Details

analyze1.3s

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

sample212.0ms

Algorithm

intervals

Results

64.0ms	115×	body	1280	valid
33.0ms	28×	body	1280	nan
27.0ms	57×	body	640	valid
18.0ms	26×	body	640	nan
17.0ms	96×	body	80	overflowed
7.0ms	23×	body	320	valid
7.0ms	5×	body	1280	invalid
6.0ms	15×	body	320	nan
6.0ms	8×	body	640	invalid
4.0ms	46×	body	80	valid
3.0ms	15×	body	160	valid
2.0ms	8×	body	160	nan
2.0ms	4×	body	320	invalid
1.0ms	16×	body	80	nan
1.0ms	3×	body	160	invalid
1.0ms	5×	body	80	invalid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune3.0ms

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: 32.7b

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))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite22.0ms

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:

4.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series77.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
46.0ms	(- (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

prune187.0ms

Filtered

71 candidates to 87 candidates (-22.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 23.0b

Counts

88 → 6

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))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite34.0ms

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

Counts

4 → 107

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(- (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)))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
42.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5051	1778

prune274.0ms

Filtered

96 candidates to 119 candidates (-24.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	117	8	125

Merged error: 23.0b

Counts

125 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
64×	`unpow-prod-down`
55×	`*-un-lft-identity`
36×	`sqrt-prod`
32×	`difference-of-squares`
26×	`pow-unpow`
24×	`add-cube-cbrt`
23×	`associate-r`
18×	`times-frac` `sqr-pow`
10×	`pow1`
9×	`distribute-lft-out`
8×	`add-exp-log` `distribute-lft-out--`
7×	`associate-l`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `sqrt-pow2` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

33.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
31.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
32.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
114.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify59.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5022	3716

prune464.0ms

Filtered

114 candidates to 163 candidates (-43.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	163	8	171

Merged error: 23.0b

Counts

171 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`unpow-prod-down`
39×	`pow-unpow`
31×	`add-cube-cbrt`
27×	`times-frac`
24×	`sqrt-prod`
16×	`difference-of-squares`
11×	`sqr-pow`
10×	`pow1`
9×	`pow-pow`
7×	`add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
3×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-pow2` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 133

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
9.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
33.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
32.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
112.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify50.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5136	2249

prune534.0ms

Filtered

102 candidates to 145 candidates (-42.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	145	8	153

Merged error: 23.0b

Counts

153 → 8

regimes338.0ms

Accuracy

83.4% (1.8b remaining)

Error of 24.0b against oracle of 22.3b and baseline of 32.9b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	191	105
1	191	105

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.1s	3834×	body	1280	valid
1.2s	1070×	body	1280	nan
696.0ms	1562×	body	640	valid
647.0ms	914×	body	640	nan
466.0ms	2643×	body	80	overflowed
231.0ms	710×	body	320	valid
194.0ms	445×	body	320	nan
172.0ms	246×	body	640	invalid
136.0ms	1552×	body	80	valid
131.0ms	101×	body	1280	invalid
75.0ms	177×	body	320	invalid
72.0ms	342×	body	160	valid
56.0ms	235×	body	160	nan
33.0ms	548×	body	80	nan
26.0ms	210×	body	80	invalid
17.0ms	71×	body	160	invalid

Details

analyze1.3s

sample212.0ms

simplify51.0ms

prune3.0ms

localize9.0ms

rewrite22.0ms

series77.0ms

simplify57.0ms

prune187.0ms

localize11.0ms

rewrite34.0ms

series112.0ms

simplify50.0ms

prune274.0ms

localize16.0ms

rewrite65.0ms

series390.0ms

simplify59.0ms

prune464.0ms

localize16.0ms

rewrite40.0ms

series209.0ms

simplify50.0ms

prune534.0ms

regimes338.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample6.6s

Profiling