Details

Time bar (total: 1.8m)

sample263.0ms

Algorithm
intervals
Results
78.0ms489×body80nan
44.0ms298×body80valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02128
14928
215427
366427
4414327
done500027

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize72.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0b
(/ (* l l) Om)
10.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite562.0ms

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:
87.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.0ms
(/ (* l l) Om)
246.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
197.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series12.5s

Counts
4 → 12
Calls
4 calls:
740.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
40.0ms
(/ (* l l) Om)
2.5s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.1s

Counts
153 → 153
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04114799
112784444
done50003908

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.8b

localize74.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (pow (/ l Om) 2.0))
5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite667.0ms

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:
52.0ms
(* n (pow (/ l Om) 2.0))
102.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
280.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
218.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series13.4s

Counts
4 → 12
Calls
4 calls:
271.0ms
(* n (pow (/ l Om) 2.0))
665.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.0s

Counts
169 → 169
Iterations

Useful iterations: done (1.0s)

IterNodesCost
04425038
113164661
done50014111

prune1.9s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 22.4b

localize62.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)
5.7b
(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U))
11.3b
(* (* (- U U*) n) (pow (/ l Om) 2.0))
21.3b
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
31×pow1
23×add-cbrt-cube
21×associate-*r* prod-exp
18×add-sqr-sqrt
17×pow-prod-down
16×*-un-lft-identity
14×add-cube-cbrt
13×unpow-prod-down
12×cbrt-unprod
10×associate-*l/
9×times-frac
7×associate-*l*
5×sqrt-pow1
4×expm1-log1p-u flip3-- associate-*r/ pow-exp flip-- log1p-expm1-u add-log-exp
3×*-commutative
2×pow-to-exp sqrt-div div-exp
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 108
Calls
4 calls:
51.0ms
(* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)
92.0ms
(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U))
107.0ms
(* (* (- U U*) n) (pow (/ l Om) 2.0))
88.0ms
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)))

series25.6s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)
1.8s
(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U))
612.0ms
(* (* (- U U*) n) (pow (/ l Om) 2.0))
22.1s
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)))

simplify3.3s

Counts
120 → 120
Iterations

Useful iterations: done (3.3s)

IterNodesCost
02823077
17562952
239292537
done50002521

prune1.4s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 18.8b

localize62.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (pow (/ l Om) 2.0))
5.4b
(* (- U U*) (* n (pow (/ l Om) 2.0)))
5.7b
(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (- U U*) (* n (pow (/ l Om) 2.0))))) U))
21.3b
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (- U U*) (* n (pow (/ l Om) 2.0))))) U)))

rewrite309.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
31×pow1
24×add-sqr-sqrt
23×add-cbrt-cube
21×prod-exp
19×associate-*r*
17×pow-prod-down
16×*-un-lft-identity
15×unpow-prod-down
14×add-cube-cbrt
12×cbrt-unprod
10×times-frac
9×associate-*l*
6×associate-*l/
5×sqrt-pow1
4×expm1-log1p-u associate-*r/ pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×pow-to-exp sqrt-div div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 109
Calls
4 calls:
44.0ms
(* n (pow (/ l Om) 2.0))
83.0ms
(* (- U U*) (* n (pow (/ l Om) 2.0)))
84.0ms
(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (- U U*) (* n (pow (/ l Om) 2.0))))) U))
90.0ms
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (- U U*) (* n (pow (/ l Om) 2.0))))) U)))

series25.5s

Counts
4 → 12
Calls
4 calls:
314.0ms
(* n (pow (/ l Om) 2.0))
644.0ms
(* (- U U*) (* n (pow (/ l Om) 2.0)))
1.9s
(* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (- U U*) (* n (pow (/ l Om) 2.0))))) U))
22.6s
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (- U U*) (* n (pow (/ l Om) 2.0))))) U)))

simplify2.5s

Counts
121 → 121
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02722560
16982432
230352088
done50002083

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.6b

regimes2.2s

Accuracy

27.5% (9.6b remaining)

Error of 28.8b against oracle of 19.2b and baseline of 32.5b

bsearch993.0ms

Steps
ItersRangePoint
8
1.5960440770984533e+42
6.368835404482097e+45
2.966212205685807e+43
8
2.1227629598124326e-217
1.9494296208241896e-213
1.2408046941130587e-213
9
-5.916009956429166e-306
1.1855271254647856e-304
3.330205482826e-310
6
-3.604147204230947e+187
-6.120349737567292e+186
-6.567149799254256e+186

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
042155
155128
done55128

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.8s14995×body80nan
2.5s9126×body80valid