Details

Time bar (total: 36.2s)

sample99.0ms

Algorithm
intervals
Results
30.0ms481×body80nan
23.0ms298×body80valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214
done500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize20.0ms

Local error

Found 4 expressions with local error:

6.9b
(* n (pow (/ l Om) 2.0))
8.0b
(/ (* l l) Om)
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite233.0ms

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:
23.0ms
(* n (pow (/ l Om) 2.0))
9.0ms
(/ (* l l) Om)
119.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
78.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
152.0ms
(* n (pow (/ l Om) 2.0))
19.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify124.0ms

Counts
124 → 124
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09641525
147931370
250011370
done50011370

prune505.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.4b

localize19.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.9b
(* n (pow (/ l Om) 2.0))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite269.0ms

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:
43.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
24.0ms
(* n (pow (/ l Om) 2.0))
119.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
77.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.9s

Counts
4 → 12
Calls
4 calls:
386.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
147.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify41.0ms

Counts
131 → 131
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09871664
150011508
done50011508

prune679.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.9b

localize26.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log sqrt-pow1 frac-sub add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 85
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
157.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

series5.1s

Counts
4 → 12
Calls
4 calls:
66.0ms
(cbrt (/ l Om))
66.0ms
(cbrt (/ l Om))
60.0ms
(cbrt (/ l Om))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify69.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05891100
124611054
250031048
done50031048

prune563.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.9b

localize31.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))
19.2b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-prod
24×pow1
20×associate-*r/
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
12×sqrt-div pow-prod-down
10×flip3-- flip--
8×sqrt-pow1 frac-sub
4×add-exp-log add-cbrt-cube add-log-exp
2×cbrt-div pow1/2 pow1/3 sqrt-prod div-inv
Counts
4 → 82
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
154.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))
158.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

series10.3s

Counts
4 → 12
Calls
4 calls:
66.0ms
(cbrt (/ l Om))
59.0ms
(cbrt (/ l Om))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify73.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05891620
124731564
250021560
done50021560

prune703.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.9b

regimes451.0ms

Accuracy

16.1% (8.0b remaining)

Error of 30.2b against oracle of 22.2b and baseline of 31.8b

bsearch144.0ms

Steps
ItersRangePoint
10
5.9142685482905006e+106
1.1318126295060305e+120
4.212962541612979e+117

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04762
14762
done4762

end0.0ms

sample2.7s

Algorithm
intervals
Results
955.0ms14744×body80nan
598.0ms9169×body80valid