Details

Time bar (total: 32.3s)

sample192.0ms

Algorithm
intervals
Results
79.0ms284×body80nan
54.0ms126×body160valid
26.0ms130×body80valid

simplify1.2s

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
7.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite33.0ms

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:
13.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(/ (- 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)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (/ Om Omc) (/ Om Omc))
89.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
14.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
141.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify6.4s

Counts
168 → 168
Iterations
IterNodes
36581
21847
1641
0257

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.7b

localize65.0ms

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)))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
7.7b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite53.0ms

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:
26.0ms
(* (/ Om Omc) (/ Om Omc))
20.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(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))

series343.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (/ Om Omc) (/ Om Omc))
193.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
17.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
89.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.9s

Counts
189 → 189
Iterations
IterNodes
35593
21736
1634
0271

prune2.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
0.6b
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1)))))
7.8b
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
72×times-frac
61×*-un-lft-identity
45×add-cube-cbrt
18×add-cbrt-cube add-exp-log
16×difference-of-squares
14×pow1
13×swap-sqr associate-*r* associate-*l*
8×associate-/l*
5×cbrt-undiv sqrt-div div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp unswap-sqr
3×frac-times associate-/r* associate-*l/
2×sqrt-pow1 flip3-+ pow-prod-down associate-*r/ flip-+ associate-/l/
1×pow2 asin-acos clear-num frac-2neg pow-plus flip3-- pow1/2 div-sub pow-sqr *-commutative pow-prod-up sqrt-prod flip--
Counts
4 → 153
Calls
4 calls:
12.0ms
(* (/ t l) (/ t l))
22.0ms
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1)))))
19.0ms
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))))

series773.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (/ t l) (/ t l))
136.0ms
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
18.0ms
(asin (sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1)))))
589.0ms
(sqrt (* (+ (/ Om Omc) 1) (/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))))

simplify1.0s

Counts
165 → 165
Iterations
IterNodes
22060
1709
0274

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize61.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
14.0b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
14.0b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
14.0b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite14.0ms

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:
11.0ms
(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))

series756.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
210.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
210.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
153.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify1.8s

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

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

regimes584.0ms

Accuracy

97.9% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.1b

bsearch5.0ms

simplify9.0ms

Iterations
IterNodes
225
125
024

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.1s8015×body80nan
1.7s3829×body160valid
1.0s4171×body80valid