Details

Time bar (total: 58.3s)

sample175.0ms

Algorithm
intervals
Results
92.0ms521×body80nan
37.0ms299×body80valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
02128
14928
215427
364227
4323927
done500027

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize38.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite433.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
30×prod-diff
26×add-sqr-sqrt *-un-lft-identity
25×pow1
24×add-cube-cbrt
23×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×associate--l+ cbrt-unprod
8×associate-*r* frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u 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 → 141
Calls
4 calls:
11.0ms
(/ (* l l) Om)
85.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
180.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
151.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.6s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* l l) Om)
594.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.3s

Counts
153 → 153
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
04114799
111414430
246813850
done50003850

prune881.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize37.0ms

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*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×add-exp-log
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×add-cbrt-cube
19×prod-exp
15×unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac associate--l+ cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u 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 → 157
Calls
4 calls:
48.0ms
(* n (pow (/ l Om) 2.0))
67.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
232.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
128.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.1s

Counts
4 → 12
Calls
4 calls:
196.0ms
(* n (pow (/ l Om) 2.0))
570.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.7s

Counts
169 → 169
Iterations

Useful iterations: 2 (1.6s)

IterNodesCost
04435038
111974647
247024089
done50004089

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 25.6b

localize50.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b
(* n (pow (/ l Om) (/ 2.0 2)))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite790.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
41×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
24×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×pow-exp
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp associate--l+
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u 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 → 174
Calls
4 calls:
209.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
33.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
351.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
181.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.2s

Counts
4 → 12
Calls
4 calls:
568.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
237.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.0s

Counts
186 → 186
Iterations

Useful iterations: done (990.0ms)

IterNodesCost
04797307
112905730
done50005038

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 25.5b

localize104.0ms

Local error

Found 4 expressions with local error:

16.4b
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
16.4b
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
16.4b
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) (* (* U (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))) (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite788.0ms

Algorithm
rewrite-expression-head
Rules
158×associate-*r/
148×cbrt-div
94×flip3-- flip--
76×frac-times
62×sqrt-div
40×frac-sub
34×pow1
22×pow-prod-down associate-*l/
13×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity
8×sqrt-pow1
7×add-cube-cbrt
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×distribute-lft-out-- difference-of-squares
1×pow1/2 sqrt-prod
Counts
4 → 134
Calls
4 calls:
4.0ms
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
4.0ms
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
47.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
721.0ms
(sqrt (* (* (* 2.0 n) (* (* U (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))) (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series5.7s

Counts
4 → 12
Calls
4 calls:
1.0s
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
1.1s
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
1.1s
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
2.5s
(sqrt (* (* (* 2.0 n) (* (* U (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))) (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify2.6s

Counts
146 → 146
Iterations

Useful iterations: done (2.6s)

IterNodesCost
053619420
1133717447
2432015673
done500015534

prune2.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 24.9b

regimes1.2s

bsearch6.0ms