Details

Time bar (total: 28.2s)

sample186.0ms

Algorithm
intervals
Results
76.0ms122×body160valid
51.0ms271×body80nan
27.0ms134×body80valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
63286
5888
4311
3124
259
130
016

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
14.0ms
(* (/ t l) (/ t l))
17.0ms
(* (/ Om Omc) (/ Om Omc))
2.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
7.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (/ t l) (/ t l))
44.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
166.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify793.0ms

Counts
197 → 197
Iterations
IterNodes
22696
1903
0324

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.7b

localize52.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (/ 1 (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
7.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
7.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
7.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
89×sqrt-prod
56×add-sqr-sqrt
54×times-frac
44×*-un-lft-identity
36×add-cube-cbrt
12×difference-of-squares
10×pow1 rem-sqrt-square
9×sqrt-pow1
5×pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow-flip
2×sqrt-div div-inv
1×inv-pow
Counts
4 → 126
Calls
4 calls:
4.0ms
(sqrt (/ 1 (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
7.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series663.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(sqrt (/ 1 (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
273.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
113.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
78.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify4.2s

Counts
138 → 138
Iterations
IterNodes
43458
31329
2603
1366
0235

prune3.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.7b

localize89.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
7.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
7.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
7.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod
14×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
7×sqrt-pow1
5×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
3.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
3.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series964.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
114.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
98.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
517.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify2.6s

Counts
82 → 82
Iterations
IterNodes
42112
3705
2248
1117
068

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.7b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) t) (/ 1 l)) 2 1))))
3.9b
(* (* (/ t l) t) (/ 1 l))
8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) t) (/ 1 l)) 2 1)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
65×times-frac
55×add-exp-log
51×*-un-lft-identity
48×add-cube-cbrt
37×add-cbrt-cube
26×associate-*r*
24×prod-exp
19×sqrt-prod
17×pow1
14×div-exp associate-*l* cbrt-unprod
13×swap-sqr
9×cbrt-undiv
6×div-inv difference-of-squares
4×expm1-log1p-u pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×rec-exp 1-exp
2×frac-times rem-sqrt-square associate-*r/ *-commutative
1×pow2 asin-acos sqrt-pow1 pow-plus pow1/2 sqrt-div pow-sqr un-div-inv pow-prod-up
Counts
4 → 164
Calls
4 calls:
13.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) t) (/ 1 l)) 2 1))))
45.0ms
(* (* (/ t l) t) (/ 1 l))
11.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) t) (/ 1 l)) 2 1)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (/ Om Omc) (/ Om Omc))
9.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) t) (/ 1 l)) 2 1))))
27.0ms
(* (* (/ t l) t) (/ 1 l))
131.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) t) (/ 1 l)) 2 1)))

simplify763.0ms

Counts
176 → 176
Iterations
IterNodes
22511
1841
0314

prune2.7s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.7b

regimes471.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.3b and baseline of 10.3b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
115
015

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.2s7856×body80nan
1.6s3745×body160valid
867.0ms4255×body80valid