Details

Time bar (total: 21.5s)

sample134.0ms

Algorithm
intervals
Results
53.0ms225×body80nan
36.0ms114×body160valid
22.0ms142×body80valid

simplify900.0ms

Counts
1 → 1
Iterations
IterNodes
done2050
62050
51097
4396
3153
263
132
016

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite48.0ms

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:
15.0ms
(* (/ Om Omc) (/ Om Omc))
23.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
7.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (/ Om Omc) (/ Om Omc))
84.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
13.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
161.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.1s

Counts
168 → 168
Iterations
IterNodes
done2003
32003
21936
1643
0255

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite38.0ms

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:
12.0ms
(* (/ Om Omc) (/ Om Omc))
15.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
8.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (/ Om Omc) (/ Om Omc))
99.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
9.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
153.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.3s

Counts
168 → 168
Iterations
IterNodes
done2003
32003
21936
1643
0255

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (/ t l) 2) (/ t l) 1)
0.4b
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1))
0.7b
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1)))))
10.2b
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
33×*-un-lft-identity
32×times-frac
17×add-cube-cbrt
16×difference-of-squares
8×associate-/l*
7×pow1
6×add-cbrt-cube add-exp-log
5×sqrt-div
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
3×associate-/r*
2×frac-times sqrt-pow1 flip3-+ associate-*l/ flip-+ associate-/l/
1×cbrt-undiv asin-acos clear-num frac-2neg flip3-- pow1/2 div-sub div-exp pow-prod-down associate-*r/ sqrt-prod fma-udef div-inv flip--
Counts
4 → 94
Calls
4 calls:
0.0ms
(fma (* (/ t l) 2) (/ t l) 1)
30.0ms
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1)))))
21.0ms
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1))))

series329.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(fma (* (/ t l) 2) (/ t l) 1)
96.0ms
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1))
13.0ms
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1)))))
165.0ms
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) 2) (/ t l) 1))))

simplify1.2s

Counts
106 → 106
Iterations
IterNodes
done2000
32000
2960
1379
0181

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.4b

localize55.0ms

Local error

Found 4 expressions with local error:

10.7b
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))))
17.1b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
17.1b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
17.1b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
57×cbrt-prod
45×times-frac
40×add-sqr-sqrt *-un-lft-identity
31×add-cube-cbrt
18×difference-of-squares
12×pow1
9×sqrt-pow1 pow1/3
7×cbrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-div div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 118
Calls
4 calls:
10.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))))
3.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
3.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
3.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series984.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))))
255.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
265.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))
216.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.3s

Counts
130 → 130
Iterations
IterNodes
done2004
42004
31969
2637
1296
0166

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.4b

regimes483.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done23
123
018

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.1s3730×body160valid
1.8s8006×body80nan
928.0ms4270×body80valid