Details

Time bar (total: 39.4s)

sample329.0ms

Algorithm
intervals
Results
28.0ms415×body80nan
19.0ms292×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
02128
14928
215127
360127
4310127
done500127

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.0b

localize28.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.8b
(* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
8.0b
(/ (* l l) Om)
23.2b
(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
55×distribute-rgt-in distribute-lft-in
54×prod-diff
48×add-sqr-sqrt
46×*-un-lft-identity
44×add-cube-cbrt
31×pow1
23×add-exp-log add-cbrt-cube
17×pow-prod-down
10×associate-*r/ prod-exp cbrt-unprod
6×sub-neg associate-*r*
5×sqrt-pow1
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
3×flip3-- times-frac associate-/r* flip--
2×cbrt-undiv sqrt-div div-exp *-commutative
1×frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 157
Calls
4 calls:
25.0ms
(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
11.0ms
(* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
3.0ms
(/ (* l l) Om)
32.0ms
(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series6.4s

Counts
4 → 12
Calls
4 calls:
1.2s
(* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
791.0ms
(* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
24.0ms
(/ (* l l) Om)
4.3s
(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify1.1s

Counts
169 → 169
Iterations

Useful iterations: 2 (476.0ms)

IterNodesCost
035110299
19156970
230735322
done50015322

prune525.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.5b

localize24.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.5b
(* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.8b
(* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
23.2b
(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
72×prod-diff
66×distribute-rgt-in distribute-lft-in
61×add-sqr-sqrt
59×*-un-lft-identity
55×add-cube-cbrt
33×pow1
32×add-exp-log
23×add-cbrt-cube
18×pow-prod-down prod-exp
12×associate-*r/ cbrt-unprod
11×associate-*r*
8×sub-neg
5×sqrt-pow1 associate-*l*
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
3×*-commutative
2×sqrt-div pow-exp distribute-lft-out-- difference-of-squares
1×pow-to-exp pow1/2 div-exp sqrt-prod unswap-sqr
Counts
4 → 182
Calls
4 calls:
25.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
25.0ms
(* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
11.0ms
(* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
30.0ms
(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series6.9s

Counts
4 → 12
Calls
4 calls:
374.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s
(* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
925.0ms
(* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.4s
(sqrt (* (* 2.0 n) (* U (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify1.6s

Counts
194 → 194
Iterations

Useful iterations: done (1.6s)

IterNodesCost
042311342
111327816
239136070
done50016052

prune483.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.3b

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b
(* n (pow (/ l Om) 2.0))
5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.9b
(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
23.2b
(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×*-un-lft-identity
39×add-cube-cbrt
36×prod-diff
35×add-exp-log
27×associate-*r*
25×pow1
22×distribute-rgt-in distribute-lft-in
20×add-cbrt-cube
19×prod-exp
15×unpow-prod-down
13×pow-prod-down
10×times-frac cbrt-unprod
6×associate-*r/
5×associate-*l*
4×expm1-log1p-u sub-neg sqrt-pow1 pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×pow-to-exp sqrt-div div-exp distribute-lft-out-- difference-of-squares sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 153
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) 2.0))
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
27.0ms
(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
29.0ms
(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.0s

Counts
4 → 12
Calls
4 calls:
148.0ms
(* n (pow (/ l Om) 2.0))
372.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s
(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.3s
(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify1.6s

Counts
165 → 165
Iterations

Useful iterations: done (1.6s)

IterNodesCost
04145992
110784615
240673806
done50013788

prune552.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 19.6b

localize21.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
5.5b
(* n (pow (/ l Om) (/ 2.0 2)))
8.9b
(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
23.2b
(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
51×add-sqr-sqrt
43×*-un-lft-identity
39×add-cube-cbrt
36×prod-diff
27×associate-*r*
25×pow1
24×add-cbrt-cube
22×distribute-rgt-in distribute-lft-in
20×pow-exp
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
10×pow-to-exp times-frac div-exp
6×associate-*r/
5×associate-*l*
4×expm1-log1p-u sub-neg sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×sqrt-div distribute-lft-out-- difference-of-squares sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 170
Calls
4 calls:
82.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
27.0ms
(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
30.0ms
(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series6.0s

Counts
4 → 12
Calls
4 calls:
359.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
162.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.2s
(* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.4s
(sqrt (* (* (* 2.0 n) U) (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify1.8s

Counts
182 → 182
Iterations

Useful iterations: 2 (969.0ms)

IterNodesCost
04508991
112045778
245694779
done50004779

prune511.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.6b

regimes636.0ms

Accuracy

32.2% (9.4b remaining)

Error of 27.8b against oracle of 18.4b and baseline of 32.3b

bsearch195.0ms

Steps
ItersRangePoint
7
-3.239627375911032e-303
-4.3939532820442994e-305
-4.448978028228541e-305
7
-3.499955729219133e-161
-7.334271302728465e-163
-1.324726673018472e-161

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
059137
181137
done81137

end0.0ms

sample2.5s

Algorithm
intervals
Results
980.0ms15017×body80nan
612.0ms9185×body80valid