Details

Time bar (total: 17.4s)

sample170.0ms

Algorithm
intervals
Results
69.0ms299×body80nan
45.0ms118×body160valid
28.0ms138×body80valid

simplify1.1s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.6b
(/ (- 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))))
8.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite52.0ms

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:
21.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(/ (- 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))))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (/ Om Omc) (/ Om Omc))
92.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
144.0ms
(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

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.6b
(/ (- 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))))
8.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite56.0ms

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:
21.0ms
(* (/ Om Omc) (/ Om Omc))
21.0ms
(/ (- 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))))
9.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (/ Om Omc) (/ Om Omc))
83.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
129.0ms
(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

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
8.8b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
8.9b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
8.9b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
429×sqrt-prod
424×times-frac
258×add-sqr-sqrt
239×*-un-lft-identity
196×add-cube-cbrt
86×difference-of-squares
9×rem-sqrt-square
8×div-inv
7×pow1
6×associate-/r* add-cbrt-cube add-exp-log
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2
2×associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- sqrt-div div-sub div-exp flip--
Counts
4 → 319
Calls
4 calls:
22.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
16.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))) (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))

series442.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
130.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
76.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
100.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

simplify1.2s

Counts
331 → 331
Iterations
IterNodes
done2000
22000
11035
0595

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.2b

localize65.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
8.9b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
8.9b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
9.5b
(sqrt (sqrt (fma (* (/ t l) 2) (/ t l) 1)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
66×sqrt-prod
40×add-sqr-sqrt
32×times-frac
31×*-un-lft-identity
25×add-cube-cbrt
12×difference-of-squares
9×pow1
7×rem-sqrt-square sqrt-pow1
5×pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×sqrt-div div-inv
Counts
4 → 104
Calls
4 calls:
10.0ms
(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))
3.0ms
(sqrt (sqrt (fma (* (/ t l) 2) (/ t l) 1)))

series647.0ms

Counts
4 → 12
Calls
4 calls:
267.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
99.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
86.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
194.0ms
(sqrt (sqrt (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.0s

Counts
116 → 116
Iterations
IterNodes
done2005
42005
31724
2699
1338
0200

prune767.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.2b

regimes478.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s3791×body160valid
1.4s8087×body80nan
728.0ms4209×body80valid