Details

Time bar (total: 1.1m)

sample167.0ms

Algorithm
intervals
Results
43.0ms127×body160valid
37.0ms224×body80nan
22.0ms129×body80valid

simplify7.1s

Counts
1 → 1
Iterations
IterNodes
done5000
62611
5774
4250
3102
251
129
016

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize144.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
8.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp associate-/l/
1×pow-to-exp cbrt-undiv asin-acos clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 138
Calls
4 calls:
14.0ms
(pow (/ Om Omc) 2.0)
180.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
2.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
86.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
185.0ms
(pow (/ Om Omc) 2.0)
591.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
85.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
1.0s
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify9.4s

Counts
150 → 150
Iterations
IterNodes
done5002
34209
21307
1599
0280

prune2.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.9b

localize189.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ Om Omc) (/ Om Omc))
0.3b
(/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.5b
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.0b
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
65×times-frac
49×*-un-lft-identity add-cube-cbrt
18×add-cbrt-cube add-exp-log
16×sqrt-prod
13×swap-sqr associate-*r* associate-*l*
12×pow1
7×difference-of-squares
6×div-inv
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 149
Calls
4 calls:
49.0ms
(* (/ Om Omc) (/ Om Omc))
33.0ms
(/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
16.0ms
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (/ Om Omc) (/ Om Omc))
673.0ms
(/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))
58.0ms
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.1s
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify4.8s

Counts
161 → 161
Iterations
IterNodes
done5001
21907
1636
0249

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.9b

localize234.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ Om Omc) (/ Om Omc))
0.3b
(/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.5b
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.0b
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
65×times-frac
49×*-un-lft-identity add-cube-cbrt
18×add-cbrt-cube add-exp-log
16×sqrt-prod
13×swap-sqr associate-*r* associate-*l*
12×pow1
7×difference-of-squares
6×div-inv
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 149
Calls
4 calls:
91.0ms
(* (/ Om Omc) (/ Om Omc))
61.0ms
(/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))
4.0ms
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
31.0ms
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series1.8s

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (/ Om Omc) (/ Om Omc))
677.0ms
(/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))
63.0ms
(asin (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0s
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify5.1s

Counts
161 → 161
Iterations
IterNodes
done5001
21907
1636
0249

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.9b

localize252.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
7.7b
(sqrt (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.0b
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
8.0b
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
64×add-sqr-sqrt
52×times-frac
38×*-un-lft-identity add-cube-cbrt
12×difference-of-squares
10×pow1 rem-sqrt-square sqrt-pow1
6×pow1/2 sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
4 → 136
Calls
4 calls:
34.0ms
(sqrt (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
28.0ms
(sqrt (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
19.0ms
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
27.0ms
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series4.5s

Counts
4 → 12
Calls
4 calls:
1.2s
(sqrt (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.2s
(sqrt (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0s
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
984.0ms
(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify8.5s

Counts
148 → 148
Iterations
IterNodes
done5000
44685
31359
2490
1258
0159

prune2.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.9b

regimes2.1s

Accuracy

0% (0.0b remaining)

Error of 9.7b against oracle of 9.7b and baseline of 9.7b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done17
017

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.5s3882×body160valid
1.2s7943×body80nan
797.0ms4118×body80valid