Details

Time bar (total: 42.7s)

sample185.0ms

Algorithm
intervals
Results
67.0ms428×body80nan
42.0ms295×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
02128
14928
215427
366427
4414327
done500027

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize29.0ms

Local error

Found 4 expressions with local error:

7.5b
(* n (pow (/ l Om) 2.0))
8.2b
(/ (* l l) Om)
10.0b
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
19.5b
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log add-sqr-sqrt
23×pow1
20×add-cbrt-cube
18×*-un-lft-identity associate-*r*
16×add-cube-cbrt
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
8×associate-*l* cbrt-unprod
4×expm1-log1p-u sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv flip3-- sqrt-div pow-exp *-commutative flip-- div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
31.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(/ (* l l) Om)
111.0ms
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
72.0ms
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series3.9s

Counts
4 → 12
Calls
4 calls:
184.0ms
(* n (pow (/ l Om) 2.0))
21.0ms
(/ (* l l) Om)
1.2s
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
2.5s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify2.0s

Counts
118 → 118
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02512234
16452134
233481861
done50021856

prune781.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.7b

localize38.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.5b
(* n (pow (/ l Om) 2.0))
10.0b
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
19.5b
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite249.0ms

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:
54.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
39.0ms
(* n (pow (/ l Om) 2.0))
91.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
59.0ms
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series4.4s

Counts
4 → 12
Calls
4 calls:
496.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
235.0ms
(* n (pow (/ l Om) 2.0))
995.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
2.6s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify3.1s

Counts
143 → 143
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03133277
18403008
245072611
done50002607

prune842.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.6b

localize53.0ms

Local error

Found 4 expressions with local error:

5.4b
(* n (pow (/ l Om) (/ 2.0 2)))
5.5b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.0b
(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
19.5b
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

rewrite416.0ms

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:
29.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
213.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
93.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
66.0ms
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

series4.9s

Counts
4 → 12
Calls
4 calls:
263.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
583.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.1s
(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
2.9s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

simplify584.0ms

Counts
160 → 160
Iterations

Useful iterations: done (574.0ms)

IterNodesCost
03485166
19474089
done50003432

prune796.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.6b

localize45.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.2b
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n))
7.5b
(* n (pow (/ l Om) 2.0))
19.5b
(sqrt (* (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×add-exp-log *-un-lft-identity
27×add-cube-cbrt
23×associate-*r*
21×pow1
18×prod-diff
16×prod-exp add-cbrt-cube
15×unpow-prod-down
11×distribute-rgt-in distribute-lft-in
10×times-frac pow-prod-down
9×associate-*l*
7×cbrt-unprod
6×associate-*l/
4×expm1-log1p-u sqrt-pow1 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 → 128
Calls
4 calls:
58.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
50.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n))
41.0ms
(* n (pow (/ l Om) 2.0))
81.0ms
(sqrt (* (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

series4.8s

Counts
4 → 12
Calls
4 calls:
564.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n))
252.0ms
(* n (pow (/ l Om) 2.0))
2.9s
(sqrt (* (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

simplify2.9s

Counts
140 → 140
Iterations

Useful iterations: done (2.9s)

IterNodesCost
03043083
17982812
240572478
done50012473

prune760.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.0b

regimes783.0ms

Accuracy

9.9% (11.6b remaining)

Error of 29.7b against oracle of 18.1b and baseline of 31.0b

bsearch165.0ms

Steps
ItersRangePoint
7
3.597730435441497e+57
8.395231488569078e+59
5.612004155267624e+59

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03369
14369
done4369

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.4s14396×body80nan
1.8s9170×body80valid