Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample198.0ms

Algorithm

intervals

Results

63.0ms	118×	body	1280	valid
32.0ms	32×	body	1280	nan
25.0ms	37×	body	640	nan
18.0ms	43×	body	640	valid
11.0ms	68×	body	80	overflowed
8.0ms	25×	body	320	valid
7.0ms	9×	body	640	invalid
5.0ms	13×	body	320	nan
5.0ms	61×	body	80	valid
3.0ms	3×	body	1280	invalid
2.0ms	6×	body	320	invalid
2.0ms	9×	body	160	valid
1.0ms	21×	body	80	nan
1.0ms	7×	body	80	invalid
1.0ms	3×	body	160	nan

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune7.0ms

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: 33.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
2.6b	(- (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 → 78

Calls

3 calls:

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

series74.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify57.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4985	1250
1	4985	1250

prune182.0ms

Filtered

71 candidates to 87 candidates (-22.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 20.5b

Counts

88 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
0.0b	(pow x (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
54×	`sqrt-prod`
32×	`add-cube-cbrt` `*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
18×	`times-frac`
16×	`unswap-sqr`
15×	`sqr-pow`
13×	`pow1`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
8×	`add-exp-log`
6×	`sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`pow-prod-down` `pow-sqr` `pow-prod-up` `difference-of-squares`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 139

Calls

4 calls:

9.0ms	(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow x (/ 1.0 n))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
12.0ms	(pow x (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4957	1927
1	4957	1927

prune281.0ms

Filtered

98 candidates to 151 candidates (-54.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	150	6	156

Merged error: 20.4b

Counts

156 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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`
15×	`log-prod` `exp-sum`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`exp-prod` `add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `exp-diff` `pow-exp` `flip--` `div-inv`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 107

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
11.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
38.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify33.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5230	1966

prune280.0ms

Filtered

94 candidates to 119 candidates (-26.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	116	9	125

Merged error: 20.4b

Counts

125 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (pow (exp (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`unpow-prod-down`
29×	`*-un-lft-identity`
27×	`difference-of-squares`
20×	`sqr-pow`
10×	`add-log-exp`
9×	`distribute-lft-out--`
8×	`add-cube-cbrt`
7×	`pow-unpow`
5×	`pow1` `add-exp-log`
4×	`cbrt-prod` `pow-exp` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
2×	`pow-to-exp`
1×	`pow-pow` `log-pow`

Counts

4 → 96

Calls

4 calls:

4.0ms	(pow (pow (exp (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

524.0ms	(pow (pow (exp (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify63.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5066	3595

prune611.0ms

Filtered

91 candidates to 108 candidates (-18.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	108	9	117

Merged error: 20.4b

Counts

117 → 9

regimes455.0ms

Accuracy

82.7% (1.8b remaining)

Error of 24.3b against oracle of 22.5b and baseline of 33.0b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	211	179
1	211	179

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.1s	3795×	body	1280	valid
1.1s	1041×	body	1280	nan
664.0ms	1510×	body	640	valid
635.0ms	912×	body	640	nan
477.0ms	2767×	body	80	overflowed
225.0ms	736×	body	320	valid
205.0ms	477×	body	320	nan
180.0ms	268×	body	640	invalid
147.0ms	1617×	body	80	valid
122.0ms	101×	body	1280	invalid
71.0ms	180×	body	320	invalid
66.0ms	342×	body	160	valid
45.0ms	209×	body	160	nan
32.0ms	255×	body	80	invalid
31.0ms	513×	body	80	nan
19.0ms	80×	body	160	invalid

Details

analyze1.1s

sample198.0ms

simplify49.0ms

prune7.0ms

localize9.0ms

rewrite21.0ms

series74.0ms

simplify57.0ms

prune182.0ms

localize11.0ms

rewrite30.0ms

series77.0ms

simplify62.0ms

prune281.0ms

localize11.0ms

rewrite33.0ms

series108.0ms

simplify33.0ms

prune280.0ms

localize17.0ms

rewrite37.0ms

series643.0ms

simplify63.0ms

prune611.0ms

regimes455.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample6.4s

Profiling