Details

analyze138.0ms

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

sample43.0ms

Algorithm

intervals

Results

13.0ms	211×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	15×	body	1280	valid
4.0ms	17×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5446	29

prune12.0ms

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: 17.5b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.6b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
3.4b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
17.4b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

13.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
24.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
20.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
16.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
65.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
84.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
38.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5522	3306

prune294.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Merged error: 6.8b

Counts

134 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))
0.0b	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.6b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
3.4b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

667×	`*-un-lft-identity`
503×	`times-frac`
287×	`add-sqr-sqrt`
221×	`distribute-lft-out`
180×	`add-cube-cbrt`
136×	`associate-r`
49×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/l*`
28×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`div-inv`
9×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 399

Calls

4 calls:

11.0ms	(/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))
19.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
46.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
29.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))
38.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
66.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
88.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

simplify119.0ms

Algorithm

egg-herbie

Counts

411 → 411

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4997	11341
1	4997	11341

prune685.0ms

Filtered

207 candidates to 411 candidates (-98.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	406	5	411
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	409	8	417

Merged error: 6.8b

Counts

417 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
0.8b	(* (* (+ alpha beta) (* (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
4.1b	(+ (* (* (+ alpha beta) (* (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

605×	`*-un-lft-identity`
560×	`times-frac`
360×	`cbrt-prod`
310×	`associate-r`
287×	`add-sqr-sqrt`
219×	`add-cube-cbrt`
178×	`distribute-lft-out`
97×	`add-exp-log`
55×	`add-cbrt-cube`
45×	`prod-exp` `cbrt-unprod`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`cbrt-undiv` `div-exp`
29×	`frac-times`
21×	`associate-*l/`
18×	`flip3-+` `associate-/r/` `flip-+`
13×	`pow1` `associate-*r/`
9×	`div-inv`
6×	`cbrt-div` `pow-prod-down` `add-log-exp`
2×	`flip3--` `pow1/3` `flip--`
1×	`+-commutative` `associate-l` `sum-log` `*-commutative`

Counts

4 → 422

Calls

4 calls:

3.0ms	(cbrt (- beta alpha))
3.0ms	(cbrt (- beta alpha))
100.0ms	(* (* (+ alpha beta) (* (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
75.0ms	(+ (* (* (+ alpha beta) (* (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

series204.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- beta alpha))
26.0ms	(cbrt (- beta alpha))
66.0ms	(* (* (+ alpha beta) (* (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
87.0ms	(+ (* (* (+ alpha beta) (* (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (cbrt (- beta alpha)) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))) (/ (/ (cbrt (- beta alpha)) (+ beta (+ alpha (* 2.0 i)))) (cbrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

simplify131.0ms

Algorithm

egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5482	22699

prune1.7s

Filtered

237 candidates to 434 candidates (-83.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	432	2	434
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	433	9	442

Merged error: 6.8b

Counts

442 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
0.3b	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
0.4b	(/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
4.9b	(+ (* (/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

967×	`*-un-lft-identity`
848×	`times-frac`
511×	`add-sqr-sqrt`
321×	`sqrt-prod`
317×	`add-cube-cbrt`
288×	`distribute-lft-out`
214×	`associate-r`
68×	`distribute-lft-out--` `difference-of-squares`
42×	`associate-/r/`
38×	`associate-l`
32×	`add-exp-log` `add-cbrt-cube`
30×	`associate-/l*`
23×	`flip3-+` `flip-+`
21×	`div-inv`
16×	`associate-/r*`
15×	`unswap-sqr`
13×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 622

Calls

4 calls:

154.0ms	(* (/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
22.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
12.0ms	(/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
48.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
42.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
35.0ms	(/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
83.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)

simplify164.0ms

Algorithm

egg-herbie

Counts

634 → 634

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5040	22635

prune1.6s

Filtered

260 candidates to 634 candidates (-143.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	632	2	634
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	634	9	643

Merged error: 6.8b

Counts

643 → 9

regimes376.0ms

Accuracy

0% (6.6b remaining)

Error of 12.7b against oracle of 6.1b and baseline of 12.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	63
1	43	63

end0.0ms

sample1.2s

Algorithm

intervals

Results

404.0ms	6313×	body	80	valid
188.0ms	8000×	pre	80	true
160.0ms	508×	body	1280	valid
146.0ms	588×	body	640	valid
73.0ms	379×	body	320	valid
26.0ms	212×	body	160	valid

Details

analyze138.0ms

sample43.0ms

simplify46.0ms

prune12.0ms

localize17.0ms

rewrite78.0ms

series208.0ms

simplify50.0ms

prune294.0ms

localize17.0ms

rewrite134.0ms

series206.0ms

simplify119.0ms

prune685.0ms

localize25.0ms

rewrite225.0ms

series204.0ms

simplify131.0ms

prune1.7s

localize20.0ms

rewrite292.0ms

series224.0ms

simplify164.0ms

prune1.6s

regimes376.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling