Details

Time bar (total: 57.4s)

sample278.0ms

Algorithm
intervals
Results
137.0ms481×body80nan
27.0ms298×body80valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02128
14928
215228
362728
4297828
done500028

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize46.0ms

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*)))))

rewrite434.0ms

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:
41.0ms
(* n (pow (/ l Om) 2.0))
14.0ms
(/ (* l l) Om)
205.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
167.0ms
(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:
178.0ms
(* n (pow (/ l Om) 2.0))
35.0ms
(/ (* l l) Om)
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.6s

Counts
124 → 124
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
03443129
19462953
238472649
done50002649

prune713.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.4b

localize37.0ms

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*)))))

rewrite399.0ms

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:
65.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
45.0ms
(* n (pow (/ l Om) 2.0))
160.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
124.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.7s

Counts
4 → 12
Calls
4 calls:
568.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
246.0ms
(* n (pow (/ l Om) 2.0))
1.8s
(* (* (* 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*)))))

simplify2.8s

Counts
131 → 131
Iterations

Useful iterations: 2 (992.0ms)

IterNodesCost
03493452
19733239
240912945
done50012945

prune706.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.9b

localize25.0ms

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*)))))

rewrite229.0ms

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:
5.0ms
(cbrt (/ l Om))
4.0ms
(cbrt (/ l Om))
5.0ms
(cbrt (/ l Om))
209.0ms
(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*)))))

series7.6s

Counts
4 → 12
Calls
4 calls:
87.0ms
(cbrt (/ l Om))
109.0ms
(cbrt (/ l Om))
90.0ms
(cbrt (/ l Om))
7.3s
(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*)))))

simplify1.2s

Counts
97 → 97
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02282019
15901867
223721798
done50001775

prune759.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.7b

localize49.0ms

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*)))))

rewrite492.0ms

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:
4.0ms
(cbrt (/ l Om))
4.0ms
(cbrt (/ l Om))
237.0ms
(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*)))))
240.0ms
(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*)))))

series11.8s

Counts
4 → 12
Calls
4 calls:
59.0ms
(cbrt (/ l Om))
63.0ms
(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*)))))
6.8s
(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*)))))

simplify766.0ms

Counts
94 → 94
Iterations

Useful iterations: done (762.0ms)

IterNodesCost
02283090
15902826
223722728
done50002706

prune616.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.7b

regimes422.0ms

Accuracy

15.6% (8.4b remaining)

Error of 30.2b against oracle of 21.9b and baseline of 31.8b

bsearch135.0ms

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
036118
147118
done47118

end0.0ms

sample2.7s

Algorithm
intervals
Results
938.0ms14744×body80nan
577.0ms9169×body80valid