Details

sample103.0ms

Algorithm

intervals

Results

39.0ms	426×	body	80	nan
30.0ms	294×	body	80	valid

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	153	14
2	652	14
3	3624	14
4	5002	14

prune4.0ms

Filtered

1 candidates to 0 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: 33.7b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.7b	(/ (* l l) Om)
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `add-log-exp`
3×	`times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 103

Calls

4 calls:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms	(/ (* l l) Om)
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

360.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify127.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	937	1544
1	4764	1385
2	5001	1385

prune412.0ms

Filtered

115 candidates to 75 candidates (65.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Merged error: 22.4b

Counts

116 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts

4 → 12

Calls

4 calls:

140.0ms	(* n (pow (/ l Om) 2.0))
370.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune451.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	132	10	142

Merged error: 20.2b

Counts

142 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

5.5b	(* n (pow (/ l Om) (/ 2.0 2)))
7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
19.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
11.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

161.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
358.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1113	2385
1	5002	2030

prune457.0ms

Filtered

148 candidates to 89 candidates (60.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	148	10	158

Merged error: 20.2b

Counts

158 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
6.0b	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
7.7b	(* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
19.9b	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

10.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
13.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
8.0ms	(* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
3.0ms	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

series11.2s

Counts

4 → 12

Calls

4 calls:

147.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
1.1s	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
292.0ms	(* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
9.6s	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (neg (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

simplify118.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	770	1582
1	4137	1371
2	5001	1363

prune638.0ms

Filtered

118 candidates to 88 candidates (74.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	115	13	128

Merged error: 17.4b

Counts

128 → 13

regimes737.0ms

Accuracy

14% (10.0b remaining)

Error of 28.6b against oracle of 18.6b and baseline of 30.2b

bsearch685.0ms

Steps

Iters	Range		Point
8	4.3485302127787375e+158	3.873486335291485e+161	4.390330063948556e+158
9	2.637416459195156e+83	3.73396300242758e+88	3.680851853382252e+88
9	2.4521432539025246e-306	1.307588242144421e-299	2.4832562525324398e-306
9	-1.940887443394291e-298	-4.697589310575328e-305	-1.7004139121488585e-298
9	-2.537940135630311e-116	-5.5453851195829135e-123	-2.3445809877238203e-120

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	117
1	109	117
2	110	117
3	110	117

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	14929×	body	80	nan
856.0ms	9217×	body	80	valid

Details

sample103.0ms

simplify125.0ms

prune4.0ms

localize19.0ms

rewrite45.0ms

series6.3s

simplify127.0ms

prune412.0ms

localize18.0ms

rewrite46.0ms

series6.5s

simplify45.0ms

prune451.0ms

localize27.0ms

rewrite56.0ms

series6.7s

simplify50.0ms

prune457.0ms

localize28.0ms

rewrite37.0ms

series11.2s

simplify118.0ms

prune638.0ms

regimes737.0ms

bsearch685.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling