Details

Time bar (total: 53.5s)

sample214.0ms

Algorithm
intervals
Results
67.0ms309×body80valid
61.0ms449×body80nan

simplify2.5s

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.4b

localize47.0ms

Local error

Found 4 expressions with local error:

5.1b
(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
5.8b
(* n (pow (/ l Om) 2.0))
12.0b
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
17.6b
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

rewrite152.0ms

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:
1.0ms
(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
34.0ms
(* n (pow (/ l Om) 2.0))
51.0ms
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
61.0ms
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

series7.7s

Counts
4 → 12
Calls
4 calls:
1.5s
(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
204.0ms
(* n (pow (/ l Om) 2.0))
1.7s
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
4.3s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

simplify946.0ms

Counts
101 → 101
Iterations
IterNodes
done5000
22103
1442
0187

prune850.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.4b

localize58.0ms

Local error

Found 4 expressions with local error:

5.1b
(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
6.0b
(* n (pow (/ l Om) (/ 2.0 2)))
12.0b
(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
17.6b
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (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:
0.0ms
(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
33.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
74.0ms
(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
60.0ms
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

series8.2s

Counts
4 → 12
Calls
4 calls:
1.6s
(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
250.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.8s
(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
4.6s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))

simplify1.1s

Counts
101 → 101
Iterations
IterNodes
done5002
22211
1463
0194

prune980.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.4b

localize102.0ms

Local error

Found 4 expressions with local error:

13.1b
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
13.1b
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
13.1b
(cbrt (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
17.6b
(sqrt (* (* (* (* (cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t))) (cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))) U) (* n 2.0)) (cbrt (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))))

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
34×pow1
22×pow-prod-down
9×cbrt-prod
8×sqrt-pow1
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
1×pow1/2 sqrt-prod
Counts
4 → 58
Calls
4 calls:
1.0ms
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
1.0ms
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
1.0ms
(cbrt (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
410.0ms
(sqrt (* (* (* (* (cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t))) (cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))) U) (* n 2.0)) (cbrt (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
435.0ms
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
354.0ms
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
1.0s
(cbrt (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
1.7s
(sqrt (* (* (* (* (cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t))) (cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))) U) (* n 2.0)) (cbrt (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))))

simplify2.2s

Counts
70 → 70
Iterations
IterNodes
done5000
34204
21177
1469
0197

prune1.3s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 20.4b

localize84.0ms

Local error

Found 4 expressions with local error:

5.5b
(* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
5.8b
(* (pow (/ l Om) (* 2 (/ 2.0 2))) n)
7.4b
(* (* 2.0 n) (* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t))))
17.6b
(sqrt (* (* 2.0 n) (* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
31×pow1
26×add-exp-log
25×add-sqr-sqrt
21×associate-*l*
20×add-cbrt-cube
17×pow-prod-down
15×unpow-prod-down *-un-lft-identity add-cube-cbrt
13×prod-exp
10×times-frac cbrt-unprod
7×associate-*r*
6×fma-udef
5×distribute-rgt-in distribute-lft-in sqrt-pow1 unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative
2×pow-exp sqr-pow
1×pow-to-exp pow1/2 div-exp sqrt-prod div-inv
Counts
4 → 105
Calls
4 calls:
11.0ms
(* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
49.0ms
(* (pow (/ l Om) (* 2 (/ 2.0 2))) n)
21.0ms
(* (* 2.0 n) (* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t))))
27.0ms
(sqrt (* (* 2.0 n) (* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))))

series10.6s

Counts
4 → 12
Calls
4 calls:
1.2s
(* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
359.0ms
(* (pow (/ l Om) (* 2 (/ 2.0 2))) n)
1.7s
(* (* 2.0 n) (* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t))))
7.4s
(sqrt (* (* 2.0 n) (* U (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))))

simplify1.6s

Counts
117 → 117
Iterations
IterNodes
done5000
23378
1718
0275

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 16.9b

regimes2.2s

Accuracy

16.9% (11.7b remaining)

Error of 29.0b against oracle of 17.4b and baseline of 31.4b

bsearch524.0ms

Steps
ItersRangePoint
8
1.9034131584556183e-80
1.0188459734253492e-75
4.2213711999837046e-78
9
-2.2840861367093013e+101
-3.4248176785688746e+96
-2.4843602301315434e+99

simplify11.0ms

Iterations
IterNodes
done66
366
263
158
041

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.8s14813×body80nan
2.0s9174×body80valid