Details

sample132.0ms

Algorithm

intervals

Results

49.0ms	495×	body	80	nan
29.0ms	309×	body	80	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5859	28

prune18.0ms

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: 26.7b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
5.7b	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
6.3b	(* (pow (/ l Om) 2.0) (- U* U))
20.6b	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite54.0ms

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

134.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
341.0ms	(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
126.0ms	(* (pow (/ l Om) 2.0) (- U* U))
2.0s	(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	6465	2386

prune290.0ms

Filtered

85 candidates to 126 candidates (-48.2%)

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: 23.8b

Counts

128 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.3b	(* (pow (/ l Om) 2.0) (- U* U))
7.3b	(* (* n U) (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
20.6b	(sqrt (* 2.0 (* (* n U) (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
25×	`add-sqr-sqrt`
21×	`pow1` `associate-l`
19×	`*-un-lft-identity`
16×	`prod-exp` `add-cbrt-cube`
15×	`add-cube-cbrt` `unpow-prod-down`
12×	`associate-*r/`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `associate-r` `pow-prod-down`
7×	`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` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

11.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
10.0ms	(* (pow (/ l Om) 2.0) (- U* U))
13.0ms	(* (* n U) (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
13.0ms	(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:

131.0ms	(* n (* (pow (/ l Om) 2.0) (- U* U)))
126.0ms	(* (pow (/ l Om) 2.0) (- U* U))
348.0ms	(* (* 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))))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	6343	2354

prune259.0ms

Filtered

80 candidates to 125 candidates (-56.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	124	15	139

Merged error: 23.8b

Counts

139 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
7.3b	(* (* n U) (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om))))))
7.6b	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
20.6b	(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

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

Counts

4 → 118

Calls

4 calls:

16.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
16.0ms	(* (* n U) (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om))))))
11.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
16.0ms	(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))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

133.0ms	(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
348.0ms	(* (* n U) (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om))))))
94.0ms	(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
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))))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5031	2696

prune281.0ms

Filtered

83 candidates to 130 candidates (-56.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	132	13	145

Merged error: 23.1b

Counts

145 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (* 2.0 (* (* n U) (+ t (- (* n (* (* (cbrt (pow (/ l Om) 2.0)) (cbrt (pow (/ l Om) 2.0))) (* (- U* U) (cbrt (pow (/ l Om) 2.0))))) (* 2.0 (* l (/ l Om))))))))
28.2b	(cbrt (pow (/ l Om) 2.0))
28.2b	(cbrt (pow (/ l Om) 2.0))
28.2b	(cbrt (pow (/ l Om) 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`unpow-prod-down`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
14×	`pow1`
6×	`pow-prod-down`
4×	`add-exp-log` `sqrt-pow1` `associate-*r/` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `div-inv` `sqr-pow`
2×	`sqrt-div`
1×	`flip3-+` `pow1/2` `sqrt-prod` `flip-+`

Counts

4 → 90

Calls

4 calls:

24.0ms	(sqrt (* 2.0 (* (* n U) (+ t (- (* n (* (* (cbrt (pow (/ l Om) 2.0)) (cbrt (pow (/ l Om) 2.0))) (* (- U* U) (cbrt (pow (/ l Om) 2.0))))) (* 2.0 (* l (/ l Om))))))))
4.0ms	(cbrt (pow (/ l Om) 2.0))
4.0ms	(cbrt (pow (/ l Om) 2.0))
4.0ms	(cbrt (pow (/ l Om) 2.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt (* 2.0 (* (* n U) (+ t (- (* n (* (* (cbrt (pow (/ l Om) 2.0)) (cbrt (pow (/ l Om) 2.0))) (* (- U* U) (cbrt (pow (/ l Om) 2.0))))) (* 2.0 (* l (/ l Om))))))))
50.0ms	(cbrt (pow (/ l Om) 2.0))
48.0ms	(cbrt (pow (/ l Om) 2.0))
51.0ms	(cbrt (pow (/ l Om) 2.0))

simplify29.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5013	1632

prune302.0ms

Filtered

88 candidates to 102 candidates (-15.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	102	13	115

Merged error: 23.1b

Counts

115 → 13

regimes1.2s

Accuracy

39% (5.2b remaining)

Error of 28.9b against oracle of 23.7b and baseline of 32.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	176
1	58	176

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	15072×	body	80	nan
869.0ms	9226×	body	80	valid

Details

sample132.0ms

simplify61.0ms

prune18.0ms

localize17.0ms

rewrite54.0ms

series2.6s

simplify39.0ms

prune290.0ms

localize20.0ms

rewrite52.0ms

series2.6s

simplify38.0ms

prune259.0ms

localize22.0ms

rewrite66.0ms

series2.6s

simplify58.0ms

prune281.0ms

localize25.0ms

rewrite39.0ms

series2.1s

simplify29.0ms

prune302.0ms

regimes1.2s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample4.0s

Profiling