Details

Time bar (total: 46.3s)

sample343.0ms

Algorithm
intervals
Results
136.0ms484×body80nan
49.0ms281×body80valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
02128
14928
215427
364227
4323927
done500027

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize55.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.3b
(/ (* l l) Om)
12.2b
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
20.4b
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite329.0ms

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:
102.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
21.0ms
(/ (* l l) Om)
124.0ms
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
71.0ms
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series4.8s

Counts
4 → 12
Calls
4 calls:
620.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
27.0ms
(/ (* l l) Om)
1.2s
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
3.0s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify2.0s

Counts
127 → 127
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02813038
17062772
225382368
done50022339

prune705.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize42.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.3b
(/ (* l l) Om)
8.1b
(* (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U)
20.4b
(sqrt (* (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
25×pow1
23×add-cbrt-cube
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×prod-exp
13×pow-prod-down
11×distribute-rgt-in distribute-lft-in
10×cbrt-unprod
8×associate-*r* associate-*l/
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×flip3-- times-frac div-exp associate-/r* flip--
2×cbrt-undiv sub-neg sqrt-div associate-*r/ 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 → 113
Calls
4 calls:
83.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms
(/ (* l l) Om)
121.0ms
(* (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U)
111.0ms
(sqrt (* (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

series4.8s

Counts
4 → 12
Calls
4 calls:
607.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
21.0ms
(/ (* l l) Om)
1.1s
(* (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U)
3.0s
(sqrt (* (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

simplify2.0s

Counts
125 → 125
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02782968
17072698
225842296
done50022267

prune691.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.3b

localize32.0ms

Local error

Found 4 expressions with local error:

4.2b
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.1b
(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U)
20.4b
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log
25×pow1
20×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt prod-diff add-cbrt-cube
15×prod-exp
13×pow-prod-down
11×distribute-rgt-in distribute-lft-in
9×cbrt-unprod
8×associate-*r* associate-*l/
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×flip3-- flip--
2×sub-neg sqrt-div associate-*r/ associate-*l* pow-exp *-commutative
1×pow-to-exp pow1/2 div-exp sqrt-prod fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 100
Calls
4 calls:
1.0ms
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
67.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
77.0ms
(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U)
81.0ms
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

series5.6s

Counts
4 → 12
Calls
4 calls:
505.0ms
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
539.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s
(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U)
3.4s
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))

simplify1.9s

Counts
112 → 112
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02583090
16622790
224352417
done50002388

prune631.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.1b

localize39.0ms

Local error

Found 4 expressions with local error:

4.2b
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
5.5b
(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) (* (cbrt U) (cbrt U)))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.4b
(sqrt (* (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) (* (cbrt U) (cbrt U))) (cbrt U)))

rewrite637.0ms

Algorithm
rewrite-expression-head
Rules
57×pow1
39×add-exp-log
38×pow-prod-down
24×prod-exp add-cbrt-cube
19×add-sqr-sqrt *-un-lft-identity
18×prod-diff cbrt-unprod
17×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
10×associate-*l/
8×sqrt-pow1
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-- flip--
2×sub-neg sqrt-div associate-*r/ associate-*l* pow-exp *-commutative
1×pow-to-exp pow1/2 div-exp sqrt-prod fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 111
Calls
4 calls:
1.0ms
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
133.0ms
(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) (* (cbrt U) (cbrt U)))
82.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
411.0ms
(sqrt (* (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) (* (cbrt U) (cbrt U))) (cbrt U)))

series6.9s

Counts
4 → 12
Calls
4 calls:
518.0ms
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
2.4s
(* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) (* (cbrt U) (cbrt U)))
524.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.4s
(sqrt (* (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) (* (cbrt U) (cbrt U))) (cbrt U)))

simplify2.1s

Counts
123 → 123
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02873765
17613441
228672786
done50002718

prune620.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 20.6b

regimes1.1s

Accuracy

2.4% (12.6b remaining)

Error of 31.8b against oracle of 19.3b and baseline of 32.2b

bsearch558.0ms

Steps
ItersRangePoint
6
2.3275376251269193e+224
1.4901249453302345e+225
6.756349021085235e+224
8
3.130068600083206e-148
4.152722936813379e-144
1.774918896406388e-146
7
-2.6074652413825058e-266
-4.054657772713118e-268
-4.1115204755668855e-268

simplify11.0ms

Iterations

Useful iterations: done (10.0ms)

IterNodesCost
040136
151109
25476
35776
done5775

end0.0ms

sample7.0s

Algorithm
intervals
Results
3.1s15019×body80nan
1.9s9134×body80valid