Details

sample177.0ms

Algorithm

intervals

Results

80.0ms	533×	body	80	nan
39.0ms	305×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
4	2913
3	614
2	150
1	49
0	21

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.7b

localize57.0ms

Local error

Found 4 expressions with local error:

6.5b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.4b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
20.1b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
35×	`add-exp-log`
29×	`*-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` `associate-*r/` `cbrt-unprod`
7×	`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` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

41.0ms	(* n (pow (/ l Om) 2.0))
52.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
98.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
96.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series11.4s

Counts

4 → 12

Calls

4 calls:

221.0ms	(* n (pow (/ l Om) 2.0))
604.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.6s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
8.9s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify2.6s

Counts

141 → 141

Iterations

Iter	Nodes
done	5005
2	3241
1	968
0	353

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize85.0ms

Local error

Found 4 expressions with local error:

4.6b	(* n (pow (/ l Om) (/ 2.0 2)))
6.9b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
7.4b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
20.1b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
37×	`add-sqr-sqrt`
29×	`*-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` `associate-*r/`
7×	`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` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

42.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
172.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
83.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
76.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

series11.3s

Counts

4 → 12

Calls

4 calls:

243.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
525.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.8s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
8.8s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

simplify3.4s

Counts

158 → 158

Iterations

Iter	Nodes
done	5013
2	3679
1	1063
0	389

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.4b

localize94.0ms

Local error

Found 4 expressions with local error:

7.4b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
7.4b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
20.1b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))
20.1b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1`
24×	`pow-prod-down`
22×	`add-cbrt-cube` `add-exp-log`
16×	`associate-*r/`
12×	`prod-exp` `cbrt-unprod`
8×	`sqrt-pow1` `associate-*l/`
6×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`pow1/2` `associate-r` `*-commutative` `sqrt-prod`

Counts

4 → 84

Calls

4 calls:

77.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
87.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
86.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))
84.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

series21.7s

Counts

4 → 12

Calls

4 calls:

1.8s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
1.5s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
9.3s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))
9.1s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

simplify2.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5002
2	1937
1	493
0	175

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 22.4b

localize165.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
7.4b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
20.1b	(sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))))
20.1b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

rewrite670.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
63×	`prod-exp`
58×	`pow1`
37×	`pow-prod-down`
22×	`add-cbrt-cube`
20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `pow-exp` `add-cube-cbrt`
16×	`associate-*r/`
13×	`sqrt-pow1`
12×	`cbrt-unprod`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow-to-exp` `div-exp`
6×	`associate-r` `associate-*l/`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `associate-l` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`sub-neg` `pow1/2` `*-commutative` `sqrt-prod`
1×	`distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

209.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
126.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
246.0ms	(sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))))
80.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

series22.2s

Counts

4 → 12

Calls

4 calls:

569.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.8s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
10.5s	(sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))))
9.3s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

simplify3.5s

Counts

141 → 141

Iterations

Iter	Nodes
done	5007
2	3919
1	999
0	350

prune1.6s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 22.4b

regimes2.3s

Accuracy

28.8% (7.3b remaining)

Error of 27.8b against oracle of 20.5b and baseline of 30.8b

bsearch224.0ms

Steps

Iters	Range		Point
3	4.154283818463854e-287	5.676821860774767e-287	4.23622323501101e-287
8	-5.213180476850983e-276	-7.588625660140399e-279	-2.7471967733979886e-277

simplify25.0ms

Iterations

Iter	Nodes
done	59
1	59
0	45

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.1s	14706×	body	80	nan
1.6s	9181×	body	80	valid