Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

sample44.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	105×	body	80	invalid
2.0ms	51×	body	80	nan

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4961	13
1	4961	13

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: 2.2b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* a (pow k m))
2.2b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`prod-exp`
4×	`pow1` `unpow-prod-down` `div-exp` `sum-log`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 74

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms	(* a (pow k m))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (* 10.0 k))
3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
15.0ms	(* a (pow k m))
36.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4953	920
1	4953	920

prune115.0ms

Filtered

60 candidates to 86 candidates (-43.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
0.6b	(cbrt k)
2.2b	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
30×	`prod-exp`
16×	`div-exp`
13×	`add-cbrt-cube`
11×	`pow-exp`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow-to-exp`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `pow1/3` `associate-/r*` `cbrt-unprod`
2×	`associate-/r/`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 71

Calls

4 calls:

1.0ms	(cbrt k)
1.0ms	(cbrt k)
1.0ms	(cbrt k)
12.0ms	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt k)
22.0ms	(cbrt k)
22.0ms	(cbrt k)
112.0ms	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify27.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5357	1174

prune113.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Merged error: 0.0b

Counts

87 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* k (+ k 10.0))
0.0b	(* a (pow k m))
0.2b	(/ 1 (/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m))))
2.1b	(/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
36×	`times-frac`
34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
26×	`div-exp`
22×	`add-cbrt-cube`
16×	`prod-exp`
11×	`associate-r`
8×	`associate-/r*`
7×	`pow1` `cbrt-undiv`
6×	`associate-l` `div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`unpow-prod-down` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `associate-r/` `clear-num` `-commutative` `flip-+` `associate-/l/` `sqr-pow`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `pow-prod-down` `associate-/r/` `distribute-lft-out` `inv-pow`

Counts

4 → 135

Calls

4 calls:

6.0ms	(* k (+ k 10.0))
5.0ms	(* a (pow k m))
8.0ms	(/ 1 (/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m))))
7.0ms	(/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* k (+ k 10.0))
18.0ms	(* a (pow k m))
30.0ms	(/ 1 (/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m))))
30.0ms	(/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m)))

simplify65.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4943	2014
1	4943	2014

prune161.0ms

Filtered

88 candidates to 147 candidates (-67.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	147	4	151

Merged error: 0.0b

Counts

151 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ a (+ 1.0 (* k (+ k 10.0))))
7.8b	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))
7.8b	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))
7.8b	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-l/` `associate-/r` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 59

Calls

4 calls:

4.0ms	(/ a (+ 1.0 (* k (+ k 10.0))))
5.0ms	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))
6.0ms	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))
6.0ms	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ a (+ 1.0 (* k (+ k 10.0))))
62.0ms	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))
60.0ms	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))
64.0ms	(cbrt (* (/ a (+ 1.0 (* k (+ k 10.0)))) (pow k m)))

simplify80.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4926	1200
1	4926	1200

prune191.0ms

Filtered

62 candidates to 71 candidates (-14.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	71	4	75

Merged error: 0.0b

Counts

75 → 4

regimes168.0ms

Accuracy

97.7% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.2b

bsearch24.0ms

Steps

Iters	Range		Point
8	1.9183459489442965e+95	4.846553314372994e+99	9.999499964503198e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	53
1	51	53

end0.0ms

sample1.2s

Algorithm

intervals

Results

516.0ms	8000×	body	80	valid
260.0ms	3234×	body	80	invalid
95.0ms	1987×	body	80	nan

Details

analyze1.0s

sample44.0ms

simplify82.0ms

prune11.0ms

localize10.0ms

rewrite23.0ms

series58.0ms

simplify52.0ms

prune115.0ms

localize16.0ms

rewrite18.0ms

series178.0ms

simplify27.0ms

prune113.0ms

localize13.0ms

rewrite30.0ms

series83.0ms

simplify65.0ms

prune161.0ms

localize14.0ms

rewrite22.0ms

series200.0ms

simplify80.0ms

prune191.0ms

regimes168.0ms

bsearch24.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling