Details

sample244.0ms

Algorithm

intervals

Results

91.0ms	293×	body	80	valid
44.0ms	433×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	664	27
4	4143	27
done	5000	27

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize29.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(/ (* l l) Om)
9.1b	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
21.4b	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cbrt-cube`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-unprod`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `times-frac` `div-exp` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `associate-r/` `pow-exp` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*`

Counts

4 → 115

Calls

4 calls:

69.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
17.0ms	(/ (* l l) Om)
103.0ms	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
64.0ms	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.7s

Counts

4 → 12

Calls

4 calls:

556.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
35.0ms	(/ (* l l) Om)
1.2s	(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.8s	(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify510.0ms

Counts

127 → 127

Iterations

Useful iterations: done (504.0ms)

Iter	Nodes	Cost
0	281	3038
1	798	2788
done	5000	2386

prune702.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.3b

localize40.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
21.4b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`add-exp-log`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
23×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `cbrt-unprod`
9×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sub-neg` `sqrt-div` `associate-*r/` `div-exp` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 131

Calls

4 calls:

27.0ms	(* n (pow (/ l Om) 2.0))
61.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
69.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
97.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

series4.8s

Counts

4 → 12

Calls

4 calls:

239.0ms	(* n (pow (/ l Om) 2.0))
572.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.1s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U))
2.9s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U)))) ( (* 2.0 n) U)))

simplify3.0s

Counts

143 → 143

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	314	3277
1	841	3008
2	4509	2611
done	5000	2607

prune831.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.4b

localize56.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) (/ 2.0 2)))
6.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.1b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
21.4b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
39×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
24×	`add-cbrt-cube`
23×	`associate-r`
20×	`pow-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-to-exp` `times-frac` `div-exp`
9×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 148

Calls

4 calls:

33.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
223.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
95.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
110.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

series5.1s

Counts

4 → 12

Calls

4 calls:

256.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
521.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.2s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U))
3.1s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U)))) ( (* 2.0 n) U)))

simplify567.0ms

Counts

160 → 160

Iterations

Useful iterations: done (561.0ms)

Iter	Nodes	Cost
0	349	5166
1	949	3930
done	5000	3432

prune927.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.9b

localize60.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) (/ 2.0 2)))
7.5b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
9.1b	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U))
21.4b	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U)))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
35×	`associate-r`
30×	`unpow-prod-down`
29×	`add-exp-log`
27×	`*-un-lft-identity`
23×	`pow1` `add-cube-cbrt`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
13×	`associate-l`
12×	`pow-prod-down`
8×	`cbrt-unprod` `unswap-sqr`
6×	`associate-*l/`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sqrt-div` `div-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 126

Calls

4 calls:

33.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
56.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
86.0ms	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U))
81.0ms	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U)))

series5.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
894.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
1.1s	(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U))
2.9s	(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U) (pow (/ l Om) (/ 2.0 2)))))) ( (* 2.0 n) U)))

simplify2.4s

Counts

138 → 138

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	286	3399
1	701	3221
2	3281	2583
done	5001	2578

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.2b

regimes914.0ms

Accuracy

12.9% (8.7b remaining)

Error of 30.0b against oracle of 21.3b and baseline of 31.3b

bsearch643.0ms

Steps

Iters	Range		Point
8	1.7165135950983277e+117	2.5714042224113083e+120	9.260196814501474e+119
10	1.713202050375768e-106	8.437061114098603e-88	7.551608221022999e-93
8	1.110000930973235e-152	3.3367201306177223e-149	4.7393434495258717e-151

simplify20.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	54	155
1	69	124
2	71	124
3	73	124
done	73	124

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	14858×	body	80	nan
1.7s	9220×	body	80	valid