Details

Time bar (total: 51.8s)

sample451.0ms

Algorithm
intervals
Results
226.0ms449×body80nan
51.0ms309×body80valid

simplify3.1s

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

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.4b

localize69.0ms

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))))

rewrite138.0ms

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))
39.0ms
(* n (pow (/ l Om) 2.0))
47.0ms
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
43.0ms
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

series9.2s

Counts
4 → 12
Calls
4 calls:
1.8s
(fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))
203.0ms
(* n (pow (/ l Om) 2.0))
2.0s
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
5.2s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))

simplify1.4s

Counts
101 → 101
Iterations
IterNodes
done5000
22103
1442
0187

prune946.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.4b

localize63.0ms

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))))

rewrite140.0ms

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))
22.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
75.0ms
(* (* (* 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)))
39.0ms
(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))))

series9.3s

Counts
4 → 12
Calls
4 calls:
1.8s
(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
283.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
2.0s
(* (* (* 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)))
5.2s
(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))))

simplify1.4s

Counts
101 → 101
Iterations
IterNodes
done5002
22211
1463
0194

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.4b

localize135.0ms

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)))))

rewrite414.0ms

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)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
392.0ms
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
376.0ms
(cbrt (fma (* (pow (/ l Om) (* 2 (/ 2.0 2))) n) (- U* U) (fma l (* (/ l Om) (- 2.0)) t)))
1.1s
(cbrt (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)))
1.5s
(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)))))

simplify2.4s

Counts
70 → 70
Iterations
IterNodes
done5000
34204
21177
1469
0197

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.4b

localize40.0ms

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) (pow (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)) 1))
17.6b
(sqrt (* (* (* 2.0 n) U) (pow (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)) 1)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
36×add-exp-log
24×associate-*r*
23×add-sqr-sqrt
22×prod-exp
18×unpow-prod-down
17×pow1
15×*-un-lft-identity add-cbrt-cube add-cube-cbrt
12×pow-prod-down
10×times-frac
7×cbrt-unprod
5×pow-exp
4×expm1-log1p-u pow-to-exp sqrt-pow1 associate-*l* log1p-expm1-u add-log-exp unswap-sqr
3×sqr-pow
2×*-commutative
1×pow1/2 div-exp sqrt-prod fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
1.0ms
(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
27.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
79.0ms
(* (* (* 2.0 n) U) (pow (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)) 1))
46.0ms
(sqrt (* (* (* 2.0 n) U) (pow (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)) 1)))

series8.2s

Counts
4 → 12
Calls
4 calls:
1.4s
(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))
188.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.8s
(* (* (* 2.0 n) U) (pow (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)) 1))
4.8s
(sqrt (* (* (* 2.0 n) U) (pow (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t)) 1)))

simplify1.5s

Counts
109 → 109
Iterations
IterNodes
done5001
22581
1519
0210

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.2b

regimes1.0s

Accuracy

19.9% (8.3b remaining)

Error of 29.3b against oracle of 21.0b and baseline of 31.4b

bsearch220.0ms

Steps
ItersRangePoint
6
1.0415639018024206e-169
6.407984111669537e-169
2.4777029051611257e-169
7
-8.311309869918327e-89
-3.489370936238946e-91
-2.8439302632662482e-89

simplify22.0ms

Iterations
IterNodes
done74
374
272
170
051

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.1s14813×body80nan
1.1s9174×body80valid