Details

Time bar (total: 27.4s)

sample181.0ms

Algorithm
intervals
Results
66.0ms122×body160valid
54.0ms271×body80nan
27.0ms134×body80valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
63283
5883
4308
3120
257
130
016

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite46.0ms

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*
21×sqrt-prod
19×pow1
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×insert-posit16 add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 179
Calls
4 calls:
13.0ms
(* (/ t l) (/ t l))
13.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
16.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series219.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (/ t l) (/ t l))
30.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
152.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify940.0ms

Counts
191 → 191
Iterations
IterNodes
22855
1951
0334

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.7b

localize42.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (/ 1 (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
93×sqrt-prod
56×add-sqr-sqrt
54×times-frac
44×*-un-lft-identity
36×add-cube-cbrt
12×difference-of-squares
10×pow1 rem-sqrt-square sqrt-div
9×sqrt-pow1
5×pow1/2
4×flip3-+ add-cbrt-cube add-exp-log associate-/r/ flip-+ insert-posit16 add-log-exp
3×pow-flip
2×div-inv
1×inv-pow
Counts
4 → 126
Calls
4 calls:
7.0ms
(sqrt (/ 1 (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
8.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
4.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(sqrt (/ 1 (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
270.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
73.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
74.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify1.1s

Counts
138 → 138
Iterations
IterNodes
32147
2815
1426
0255

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.7b

localize74.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
7.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.9b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod
14×add-sqr-sqrt
10×sqrt-div
9×pow1 *-un-lft-identity add-cube-cbrt
7×sqrt-pow1
5×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 70
Calls
4 calls:
8.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
6.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
6.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
104.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
79.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
91.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify6.0s

Counts
82 → 82
Iterations
IterNodes
45371
31573
2430
1169
084

prune1.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (* (/ t l) t) (/ 1 l)))))))
3.9b
(* (* (/ t l) t) (/ 1 l))
8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (* (/ t l) t) (/ 1 l))))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
65×times-frac
55×add-exp-log
51×*-un-lft-identity
48×add-cube-cbrt
37×add-cbrt-cube
26×associate-*r*
24×prod-exp
21×sqrt-prod
17×pow1
14×div-exp associate-*l* cbrt-unprod
13×swap-sqr
9×cbrt-undiv
6×div-inv difference-of-squares
4×pow-prod-down associate-*l/ insert-posit16 add-log-exp unswap-sqr
3×rec-exp 1-exp
2×frac-times rem-sqrt-square associate-*r/ associate-/r/ *-commutative
1×pow2 asin-acos sqrt-pow1 flip3-+ pow-plus pow1/2 sqrt-div pow-sqr un-div-inv pow-prod-up flip-+
Counts
4 → 158
Calls
4 calls:
13.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (* (/ t l) t) (/ 1 l)))))))
50.0ms
(* (* (/ t l) t) (/ 1 l))
12.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (* (/ t l) t) (/ 1 l))))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (* (/ t l) t) (/ 1 l)))))))
37.0ms
(* (* (/ t l) t) (/ 1 l))
159.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (* (/ t l) t) (/ 1 l))))))

simplify1.1s

Counts
170 → 170
Iterations
IterNodes
22666
1875
0324

prune2.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.7b

regimes438.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
218
118
016

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.3s3745×body160valid
1.7s7856×body80nan
984.0ms4255×body80valid