Details

Time bar (total: 16.3s)

sample138.0ms

Algorithm
intervals
Results
45.0ms287×body80nan
34.0ms142×body80valid
34.0ms114×body160valid

simplify1.2s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (/ t l) 2) (/ t l) 1)
0.2b
(* (/ Om Omc) (/ Om Omc))
1.2b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
56×times-frac
44×*-un-lft-identity
41×add-cube-cbrt
19×sqrt-prod
16×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×difference-of-squares
5×div-inv
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×rem-sqrt-square
1×pow2 frac-times asin-acos sqrt-pow1 pow-plus pow1/2 sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up fma-udef
Counts
4 → 126
Calls
4 calls:
0.0ms
(fma (* (/ t l) 2) (/ t l) 1)
15.0ms
(* (/ Om Omc) (/ Om Omc))
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:
74.0ms
(fma (* (/ t l) 2) (/ t l) 1)
33.0ms
(* (/ Om Omc) (/ Om Omc))
16.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
169.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.3s

Counts
138 → 138
Iterations
IterNodes
done2023
32023
21697
1592
0237

prune879.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
1.2b
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1))))
3.5b
(log (exp (* (/ Om Omc) (/ Om Omc))))
8.0b
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
62×times-frac
56×*-un-lft-identity
44×add-cube-cbrt
25×sqrt-prod
16×pow1 add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
6×log-pow distribute-lft-out-- difference-of-squares
5×div-inv add-log-exp
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×log-prod
2×rem-sqrt-square
1×pow2 frac-times asin-acos exp-prod sqrt-pow1 pow-plus exp-to-pow pow1/2 sqrt-div rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 138
Calls
4 calls:
26.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1))))
8.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
25.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (/ Om Omc) (/ Om Omc))
10.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1))))
43.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
141.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.2s

Counts
150 → 150
Iterations
IterNodes
done2000
32000
21579
1575
0244

prune917.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
1.2b
(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))))
3.5b
(log (exp (* (/ Om Omc) (/ Om Omc))))
7.6b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
70×*-un-lft-identity
64×add-sqr-sqrt
60×times-frac
42×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
13×pow1
10×log-pow associate-/l*
6×associate-/r* add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod
2×sqrt-div associate-/l/
1×cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv exp-prod clear-num frac-2neg sqrt-pow1 flip3-- exp-to-pow pow1/2 div-exp rem-log-exp div-inv flip--
Counts
4 → 138
Calls
4 calls:
29.0ms
(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
1.0ms
(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))))
8.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
2.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

series274.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
12.0ms
(asin (fabs (/ (sqrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))))
32.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
78.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

simplify1.2s

Counts
150 → 150
Iterations
IterNodes
done2087
42087
31432
2556
1296
0191

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

localize51.0ms

Local error

Found 4 expressions with local error:

7.6b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
7.6b
(sqrt (fma (/ t l) (* (/ t l) 2) 1))
9.3b
(sqrt (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
9.3b
(sqrt (sqrt (fma (/ t l) (* (/ t l) 2) 1)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 76
Calls
4 calls:
2.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
2.0ms
(sqrt (fma (/ t l) (* (/ t l) 2) 1))
3.0ms
(sqrt (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
3.0ms
(sqrt (sqrt (fma (/ t l) (* (/ t l) 2) 1)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))
73.0ms
(sqrt (fma (/ t l) (* (/ t l) 2) 1))
180.0ms
(sqrt (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
177.0ms
(sqrt (sqrt (fma (/ t l) (* (/ t l) 2) 1)))

simplify1.0s

Counts
88 → 88
Iterations
IterNodes
done2001
42001
3752
2305
1156
098

prune603.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.6b

regimes549.0ms

Accuracy

99.3% (0.1b remaining)

Error of 1.0b against oracle of 1.0b and baseline of 10.3b

bsearch2.0ms

simplify7.0ms

Iterations
IterNodes
done37
137
030

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.0s8113×body80nan
1.4s3875×body160valid
691.0ms4125×body80valid