Details

Time bar (total: 1.4m)

sample177.0ms

Algorithm
intervals
Results
61.0ms299×body80valid
51.0ms521×body80nan

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02128
17328
269028
done500028

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize36.0ms

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*)))))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
25×pow1
23×add-cbrt-cube
22×associate-*r/
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×add-sqr-sqrt *-un-lft-identity cbrt-unprod
8×add-cube-cbrt associate-*r* frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 associate--l+ 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 → 103
Calls
4 calls:
11.0ms
(/ (* l l) Om)
59.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
203.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
119.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.5s

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (* l l) Om)
631.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.7s

Counts
115 → 115
Iterations

Useful iterations: done (3.7s)

IterNodesCost
03183217
125983022
done50002714

prune803.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize54.0ms

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*)))))

rewrite480.0ms

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:
35.0ms
(* n (pow (/ l Om) 2.0))
98.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
197.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
145.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.2s

Counts
4 → 12
Calls
4 calls:
240.0ms
(* n (pow (/ l Om) 2.0))
548.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify604.0ms

Counts
131 → 131
Iterations

Useful iterations: done (598.0ms)

IterNodesCost
03503452
done50013256

prune909.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.8b

localize43.0ms

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*)))))

rewrite763.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
25×pow1 add-sqr-sqrt associate-*r*
24×add-cbrt-cube
22×associate-*r/
20×pow-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 associate--l+ 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 → 136
Calls
4 calls:
223.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
28.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
314.0ms
(* (* (* 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*))))
191.0ms
(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*)))))

series10.5s

Counts
4 → 12
Calls
4 calls:
620.0ms
(* (* (* 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*))))
7.7s
(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*)))))

simplify646.0ms

Counts
148 → 148
Iterations

Useful iterations: done (640.0ms)

IterNodesCost
03865057
done50004227

prune965.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 25.7b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
456×pow1
300×pow-prod-down
264×sqrt-pow1 associate-*r/
144×sqrt-div
81×flip3-- flip--
64×frac-sub
37×pow-prod-up
36×frac-times
27×pow-sqr
19×pow1/2
18×add-exp-log
9×prod-exp add-cbrt-cube
7×add-sqr-sqrt *-un-lft-identity
6×associate-*l/
5×add-cube-cbrt associate-*r*
4×add-log-exp
3×sqrt-prod cbrt-unprod
2×distribute-rgt-in sub-neg distribute-lft-in pow-exp
1×pow2 pow-to-exp rem-sqrt-square pow-plus div-exp associate-*l* *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 220
Calls
4 calls:
96.0ms
(* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))
152.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))
188.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))
1.1s
(sqrt (* (sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))) (sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))))

series23.6s

Counts
4 → 12
Calls
4 calls:
594.0ms
(* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))
7.5s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))
7.4s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))
8.0s
(sqrt (* (sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))) (sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))))

simplify2.2s

Counts
232 → 232
Iterations

Useful iterations: done (2.2s)

IterNodesCost
042613277
done500010921

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 25.3b

regimes892.0ms

Accuracy

15.7% (8.5b remaining)

Error of 29.7b against oracle of 21.1b and baseline of 31.2b

bsearch540.0ms

Steps
ItersRangePoint
7
3.9531903612801053e+83
5.7320075067165725e+85
3.36636290982373e+85

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03575
14675
done4675

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.1s14816×body80nan
2.0s9208×body80valid