Details

Time bar (total: 25.7s)

sample423.0ms

Algorithm
intervals
Results
50.0ms453×body80nan
18.0ms285×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
02128
14928
215427
364227
4323927
done500027

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize22.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
9.6b
(/ (* l l) Om)
23.3b
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
25×pow1
24×add-sqr-sqrt *-un-lft-identity
23×add-cbrt-cube
20×add-cube-cbrt
18×prod-diff
16×prod-exp
13×pow-prod-down
11×distribute-rgt-in distribute-lft-in
10×cbrt-unprod
6×associate-*r* associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp
3×flip3-- times-frac div-exp associate-/r* flip--
2×cbrt-undiv sub-neg sqrt-div associate-*r/ pow-exp *-commutative distribute-lft-out-- difference-of-squares
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l*
Counts
4 → 115
Calls
4 calls:
46.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
61.0ms
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
9.0ms
(/ (* l l) Om)
52.0ms
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series3.1s

Counts
4 → 12
Calls
4 calls:
377.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
756.0ms
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
25.0ms
(/ (* l l) Om)
1.9s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify1.2s

Counts
127 → 127
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02813038
17052772
225192368
done50022339

prune452.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.4b

localize20.0ms

Local error

Found 4 expressions with local error:

5.8b
(* n (pow (/ l Om) 2.0))
6.3b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
23.3b
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×add-exp-log
31×*-un-lft-identity
27×add-cube-cbrt
25×pow1
23×associate-*r*
20×add-cbrt-cube
19×prod-exp
18×prod-diff
15×unpow-prod-down
13×pow-prod-down
11×distribute-rgt-in distribute-lft-in
10×times-frac cbrt-unprod
9×associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×pow-to-exp sub-neg sqrt-div associate-*r/ div-exp distribute-lft-out-- difference-of-squares sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 131
Calls
4 calls:
23.0ms
(* n (pow (/ l Om) 2.0))
48.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
60.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
49.0ms
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series3.2s

Counts
4 → 12
Calls
4 calls:
151.0ms
(* n (pow (/ l Om) 2.0))
383.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
759.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
1.9s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify1.2s

Counts
143 → 143
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03143277
17622989
225622595
done50022566

prune490.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.8b

localize19.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n))
5.8b
(* n (pow (/ l Om) 2.0))
6.3b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
23.3b
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×add-exp-log *-un-lft-identity
27×add-cube-cbrt
23×associate-*r*
21×pow1
18×prod-diff
16×prod-exp add-cbrt-cube
15×unpow-prod-down
11×distribute-rgt-in distribute-lft-in
10×times-frac pow-prod-down
9×associate-*l*
7×cbrt-unprod
6×associate-*l/
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×pow-to-exp sub-neg sqrt-div associate-*r/ div-exp distribute-lft-out-- difference-of-squares sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 128
Calls
4 calls:
30.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n))
22.0ms
(* n (pow (/ l Om) 2.0))
45.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
56.0ms
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

series3.2s

Counts
4 → 12
Calls
4 calls:
760.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n))
146.0ms
(* n (pow (/ l Om) 2.0))
382.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

simplify1.2s

Counts
140 → 140
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03053083
17262802
222352468
done50012439

prune480.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.7b

localize23.0ms

Local error

Found 4 expressions with local error:

4.5b
(* n (pow (/ l Om) (/ 2.0 2)))
4.7b
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* 2.0 n))
6.3b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
23.3b
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* 2.0 n)) U))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
95×add-exp-log
64×prod-exp
39×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
23×associate-*r*
21×pow1
20×pow-exp add-cbrt-cube
18×prod-diff
15×unpow-prod-down
11×distribute-rgt-in distribute-lft-in
10×pow-to-exp times-frac div-exp pow-prod-down cbrt-unprod
9×associate-*l*
6×associate-*l/
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 145
Calls
4 calls:
23.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
31.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* 2.0 n))
142.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
55.0ms
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* 2.0 n)) U))

series3.1s

Counts
4 → 12
Calls
4 calls:
171.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
734.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* 2.0 n))
380.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* 2.0 n)) U))

simplify1.2s

Counts
157 → 157
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03404922
18173717
226293273
done50013244

prune510.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 19.7b

regimes516.0ms

Accuracy

4.8% (12.3b remaining)

Error of 30.3b against oracle of 18.0b and baseline of 30.9b

bsearch296.0ms

Steps
ItersRangePoint
9
2.7403049608437093e+106
1.399530857542569e+112
7.621504539317108e+111
6
5.354858097511972e-86
3.378381856036428e-85
1.5117414702188568e-85
6
3.4608260305043595e-271
1.6692592688500799e-270
1.107792021201636e-270

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
043142
157115
done57115

end0.0ms

sample2.6s

Algorithm
intervals
Results
913.0ms14724×body80nan
561.0ms9136×body80valid