Details

Time bar (total: 57.5s)

sample317.0ms

Algorithm
intervals
Results
123.0ms512×body80nan
44.0ms289×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02128
14928
215427
364227
4323927
done500027

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize57.0ms

Local error

Found 4 expressions with local error:

6.5b
(* n (pow (/ l Om) 2.0))
7.2b
(/ (* l l) Om)
10.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
23×pow1
20×add-cube-cbrt *-un-lft-identity associate-*r/ associate-*r* add-cbrt-cube
15×unpow-prod-down
13×times-frac
12×prod-diff pow-prod-down
11×prod-exp
10×distribute-rgt-in flip3-- distribute-lft-in associate--l+ flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×expm1-log1p-u sub-neg sqrt-pow1 associate-*l* log1p-expm1-u 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 → 132
Calls
4 calls:
25.0ms
(* n (pow (/ l Om) 2.0))
18.0ms
(/ (* l l) Om)
257.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
232.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.8s

Counts
4 → 12
Calls
4 calls:
270.0ms
(* n (pow (/ l Om) 2.0))
25.0ms
(/ (* l l) Om)
2.0s
(* (* (* 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*)))))

simplify2.9s

Counts
144 → 144
Iterations

Useful iterations: done (2.9s)

IterNodesCost
03893995
110613803
242933329
done50003328

prune928.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.3b

localize23.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.5b
(* n (pow (/ l Om) 2.0))
10.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite542.0ms

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:
70.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
45.0ms
(* n (pow (/ l Om) 2.0))
229.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
190.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.0s

Counts
4 → 12
Calls
4 calls:
563.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
235.0ms
(* n (pow (/ l Om) 2.0))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.5s

Counts
169 → 169
Iterations

Useful iterations: 2 (1.9s)

IterNodesCost
04425038
111994647
247154089
done50004089

prune810.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.6b

localize25.0ms

Local error

Found 4 expressions with local error:

3.7b
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
5.8b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.1b
(* (* (* 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*))))
19.3b
(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*)))))

rewrite868.0ms

Algorithm
rewrite-expression-head
Rules
91×add-exp-log
63×prod-exp
54×prod-diff
39×add-sqr-sqrt *-un-lft-identity
37×add-cube-cbrt
32×distribute-rgt-in distribute-lft-in
26×associate-*r/
25×pow1
22×add-cbrt-cube associate--r+
18×pow-exp
16×flip3-- flip--
15×associate--l+
13×pow-prod-down
12×frac-sub cbrt-unprod
10×sub-neg
9×pow-to-exp div-exp add-log-exp
8×associate-*r*
6×sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u
3×fma-neg diff-log
2×associate-*l* *-commutative
1×associate--l- pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 188
Calls
4 calls:
86.0ms
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
234.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
327.0ms
(* (* (* 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*))))
206.0ms
(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*)))))

series10.3s

Counts
4 → 12
Calls
4 calls:
892.0ms
(- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
557.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s
(* (* (* 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*))))
6.9s
(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*)))))

simplify716.0ms

Counts
200 → 200
Iterations

Useful iterations: done (703.0ms)

IterNodesCost
04399287
112447161
done50006335

prune765.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.4b

localize39.0ms

Local error

Found 4 expressions with local error:

11.6b
(cbrt (/ l Om))
11.6b
(cbrt (/ l Om))
11.6b
(cbrt (/ l Om))
19.3b
(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*)))))

rewrite204.0ms

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 expm1-log1p-u sqrt-pow1 frac-sub add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 93
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
194.0ms
(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*)))))

series5.4s

Counts
4 → 12
Calls
4 calls:
66.0ms
(cbrt (/ l Om))
63.0ms
(cbrt (/ l Om))
66.0ms
(cbrt (/ l Om))
5.2s
(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*)))))

simplify883.0ms

Counts
105 → 105
Iterations

Useful iterations: done (879.0ms)

IterNodesCost
02322133
16101969
224631874
done50021853

prune545.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.9b

regimes501.0ms

Accuracy

14.5% (8.4b remaining)

Error of 29.5b against oracle of 21.1b and baseline of 30.9b

bsearch232.0ms

Steps
ItersRangePoint
9
6.016362318620455e+74
5.548277786689505e+80
8.207218212748528e+74
4
-1.973858281552663e-211
-1.3958819973365407e-211
-1.9400087236409523e-211

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
041119
15977
done5977

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.9s15106×body80nan
1.3s9162×body80valid