Details

Time bar (total: 41.4s)

sample199.0ms

Algorithm
intervals
Results
60.0ms278×body80valid
45.0ms458×body80nan

simplify2.4s

Counts
1 → 1
Iterations
IterNodes
done5000
44135
3665
2154
149
021

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.5b

localize38.0ms

Local error

Found 4 expressions with local error:

4.6b
(* n (pow (/ l Om) 2.0))
4.9b
(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
9.7b
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
19.2b
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
22×add-sqr-sqrt
21×add-exp-log
20×associate-*r*
15×unpow-prod-down add-cbrt-cube
14×*-un-lft-identity add-cube-cbrt
12×pow-prod-down
10×times-frac prod-exp
7×cbrt-unprod
4×expm1-log1p-u sqrt-pow1 associate-*l* log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef
2×pow-exp *-commutative sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in pow1/2 div-exp sqrt-prod div-inv
Counts
4 → 89
Calls
4 calls:
20.0ms
(* n (pow (/ l Om) 2.0))
0.0ms
(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
66.0ms
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
81.0ms
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

series8.7s

Counts
4 → 12
Calls
4 calls:
216.0ms
(* n (pow (/ l Om) 2.0))
1.8s
(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
1.8s
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
4.8s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

simplify1.1s

Counts
101 → 101
Iterations
IterNodes
done5000
22100
1443
0187

prune930.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.9b

localize65.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (* (- U* U) n) (* (pow (/ l Om) 2.0) (* (* n U) 2.0)))
7.4b
(* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))
9.0b
(* (pow (/ l Om) 2.0) (* (* n U) 2.0))
19.2b
(sqrt (+ (* (* (- U* U) n) (* (pow (/ l Om) 2.0) (* (* n U) 2.0))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

rewrite565.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
119×prod-exp
57×add-cbrt-cube
38×cbrt-unprod
22×pow1
19×associate-*l*
18×pow-exp
14×add-sqr-sqrt
13×unpow-prod-down *-un-lft-identity add-cube-cbrt
11×pow-prod-down
9×pow-to-exp times-frac div-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in associate-*l/ fma-udef log1p-expm1-u add-log-exp
3×associate-*r* *-commutative sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 flip-+ div-inv flip-- sqr-pow
Counts
4 → 138
Calls
4 calls:
167.0ms
(* (* (- U* U) n) (* (pow (/ l Om) 2.0) (* (* n U) 2.0)))
27.0ms
(* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))
68.0ms
(* (pow (/ l Om) 2.0) (* (* n U) 2.0))
298.0ms
(sqrt (+ (* (* (- U* U) n) (* (pow (/ l Om) 2.0) (* (* n U) 2.0))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
490.0ms
(* (* (- U* U) n) (* (pow (/ l Om) 2.0) (* (* n U) 2.0)))
138.0ms
(* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))
484.0ms
(* (pow (/ l Om) 2.0) (* (* n U) 2.0))
2.4s
(sqrt (+ (* (* (- U* U) n) (* (pow (/ l Om) 2.0) (* (* n U) 2.0))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

simplify2.3s

Counts
150 → 150
Iterations
IterNodes
done5000
24623
1833
0281

prune926.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.7b

localize64.0ms

Local error

Found 4 expressions with local error:

15.1b
(cbrt (/ l Om))
15.1b
(cbrt (/ l Om))
15.1b
(cbrt (/ l Om))
19.2b
(sqrt (+ (* (* (- U* U) n) (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (* n (* U 2.0)) (pow (cbrt (/ l Om)) 2.0)))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

rewrite821.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 89
Calls
4 calls:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
813.0ms
(sqrt (+ (* (* (- U* U) n) (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (* n (* U 2.0)) (pow (cbrt (/ l Om)) 2.0)))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

series2.6s

Counts
4 → 12
Calls
4 calls:
87.0ms
(cbrt (/ l Om))
94.0ms
(cbrt (/ l Om))
81.0ms
(cbrt (/ l Om))
2.3s
(sqrt (+ (* (* (- U* U) n) (* (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0) (* (* n (* U 2.0)) (pow (cbrt (/ l Om)) 2.0)))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

simplify670.0ms

Counts
101 → 101
Iterations
IterNodes
done5000
2958
1273
0137

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 18.7b

localize47.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (- U* U) (* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0))))
7.4b
(* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))
7.7b
(* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0)))
19.2b
(sqrt (+ (* (- U* U) (* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0)))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

rewrite757.0ms

Algorithm
rewrite-expression-head
Rules
147×add-exp-log
108×prod-exp
66×add-cbrt-cube
45×cbrt-unprod
40×pow1
24×pow-prod-down
12×pow-exp
9×add-sqr-sqrt
8×*-un-lft-identity
7×associate-*l*
6×pow-to-exp div-exp add-cube-cbrt
4×distribute-rgt-in expm1-log1p-u distribute-lft-in fma-udef log1p-expm1-u add-log-exp
3×associate-*r* *-commutative sqrt-prod
2×sqrt-div associate-*l/
1×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 flip-+ flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 126
Calls
4 calls:
229.0ms
(* (- U* U) (* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0))))
28.0ms
(* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))
61.0ms
(* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0)))
433.0ms
(sqrt (+ (* (- U* U) (* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0)))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

series3.6s

Counts
4 → 12
Calls
4 calls:
501.0ms
(* (- U* U) (* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0))))
133.0ms
(* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))
494.0ms
(* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0)))
2.4s
(sqrt (+ (* (- U* U) (* (* n (pow (/ l Om) 2.0)) (* n (* U 2.0)))) (* (* n 2.0) (* U (fma (/ l Om) (* l (- 2.0)) t)))))

simplify2.5s

Counts
138 → 138
Iterations
IterNodes
done5001
24288
1740
0250

prune876.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 18.7b

regimes1.1s

Accuracy

6.6% (11.1b remaining)

Error of 32.0b against oracle of 20.9b and baseline of 32.7b

bsearch353.0ms

Steps
ItersRangePoint
6
2.659657404139437e+61
1.7356687321809134e+62
1.7143508691560957e+62
9
-2.8864743413833433e+56
-6.41309587629849e+48
-7.011733841081501e+54

simplify23.0ms

Iterations
IterNodes
done66
366
265
161
044

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.9s14656×body80nan
1.4s9110×body80valid