Details

Time bar (total: 40.8s)

sample105.0ms

Algorithm
intervals
Results
35.0ms225×body80nan
30.0ms114×body160valid
19.0ms142×body80valid

simplify1.3s

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×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×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ 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 → 152
Calls
4 calls:
25.0ms
(* (/ Om Omc) (/ Om Omc))
16.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
14.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (/ Om Omc) (/ Om Omc))
90.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
170.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify958.0ms

Counts
164 → 164
Iterations
IterNodes
22110
1708
0267

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ t l) (/ t l))
0.4b
(/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc))))
0.7b
(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc))))))
10.2b
(sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc)))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
553×times-frac
436×add-sqr-sqrt
432×*-un-lft-identity
202×add-cube-cbrt
125×sqrt-prod
108×difference-of-squares
61×distribute-lft-out
30×associate-/r*
27×distribute-lft-out--
21×add-cbrt-cube add-exp-log
20×associate-/r/
15×div-inv
13×swap-sqr associate-*r* associate-*l*
12×pow1
9×flip3-- flip--
7×cbrt-undiv div-exp
4×prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp unswap-sqr
3×rem-sqrt-square
2×associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 flip3-+ pow-plus pow1/2 sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 388
Calls
4 calls:
22.0ms
(* (/ t l) (/ t l))
62.0ms
(/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc))))
1.0ms
(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc))))))
38.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc)))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (/ t l) (/ t l))
87.0ms
(/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc))))
13.0ms
(asin (sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc))))))
146.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (/ (+ 1 (* 2 (* (/ t l) (/ t l)))) (- 1 (/ Om Omc)))))

simplify9.6s

Counts
400 → 400
Iterations
IterNodes
24346
11390
0600

prune6.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.4b

localize62.0ms

Local error

Found 4 expressions with local error:

10.2b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
17.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
17.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
17.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
108×sqrt-prod
80×cbrt-div
69×add-sqr-sqrt
62×cbrt-prod
60×*-un-lft-identity
54×add-cube-cbrt
50×associate-/r/
40×flip3-+ flip-+
24×frac-times
12×associate-*l/ associate-*r/ difference-of-squares
7×div-inv
5×pow1 rem-sqrt-square
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 166
Calls
4 calls:
39.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
4.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
4.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
4.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series782.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
208.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
202.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
201.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify3.8s

Counts
178 → 178
Iterations
IterNodes
36259
21989
1833
0443

prune3.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.4b

localize49.0ms

Local error

Found 4 expressions with local error:

10.7b
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
17.1b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
17.1b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
17.1b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
45×times-frac
40×add-sqr-sqrt *-un-lft-identity
31×add-cube-cbrt
18×difference-of-squares
12×pow1
9×sqrt-pow1 pow1/3
7×cbrt-div
6×associate-/r/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ sqrt-div flip-+ div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 116
Calls
4 calls:
22.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
9.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
8.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
8.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
324.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
290.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
338.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
287.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify1.0s

Counts
128 → 128
Iterations
IterNodes
32374
2756
1346
0180

prune2.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 11.4b

regimes470.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
220
120
017

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.0s8006×body80nan
1.6s3730×body160valid
1.4s4270×body80valid