Details

analyze2.4s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample103.0ms

Algorithm

intervals

Results

40.0ms	431×	body	80	nan
27.0ms	256×	body	80	valid
4.0ms	37×	body	80	invalid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5186	28

prune16.0ms

Filtered

1 candidates to 1 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: 27.4b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

4.7b	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
5.7b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.3b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
18.1b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
23×	`pow1`
16×	`associate-*r/` `add-cbrt-cube`
13×	`prod-exp`
11×	`pow-prod-down`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
8×	`add-cube-cbrt`
7×	`cbrt-unprod`
6×	`associate-r`
4×	`sub-neg` `sqrt-pow1` `add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`sqrt-div` `pow-exp`
1×	`pow-to-exp` `flip3--` `pow1/2` `div-exp` `sqrt-prod` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

14.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
17.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
15.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series2.9s

Counts

4 → 12

Calls

4 calls:

310.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
129.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
334.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
2.1s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	6423	2359

prune250.0ms

Filtered

67 candidates to 100 candidates (-49.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	13	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	88	14	102

Merged error: 23.8b

Counts

102 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

5.6b	(* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))
5.7b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.0b	(* n (* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
18.1b	(sqrt (* 2.0 (+ (* n (* U t)) (* n (* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

53×	`distribute-rgt-in` `distribute-lft-in`
34×	`sub-neg` `associate-*r/`
25×	`add-exp-log`
24×	`associate--l+`
16×	`pow1` `add-cbrt-cube`
13×	`prod-exp`
10×	`add-sqr-sqrt`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-unprod`
6×	`pow-prod-down`
5×	`flip3--` `associate-r` `flip--`
4×	`frac-sub` `add-log-exp`
3×	`*-commutative`
2×	`sqrt-pow1` `sqrt-div` `pow-exp`
1×	`pow-to-exp` `flip3-+` `pow1/2` `div-exp` `sqrt-prod` `flip-+` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

17.0ms	(* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
17.0ms	(* n (* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
6.0ms	(sqrt (* 2.0 (+ (* n (* U t)) (* n (* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

169.0ms	(* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))
129.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
180.0ms	(* n (* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
1.7s	(sqrt (* 2.0 (+ (* n (* U t)) (* n (* U (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4997	3290
1	4997	3290

prune248.0ms

Filtered

70 candidates to 125 candidates (-78.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	123	16	139

Merged error: 23.2b

Counts

139 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

4.7b	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
5.7b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.3b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
18.1b	(sqrt (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
19×	`pow1`
16×	`add-cbrt-cube`
14×	`associate-*r/`
13×	`prod-exp`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
8×	`add-cube-cbrt` `pow-prod-down`
7×	`cbrt-unprod`
6×	`associate-r`
4×	`sub-neg` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `*-commutative` `flip-+`
2×	`sqrt-div` `pow-exp`
1×	`pow-to-exp` `flip3--` `pow1/2` `div-exp` `sqrt-prod` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

13.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
15.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
13.0ms	(sqrt (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

303.0ms	(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
125.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
331.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
1.3s	(sqrt (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5847	2318

prune264.0ms

Filtered

71 candidates to 99 candidates (-39.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	98	17	115

Merged error: 20.6b

Counts

115 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

6.3b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
6.3b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
18.1b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))
18.1b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
20×	`associate-*r/`
18×	`pow-prod-down`
14×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1`
6×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `cbrt-unprod`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
2×	`pow1/2` `associate-r` `sqrt-prod` `*-commutative`

Counts

4 → 78

Calls

4 calls:

14.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
14.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
15.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))
15.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series4.5s

Counts

4 → 12

Calls

4 calls:

335.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
337.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
1.9s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))
1.9s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5541	2612

prune240.0ms

Filtered

62 candidates to 90 candidates (-45.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	90	17	107

Merged error: 20.6b

Counts

107 → 17

regimes1.5s

Accuracy

32.5% (8.1b remaining)

Error of 28.8b against oracle of 20.7b and baseline of 32.7b

bsearch1.0ms

simplify21.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	936	152
1	936	152

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	12727×	body	80	nan
770.0ms	8000×	body	80	valid
127.0ms	1196×	body	80	invalid

Details

analyze2.4s

sample103.0ms

simplify40.0ms

prune16.0ms

localize19.0ms

rewrite59.0ms

series2.9s

simplify40.0ms

prune250.0ms

localize21.0ms

rewrite55.0ms

series2.1s

simplify58.0ms

prune248.0ms

localize22.0ms

rewrite54.0ms

series2.1s

simplify35.0ms

prune264.0ms

localize25.0ms

rewrite60.0ms

series4.5s

simplify35.0ms

prune240.0ms

regimes1.5s

bsearch1.0ms

simplify21.0ms

end0.0ms

sample2.9s

Profiling