Details

sample232.0ms

Algorithm

intervals

Results

69.0ms	131×	body	1280	valid
30.0ms	28×	body	1280	nan
25.0ms	52×	body	640	valid
21.0ms	135×	body	80	overflowed
19.0ms	29×	body	640	nan
15.0ms	31×	body	320	valid
10.0ms	214×	body	80	nan
9.0ms	88×	body	80	valid
6.0ms	15×	body	320	nan
3.0ms	17×	body	160	valid
2.0ms	10×	body	160	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune2.0ms

Filtered

1 candidates to 0 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: 32.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series485.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune233.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 21.0b

Counts

89 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
78×	`unpow-prod-down`
77×	`*-un-lft-identity`
72×	`cbrt-prod`
63×	`difference-of-squares`
42×	`sqr-pow`
27×	`distribute-lft-out--`
22×	`swap-sqr`
18×	`associate-r` `associate-l`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
10×	`add-log-exp`
9×	`flip3--` `flip--` `distribute-lft-out`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 160

Calls

4 calls:

27.0ms	(* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.3s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify69.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	496	2902
1	1650	2801
2	5001	2592

prune570.0ms

Filtered

172 candidates to 130 candidates (75.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	170	8	178

Merged error: 21.0b

Counts

178 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
283.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	541	922
1	1760	884
2	5001	863

prune338.0ms

Filtered

121 candidates to 95 candidates (78.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	120	9	129

Merged error: 21.0b

Counts

129 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.7b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.7b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-prod`
12×	`sqr-pow`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`sub-neg` `exp-sum` `log-pow` `add-cbrt-cube`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
14.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
461.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
466.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify114.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	300	1278
1	805	1194
2	3713	1170
3	5001	1170

prune423.0ms

Filtered

98 candidates to 82 candidates (83.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	97	10	107

Merged error: 20.9b

Counts

107 → 10

regimes330.0ms

Accuracy

79.8% (2.3b remaining)

Error of 23.5b against oracle of 21.3b and baseline of 32.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	38
1	42	38

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.1s	3875×	body	1280	valid
1.2s	1069×	body	1280	nan
1.0s	1760×	body	640	valid
642.0ms	888×	body	640	nan
617.0ms	4091×	body	80	overflowed
327.0ms	3098×	body	80	valid
310.0ms	6319×	body	80	nan
295.0ms	937×	body	320	valid
199.0ms	477×	body	320	nan
93.0ms	476×	body	160	valid
51.0ms	234×	body	160	nan

Details

sample232.0ms

simplify36.0ms

prune2.0ms

localize9.0ms

rewrite21.0ms

series485.0ms

simplify46.0ms

prune233.0ms

localize13.0ms

rewrite66.0ms

series2.3s

simplify69.0ms

prune570.0ms

localize11.0ms

rewrite37.0ms

series772.0ms

simplify59.0ms

prune338.0ms

localize16.0ms

rewrite46.0ms

series1.5s

simplify114.0ms

prune423.0ms

regimes330.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample7.3s

Profiling