Details

Time bar (total: 17.0s)

sample174.0ms

Algorithm
intervals
Results
69.0ms129×body160valid
48.0ms267×body80nan
24.0ms127×body80valid

simplify1.2s

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
7.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
24.0ms
(* (/ Om Omc) (/ Om Omc))
20.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
6.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (/ Om Omc) (/ Om Omc))
32.0ms
(* (/ t l) (/ t l))
9.0ms
(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)))

simplify771.0ms

Counts
197 → 197
Iterations
IterNodes
22709
1903
0324

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))
0.6b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
7.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
17.0ms
(* (/ Om Omc) (/ Om Omc))
14.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
6.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (/ Om Omc) (/ Om Omc))
30.0ms
(* (/ t l) (/ t l))
13.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
166.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify698.0ms

Counts
197 → 197
Iterations
IterNodes
22709
1903
0324

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))
0.6b
(asin (* (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (* (/ t l) (/ t l)) 2 1)))))
7.0b
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
106×times-frac
78×*-un-lft-identity
75×add-cube-cbrt
44×sqrt-prod
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 195
Calls
4 calls:
21.0ms
(* (/ Om Omc) (/ Om Omc))
26.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (* (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (* (/ t l) (/ t l)) 2 1)))))
6.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (* (/ t l) (/ t l)) 2 1)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (/ Om Omc) (/ Om Omc))
36.0ms
(* (/ t l) (/ t l))
15.0ms
(asin (* (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (* (/ t l) (/ t l)) 2 1)))))
318.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify1.1s

Counts
207 → 207
Iterations
IterNodes
22672
1910
0352

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
7.1b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square asin-acos sqrt-pow1 pow1/2
Counts
4 → 167
Calls
4 calls:
13.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series175.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (/ Om Omc) (/ Om Omc))
36.0ms
(* (/ t l) (/ t l))
14.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
80.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify662.0ms

Counts
179 → 179
Iterations
IterNodes
22495
1788
0260

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

regimes560.0ms

Accuracy

98.3% (0.1b remaining)

Error of 5.4b against oracle of 5.3b and baseline of 10.2b

bsearch2.0ms

simplify8.0ms

Iterations
IterNodes
229
129
028

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.2s8206×body80nan
1.7s3807×body160valid
1.2s4193×body80valid