Details

Time bar (total: 29.6s)

sample127.0ms

Algorithm
intervals
Results
39.0ms122×body160valid
36.0ms236×body80nan
29.0ms134×body80valid

simplify1.4s

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
8.4b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite61.0ms

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:
33.0ms
(* (/ Om Omc) (/ Om Omc))
17.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
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)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (/ Om Omc) (/ Om Omc))
135.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
9.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
148.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify7.8s

Counts
168 → 168
Iterations
IterNodes
36581
21847
1641
0257

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.5b
(expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.7b
(asin (sqrt (log1p (expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))))
8.4b
(sqrt (log1p (expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
15×times-frac add-cube-cbrt
8×difference-of-squares
6×add-cbrt-cube add-exp-log
5×pow1 log1p-expm1-u associate-/l*
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-/r* sqrt-prod
2×associate-/l/
1×cbrt-undiv rem-sqrt-square asin-acos expm1-log1p clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 div-sub div-exp div-inv flip-- expm1-udef
Counts
4 → 80
Calls
4 calls:
20.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (sqrt (log1p (expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))))
2.0ms
(sqrt (log1p (expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
110.0ms
(expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
15.0ms
(asin (sqrt (log1p (expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))))
240.0ms
(sqrt (log1p (expm1 (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

simplify1.7s

Counts
92 → 92
Iterations
IterNodes
32416
2654
1279
0145

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.7b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
8.7b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite41.0ms

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:
19.0ms
(* (/ Om Omc) (/ Om Omc))
15.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series283.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (/ Om Omc) (/ Om Omc))
144.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
14.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
87.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.0s

Counts
189 → 189
Iterations
IterNodes
35593
21736
1634
0271

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

localize67.0ms

Local error

Found 4 expressions with local error:

11.5b
(sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
16.4b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.4b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.4b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 64
Calls
4 calls:
14.0ms
(sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series1.1s

Counts
4 → 12
Calls
4 calls:
170.0ms
(sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
559.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
192.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
164.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify1.5s

Counts
76 → 76
Iterations
IterNodes
52946
41021
3431
2212
1114
067

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.2b

regimes529.0ms

Accuracy

98.8% (0.1b remaining)

Error of 5.6b against oracle of 5.6b and baseline of 10.4b

bsearch3.0ms

simplify6.0ms

Iterations
IterNodes
227
127
026

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.5s7849×body80nan
1.4s3836×body160valid
826.0ms4164×body80valid