Details

sample53.0ms

Algorithm

intervals

Results

30.0ms	387×	body	80	valid
6.0ms	148×	body	80	nan

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 2.7b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
2.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`fma-def` `prod-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `div-exp` `sum-log` `log1p-expm1-u`
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 → 88

Calls

4 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(* a (pow k m))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
37.0ms	(+ 1.0 (* 10.0 k))
54.0ms	(* a (pow k m))
117.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify58.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	477	629
1	2275	544
2	5001	524

prune248.0ms

Filtered

100 candidates to 79 candidates (79.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	96	6	102

Merged error: 0.0b

Counts

102 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
15.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
61×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-exp-log`
22×	`sqrt-div`
18×	`associate-/r/` `add-cbrt-cube`
13×	`div-exp` `associate-/l*`
12×	`associate-/r*`
11×	`flip3-+` `flip-+`
9×	`div-inv`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `cbrt-unprod` `hypot-def`
1×	`associate-/l/`

Counts

4 → 182

Calls

4 calls:

9.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
15.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
123.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
52.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
52.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify98.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	773	3506
1	3380	3103
2	5003	3090

prune466.0ms

Filtered

194 candidates to 124 candidates (63.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	193	7	200

Merged error: 0.0b

Counts

200 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (* a (pow k m)) (* (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
16.4b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.4b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
16.4b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
46×	`add-exp-log`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`associate-/r/`
21×	`prod-exp`
17×	`add-cbrt-cube`
14×	`associate-*l/`
12×	`div-exp`
9×	`cbrt-prod` `cbrt-unprod`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow1/3` `pow-exp`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 104

Calls

4 calls:

24.0ms	(/ (* a (pow k m)) (* (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
4.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (* a (pow k m)) (* (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
109.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
119.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
111.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify86.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	733	2167
1	2958	1758
2	5001	1658

prune372.0ms

Filtered

116 candidates to 85 candidates (73.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	116	7	123

Merged error: 0.0b

Counts

123 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma k 10.0 1.0)
0.3b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
4.5b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
95×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`unpow-prod-down`
18×	`add-exp-log`
16×	`associate-/r*`
14×	`sqr-pow`
10×	`div-exp` `add-cbrt-cube` `div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`associate-/r/` `fma-udef`

Counts

3 → 171

Calls

3 calls:

1.0ms	(fma k 10.0 1.0)
7.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
3.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series196.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(fma k 10.0 1.0)
112.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
53.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify93.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	705	1876
1	3255	1816
2	5001	1814

prune650.0ms

Filtered

180 candidates to 139 candidates (77.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	181	6	187

Merged error: 0.0b

Counts

187 → 6

regimes125.0ms

Accuracy

96.1% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch40.0ms

Steps

Iters	Range		Point
5	4.698039819321593e+82	1.8258673157907502e+83	1.7887581360509958e+83

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	54	34
2	54	34

end0.0ms

sample1.4s

Algorithm

intervals

Results

829.0ms	11995×	body	80	valid
189.0ms	4174×	body	80	nan

Details

sample53.0ms

simplify109.0ms

prune7.0ms

localize10.0ms

rewrite22.0ms

series226.0ms

simplify58.0ms

prune248.0ms

localize13.0ms

rewrite40.0ms

series393.0ms

simplify98.0ms

prune466.0ms

localize15.0ms

rewrite42.0ms

series459.0ms

simplify86.0ms

prune372.0ms

localize10.0ms

rewrite19.0ms

series196.0ms

simplify93.0ms

prune650.0ms

regimes125.0ms

bsearch40.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling