Details

Time bar (total: 21.1s)

sample121.0ms

Algorithm
intervals
Results
39.0ms127×body160valid
36.0ms245×body80nan
20.0ms129×body80valid

simplify1.2s

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
9.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite63.0ms

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 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 → 181
Calls
4 calls:
24.0ms
(* (/ t l) (/ t l))
27.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (/ t l) (/ t l))
34.0ms
(* (/ Om Omc) (/ Om Omc))
18.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
208.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify890.0ms

Counts
193 → 193
Iterations
IterNodes
22685
1894
0320

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
9.6b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square asin-acos sqrt-pow1 pow1/2
Counts
4 → 163
Calls
4 calls:
11.0ms
(* (/ t l) (/ t l))
11.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series193.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (/ t l) (/ t l))
36.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
97.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify785.0ms

Counts
175 → 175
Iterations
IterNodes
22485
1786
0256

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize41.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
8.5b
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
9.6b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.6b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
6.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
1.0ms
(sqrt (asin (/ (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))

series216.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
29.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
82.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
75.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify2.0s

Counts
72 → 72
Iterations
IterNodes
53477
41060
3369
2168
1101
060

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize53.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
9.6b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.6b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.6b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
1.0ms
(sqrt (asin (/ (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))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series322.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
83.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
91.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
111.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify1.8s

Counts
72 → 72
Iterations
IterNodes
53477
41060
3369
2168
1101
060

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

regimes558.0ms

Accuracy

98% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.1b

bsearch3.0ms

simplify6.0ms

Iterations
IterNodes
225
125
024

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s8076×body80nan
1.6s3801×body160valid
799.0ms4199×body80valid