0ms	(+ (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1))) 1.0)
193.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))

simplify39.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5268	2806

prune254.0ms

Filtered

100 candidates to 126 candidates (-26.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Merged error: 9.0b

Counts

128 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
0.5b	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
1.0b	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
1.3b	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

17.0ms	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
18.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
18.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
23.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
76.0ms	(/ beta (* (+ alpha (+ beta (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1)))
76.0ms	(/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
63.0ms	(- (/ alpha (* (+ beta (+ alpha (* 2.0 i))) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5060	2791

prune304.0ms

Filtered

93 candidates to 113 candidates (-21.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 3.8b

Counts

123 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ beta (+ alpha (* 2.0 i))))
0.1b	(/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
1.8b	(+ (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
3.6b	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
71×	`times-frac`
42×	`add-cube-cbrt`
32×	`add-exp-log`
26×	`associate-r`
20×	`add-cbrt-cube`
18×	`associate-l` `distribute-lft-out`
11×	`div-exp`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`prod-exp` `associate-/r` `associate-/r/` `associate-/l`
7×	`pow1`
6×	`cbrt-undiv` `add-log-exp` `unswap-sqr`
5×	`flip3-+` `flip-+`
4×	`cbrt-unprod` `div-inv`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `frac-times` `flip3--` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip--` `inv-pow`

Counts

4 → 168

Calls

4 calls:

6.0ms	(/ 1 (+ beta (+ alpha (* 2.0 i))))
15.0ms	(/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
24.0ms	(+ (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
35.0ms	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1 (+ beta (+ alpha (* 2.0 i))))
91.0ms	(/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
93.0ms	(+ (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)
195.0ms	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))

simplify62.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5016	3860

prune294.0ms

Filtered

114 candidates to 180 candidates (-57.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	175	5	180
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	180	9	189

Merged error: 3.8b

Counts

189 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha))
0.1b	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
0.4b	(/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
1.3b	(+ (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
44×	`times-frac`
32×	`add-exp-log`
28×	`add-cube-cbrt`
26×	`associate-l`
20×	`add-cbrt-cube`
14×	`distribute-lft-out`
11×	`div-exp`
9×	`pow1` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
8×	`prod-exp`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `associate-/r*` `flip-+` `add-log-exp`
4×	`frac-times` `associate-r/` `associate-r*` `cbrt-unprod` `div-inv`
3×	`rec-exp` `1-exp`
2×	`flip3--` `pow-flip` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `flip--` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sum-log` `*-commutative` `inv-pow`

Counts

4 → 147

Calls

4 calls:

9.0ms	(/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha))
29.0ms	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
21.0ms	(/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
24.0ms	(+ (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

series339.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha))
36.0ms	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))
189.0ms	(/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1)))
96.0ms	(+ (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1))) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5167	3510

prune215.0ms

Filtered

106 candidates to 159 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	159	9	168

Merged error: 3.8b

Counts

168 → 9

regimes310.0ms

Accuracy

21% (5.2b remaining)

Error of 10.9b against oracle of 5.7b and baseline of 12.3b

bsearch219.0ms

Steps

Iters	Range		Point
9	4.317814387440212e+148	3.412350807091612e+156	2.6630243519946244e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	72
1	51	72

end0.0ms

analyze130.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample1.1s

Algorithm

intervals

Results

392.0ms	6370×	body	80	valid
171.0ms	531×	body	1280	valid
169.0ms	8000×	pre	80	true
136.0ms	555×	body	640	valid
68.0ms	360×	body	320	valid
24.0ms	184×	body	160	valid

Details

analyze132.0ms

sample40.0ms

simplify70.0ms

prune11.0ms

localize15.0ms

rewrite78.0ms

series325.0ms

simplify39.0ms

prune254.0ms

localize22.0ms

rewrite80.0ms

series241.0ms

simplify41.0ms

prune304.0ms

localize16.0ms

rewrite87.0ms

series392.0ms

simplify62.0ms

prune294.0ms

localize19.0ms

rewrite89.0ms

series339.0ms

simplify63.0ms

prune215.0ms

regimes310.0ms

bsearch219.0ms

simplify2.0ms

end0.0ms

analyze130.0ms

sample1.1s

Profiling