Details

Time bar (total: 1.0m)

sample213.0ms

Algorithm
intervals
Results
88.0ms428×body80nan
45.0ms295×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02128
14928
215228
363228
4391928
done500028

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv pow-exp *-commutative div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 112
Calls
4 calls:
24.0ms
(* n (pow (/ l Om) 2.0))
10.0ms
(/ (* l l) Om)
139.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
101.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.5s

Counts
4 → 12
Calls
4 calls:
197.0ms
(* n (pow (/ l Om) 2.0))
26.0ms
(/ (* l l) Om)
1.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify615.0ms

Counts
124 → 124
Iterations

Useful iterations: done (608.0ms)

IterNodesCost
03443129
110172953
done50002685

prune758.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.6b

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
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.5b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite380.0ms

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:
46.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
40.0ms
(* n (pow (/ l Om) 2.0))
162.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
127.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.9s

Counts
4 → 12
Calls
4 calls:
597.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
262.0ms
(* n (pow (/ l Om) 2.0))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify646.0ms

Counts
131 → 131
Iterations

Useful iterations: done (640.0ms)

IterNodesCost
03493452
110223256
done50012963

prune896.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.2b

localize51.0ms

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
(* (* (* 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*))))
19.5b
(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*)))))

rewrite1.2s

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:
31.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
280.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
279.0ms
(* (* (* 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*))))
636.0ms
(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*)))))

series10.2s

Counts
4 → 12
Calls
4 calls:
248.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
555.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.0s
(* (* (* 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*))))
7.4s
(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*)))))

simplify722.0ms

Counts
148 → 148
Iterations

Useful iterations: done (711.0ms)

IterNodesCost
03855057
111384213
done50003676

prune997.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.0b

localize47.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
5.9b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
7.5b
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
19.5b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))

rewrite729.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
31×pow1
24×add-sqr-sqrt associate-*r/
23×add-cbrt-cube
21×prod-exp
19×associate-*r*
17×pow-prod-down
16×distribute-rgt-in *-un-lft-identity distribute-lft-in
15×unpow-prod-down
14×add-cube-cbrt
12×cbrt-unprod
11×flip3-- flip--
10×times-frac associate-*l/
9×associate-*l*
8×sub-neg associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1
4×pow-exp 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 → 125
Calls
4 calls:
78.0ms
(* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
320.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
47.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
278.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))

series10.3s

Counts
4 → 12
Calls
4 calls:
455.0ms
(* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
2.1s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
229.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
7.5s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))

simplify2.9s

Counts
137 → 137
Iterations

Useful iterations: 2 (941.0ms)

IterNodesCost
03584263
110404013
246613594
done50003594

prune694.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 18.2b

regimes874.0ms

Accuracy

11.2% (10.8b remaining)

Error of 29.6b against oracle of 18.8b and baseline of 30.9b

bsearch247.0ms

Steps
ItersRangePoint
9
1.7110940476642526e+180
1.6950995764331517e+185
9.73877043401371e+183

simplify23.0ms

Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
03981
15579
25779
done5779

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.0s14396×body80nan
1.8s9170×body80valid