Details

Time bar (total: 15.0s)

sample156.0ms

Algorithm
intervals
Results
55.0ms235×body80nan
45.0ms120×body160valid
25.0ms136×body80valid

simplify831.0ms

Counts
1 → 1
Iterations
IterNodes
done2040
51097
4396
3153
263
132
016

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.3b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
0.5b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
8.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
19×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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 → 156
Calls
4 calls:
14.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
13.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (/ Om Omc) (/ Om Omc))
19.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
110.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
135.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify891.0ms

Counts
168 → 168
Iterations
IterNodes
done2000
21930
1645
0255

prune863.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.3b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
0.6b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
8.5b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
85×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
8×associate-/l*
6×associate-/r*
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×sqrt-div associate-/l/
1×pow2 frac-times rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 177
Calls
4 calls:
13.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
10.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
1.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

series291.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (/ Om Omc) (/ Om Omc))
17.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
158.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
74.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

simplify871.0ms

Counts
189 → 189
Iterations
IterNodes
done2001
21844
1636
0269

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

localize59.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
7.7b
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
8.5b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
8.5b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
226×sqrt-prod
104×times-frac
96×add-sqr-sqrt
76×*-un-lft-identity
64×add-cube-cbrt
24×difference-of-squares
12×rem-sqrt-square
8×pow1
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-div div-inv
Counts
4 → 172
Calls
4 calls:
10.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
11.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
2.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
2.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

series698.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
257.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
99.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
92.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

simplify711.0ms

Counts
184 → 184
Iterations
IterNodes
done2020
31454
2623
1336
0220

prune879.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.2b

localize46.0ms

Local error

Found 4 expressions with local error:

8.4b
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))))
8.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
8.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
8.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
57×sqrt-prod
50×add-sqr-sqrt
48×times-frac
41×*-un-lft-identity
32×add-cube-cbrt
18×difference-of-squares
7×pow1
6×rem-sqrt-square
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod sqrt-pow1 pow1/2 sqrt-div div-inv
1×pow1/3
Counts
4 → 116
Calls
4 calls:
1.0ms
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))))
116.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
116.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
121.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify636.0ms

Counts
128 → 128
Iterations
IterNodes
done2000
3710
2339
1202
0126

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.1b

regimes534.0ms

Accuracy

98.8% (0.1b remaining)

Error of 5.4b against oracle of 5.4b and baseline of 10.2b

bsearch2.0ms

simplify5.0ms

Iterations
IterNodes
done28
128
024

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.8s3744×body160valid
1.4s7893×body80nan
766.0ms4256×body80valid