Details

analyze1.1s

Algorithm: search

sample220.0ms

Algorithm

intervals

Results

69.0ms	117×	body	1280	valid
36.0ms	36×	body	1280	nan
28.0ms	63×	body	640	valid
21.0ms	123×	body	80	overflowed
17.0ms	26×	body	640	nan
8.0ms	27×	body	320	valid
7.0ms	18×	body	320	nan
4.0ms	3×	body	320	invalid
3.0ms	40×	body	80	valid
3.0ms	3×	body	1280	invalid
2.0ms	3×	body	640	invalid
2.0ms	9×	body	160	valid
1.0ms	12×	body	80	invalid
1.0ms	6×	body	160	nan
1.0ms	18×	body	80	nan
1.0ms	3×	body	160	invalid

simplify32.0ms

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

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: 34.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
2.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`unpow-prod-down` `pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

2 → 51

Calls

2 calls:

3.0ms	(pow x (/ 1.0 n))
8.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series52.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(pow x (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	476	520
1	1648	503
2	5001	478

prune130.0ms

Filtered

47 candidates to 57 candidates (-21.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 24.6b

Counts

58 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* (log x) (/ 1.0 n)))
0.4b	(* (log x) (/ 1.0 n))
2.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*`
11×	`add-cube-cbrt`
10×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`difference-of-squares`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `unpow-prod-down` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `log-pow` `-commutative` `flip--` `div-inv` `rem-exp-log` `distribute-lft-out--` `sqr-pow`

Counts

3 → 59

Calls

3 calls:

2.0ms	(exp (* (log x) (/ 1.0 n)))
6.0ms	(* (log x) (/ 1.0 n))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

series62.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(exp (* (log x) (/ 1.0 n)))
10.0ms	(* (log x) (/ 1.0 n))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

simplify50.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	519	581
1	1956	532
2	5001	500

prune123.0ms

Filtered

50 candidates to 68 candidates (-36.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	67	5	72

Merged error: 24.6b

Counts

72 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3)
0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3))
0.4b	(* (log x) (/ 1.0 n))
2.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
20×	`cbrt-prod`
19×	`unpow-prod-down`
18×	`add-cube-cbrt`
15×	`difference-of-squares`
14×	`cube-prod`
13×	`associate-r`
10×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`pow1`
7×	`sqr-pow`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`cube-div` `associate-l`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `log-pow` `-commutative` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 113

Calls

4 calls:

8.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3)
8.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3))
6.0ms	(* (log x) (/ 1.0 n))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3)
36.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3))
12.0ms	(* (log x) (/ 1.0 n))
36.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

simplify84.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	845	1681
1	3687	1555
2	5001	1549

prune240.0ms

Filtered

80 candidates to 125 candidates (-56.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	124	6	130

Merged error: 24.6b

Counts

130 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3)))
0.2b	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3))
0.4b	(* (log x) (/ 1.0 n))
2.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
40×	`log-prod`
29×	`*-un-lft-identity`
20×	`exp-sum`
19×	`add-cube-cbrt` `unpow-prod-down`
15×	`difference-of-squares`
14×	`cube-prod`
13×	`associate-r`
11×	`add-exp-log`
10×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1` `sqr-pow`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`cube-div` `log-div` `exp-prod` `associate-l`
3×	`flip3--` `rem-log-exp` `log-pow` `flip--`
2×	`cube-mult` `exp-diff` `unpow3` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 116

Calls

4 calls:

10.0ms	(exp (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3)))
8.0ms	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3))
6.0ms	(* (log x) (/ 1.0 n))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

series1.3s

Counts

4 → 12

Calls

4 calls:

126.0ms	(exp (log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3)))
1.1s	(log (pow (- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n)))) 3))
12.0ms	(* (log x) (/ 1.0 n))
36.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (* (log x) (/ 1.0 n))))

simplify113.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1095	1998
1	4715	1746
2	5001	1746

prune298.0ms

Filtered

85 candidates to 128 candidates (-50.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	128	6	134

Merged error: 24.6b

Counts

134 → 6

regimes276.0ms

Accuracy

85.2% (1.6b remaining)

Error of 24.1b against oracle of 22.5b and baseline of 33.3b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	63
1	56	63
2	59	63
3	59	63

end0.0ms

analyze1.1s

Algorithm: search

sample6.6s

Algorithm

intervals

Results

2.1s	3809×	body	1280	valid
1.2s	1125×	body	1280	nan
681.0ms	1521×	body	640	valid
626.0ms	889×	body	640	nan
480.0ms	2727×	body	80	overflowed
232.0ms	741×	body	320	valid
205.0ms	451×	body	320	nan
180.0ms	259×	body	640	invalid
148.0ms	1601×	body	80	valid
128.0ms	102×	body	1280	invalid
67.0ms	166×	body	320	invalid
67.0ms	328×	body	160	valid
47.0ms	208×	body	160	nan
31.0ms	528×	body	80	nan
26.0ms	203×	body	80	invalid
24.0ms	102×	body	160	invalid

Details

analyze1.1s

sample220.0ms

simplify32.0ms

prune3.0ms

localize8.0ms

rewrite13.0ms

series52.0ms

simplify48.0ms

prune130.0ms

localize11.0ms

rewrite17.0ms

series62.0ms

simplify50.0ms

prune123.0ms

localize15.0ms

rewrite33.0ms

series208.0ms

simplify84.0ms

prune240.0ms

localize17.0ms

rewrite35.0ms

series1.3s

simplify113.0ms

prune298.0ms

regimes276.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

analyze1.1s

sample6.6s

Profiling