Details

sample126.0ms

Algorithm

intervals

Results

42.0ms	447×	body	80	nan
31.0ms	282×	body	80	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5186	28

prune17.0ms

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: 29.6b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (pow (/ l Om) 2.0) (- U* U))
6.1b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
8.6b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
20.0b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
25×	`add-sqr-sqrt`
23×	`associate-l`
21×	`pow1`
17×	`*-un-lft-identity`
16×	`associate-*r/` `prod-exp` `add-cbrt-cube`
15×	`add-cube-cbrt` `unpow-prod-down`
14×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `pow-prod-down`
7×	`associate-r` `cbrt-unprod`
6×	`sub-neg`
4×	`sqrt-pow1` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `flip3--` `flip3-+` `sqrt-div` `div-exp` `flip--` `flip-+` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

11.0ms	(* (pow (/ l Om) 2.0) (- U* U))
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)))))))
16.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (pow (/ l Om) 2.0) (- U* U))
129.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
347.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5048	2333

prune278.0ms

Filtered

83 candidates to 126 candidates (-51.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	113	13	126
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	14	128

Merged error: 25.4b

Counts

128 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
7.9b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
8.6b	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
20.0b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-exp-log`
64×	`prod-exp`
25×	`add-sqr-sqrt`
21×	`pow1`
20×	`pow-exp` `add-cbrt-cube`
19×	`associate-r`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
14×	`associate-*r/`
11×	`associate-l`
10×	`pow-to-exp` `times-frac` `div-exp` `pow-prod-down` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `associate-*l/` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 119

Calls

4 calls:

19.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
13.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
20.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
20.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

129.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
91.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
351.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4972	2719
1	4972	2719

prune295.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	131	14	145

Merged error: 23.5b

Counts

145 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
7.9b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
8.6b	(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
20.0b	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`associate-r`
30×	`unpow-prod-down`
25×	`add-exp-log` `*-un-lft-identity`
23×	`add-cube-cbrt`
20×	`times-frac`
19×	`pow1`
13×	`add-cbrt-cube`
11×	`associate-l` `prod-exp`
10×	`associate-*r/`
9×	`pow-prod-down`
8×	`unswap-sqr`
5×	`cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-exp` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `flip3-+` `sqrt-div` `div-exp` `associate-*l/` `flip-+` `div-inv`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
14.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
19.0ms	(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
19.0ms	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

50.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
95.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
410.0ms	(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4960	2511
1	4960	2511

prune360.0ms

Filtered

98 candidates to 129 candidates (-31.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	129	14	143

Merged error: 23.5b

Counts

143 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
7.9b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
10.2b	(* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
20.0b	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`associate-r`
30×	`unpow-prod-down`
27×	`*-un-lft-identity`
25×	`add-exp-log`
23×	`add-cube-cbrt`
20×	`times-frac`
19×	`pow1`
13×	`add-cbrt-cube`
11×	`prod-exp`
9×	`associate-l` `pow-prod-down`
8×	`unswap-sqr`
6×	`associate-*r/`
5×	`cbrt-unprod`
4×	`sqrt-pow1` `pow-exp` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `flip3-+` `sqrt-div` `div-exp` `associate-*l/` `flip-+` `div-inv`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
12.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
21.0ms	(* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
19.0ms	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))))

series2.5s

Counts

4 → 12

Calls

4 calls:

49.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
90.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
439.0ms	(* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
1.9s	(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4970	2492
1	4970	2492

prune259.0ms

Filtered

97 candidates to 128 candidates (-32.0%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	127	15	142

Merged error: 23.5b

Counts

142 → 15

regimes1.5s

Accuracy

33% (5.1b remaining)

Error of 28.4b against oracle of 23.3b and baseline of 30.9b

bsearch2.0ms

simplify25.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	1234	198
1	1234	198

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	15296×	body	80	nan
893.0ms	9264×	body	80	valid

Details

sample126.0ms

simplify39.0ms

prune17.0ms

localize21.0ms

rewrite58.0ms

series2.6s

simplify50.0ms

prune278.0ms

localize21.0ms

rewrite78.0ms

series2.5s

simplify43.0ms

prune295.0ms

localize21.0ms

rewrite66.0ms

series2.5s

simplify66.0ms

prune360.0ms

localize20.0ms

rewrite65.0ms

series2.5s

simplify51.0ms

prune259.0ms

regimes1.5s

bsearch2.0ms

simplify25.0ms

end0.0ms

sample4.2s

Profiling