Details

Time bar (total: 19.1s)

sample109.0ms

Algorithm
intervals
Results
31.0ms126×body160valid
30.0ms130×body80valid
24.0ms197×body80nan

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5000
64967
51097
4396
3153
263
132
016

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
11.4b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite61.0ms

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
(* (/ t l) (/ t l))
22.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
9.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (/ t l) (/ t l))
40.0ms
(* (/ Om Omc) (/ Om Omc))
15.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
141.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.9s

Counts
197 → 197
Iterations
IterNodes
done5001
22844
1919
0324

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.9b

localize50.0ms

Local error

Found 4 expressions with local error:

11.4b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 1)))
32.9b
(cbrt (* (/ t l) (/ t l)))
32.9b
(cbrt (* (/ t l) (/ t l)))
32.9b
(cbrt (* (/ t l) (/ t l)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt sqrt-prod
16×*-un-lft-identity times-frac
13×add-cube-cbrt
9×cbrt-div
6×difference-of-squares
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod frac-times pow1/3 associate-*l/ associate-*r/
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 79
Calls
4 calls:
10.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 1)))
12.0ms
(cbrt (* (/ t l) (/ t l)))
14.0ms
(cbrt (* (/ t l) (/ t l)))
12.0ms
(cbrt (* (/ t l) (/ t l)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 1)))
117.0ms
(cbrt (* (/ t l) (/ t l)))
94.0ms
(cbrt (* (/ t l) (/ t l)))
117.0ms
(cbrt (* (/ t l) (/ t l)))

simplify2.0s

Counts
91 → 91
Iterations
IterNodes
done5000
42538
3905
2420
1238
0147

prune770.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.9b

localize57.0ms

Local error

Found 4 expressions with local error:

11.4b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt (/ t l)) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l))) 1)))
15.9b
(cbrt (/ t l))
15.9b
(cbrt (/ t l))
15.9b
(cbrt (/ t l))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
40×add-sqr-sqrt
39×cbrt-prod
37×*-un-lft-identity
34×add-cube-cbrt
19×sqrt-prod
6×difference-of-squares
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 109
Calls
4 calls:
9.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt (/ t l)) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l))) 1)))
3.0ms
(cbrt (/ t l))
3.0ms
(cbrt (/ t l))
4.0ms
(cbrt (/ t l))

series404.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt (/ t l)) (cbrt (/ t l))) (* (cbrt (/ t l)) (/ t l))) 1)))
79.0ms
(cbrt (/ t l))
86.0ms
(cbrt (/ t l))
83.0ms
(cbrt (/ t l))

simplify1.7s

Counts
121 → 121
Iterations
IterNodes
done5001
42562
3987
2460
1267
0174

prune813.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.8b

localize55.0ms

Local error

Found 4 expressions with local error:

15.9b
(cbrt (/ t l))
15.9b
(cbrt (/ t l))
32.9b
(cbrt (* (/ t l) (/ t l)))
32.9b
(cbrt (* (/ t l) (/ t l)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
18×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
8×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×frac-times associate-*l/ associate-*r/ div-inv
Counts
4 → 80
Calls
4 calls:
3.0ms
(cbrt (/ t l))
3.0ms
(cbrt (/ t l))
12.0ms
(cbrt (* (/ t l) (/ t l)))
10.0ms
(cbrt (* (/ t l) (/ t l)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (/ t l))
94.0ms
(cbrt (/ t l))
111.0ms
(cbrt (* (/ t l) (/ t l)))
95.0ms
(cbrt (* (/ t l) (/ t l)))

simplify1.6s

Counts
92 → 92
Iterations
IterNodes
done5001
42040
3720
2315
1178
0115

prune784.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.8b

regimes674.0ms

Accuracy

0% (0.3b remaining)

Error of 10.2b against oracle of 10.0b and baseline of 10.2b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done22
122
018

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s3824×body160valid
971.0ms8067×body80nan
580.0ms4176×body80valid