Details

sample98.0ms

Algorithm

intervals

Results

30.0ms	128×	body	160	valid
23.0ms	215×	body	80	nan
17.0ms	128×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	265	19
5	798	19
6	3016	19
done	5001	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 106

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
13.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
68.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(pow (/ Om Omc) 2.0)
107.0ms	(pow (/ t l) 2.0)
38.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
504.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.6s

Counts

118 → 118

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	352	2388
1	693	2272
2	1438	2160
3	3929	2150
done	5001	2144

prune796.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ -1 (* l (/ -1 t)))
0.3b	(pow (/ -1 (* l (/ -1 t))) 2.0)
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0))))))
8.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0)))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
34×	`times-frac`
30×	`sqrt-prod`
27×	`*-un-lft-identity`
23×	`add-exp-log`
21×	`add-cube-cbrt`
14×	`unpow-prod-down`
13×	`add-cbrt-cube`
12×	`difference-of-squares`
8×	`div-exp`
6×	`pow1`
4×	`cbrt-undiv` `pow-exp` `prod-exp` `associate-/r/` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `div-inv` `associate-/l*` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-*r/` `cbrt-unprod`
1×	`pow-to-exp` `asin-acos` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `clear-num` `associate-/r*` `flip-+`

Counts

4 → 99

Calls

4 calls:

23.0ms	(/ -1 (* l (/ -1 t)))
29.0ms	(pow (/ -1 (* l (/ -1 t))) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0))))))
63.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0)))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ -1 (* l (/ -1 t)))
77.0ms	(pow (/ -1 (* l (/ -1 t))) 2.0)
25.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0))))))
498.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ -1 (* l (/ -1 t))) 2.0)))))

simplify1.5s

Counts

111 → 111

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	300	2717
1	624	2575
2	1510	1934
done	5000	1926

prune700.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.5b

localize22.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
55×	`times-frac`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 117

Calls

4 calls:

56.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
5.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))
12.0ms	(cbrt (pow (/ t l) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

499.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
386.0ms	(cbrt (pow (/ t l) 2.0))
312.0ms	(cbrt (pow (/ t l) 2.0))
430.0ms	(cbrt (pow (/ t l) 2.0))

simplify1.7s

Counts

129 → 129

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	269	4003
1	516	3851
2	1028	2921
3	2608	2705
done	5001	2704

prune778.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.5b

localize26.0ms

Local error

Found 4 expressions with local error:

26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

68×	`cbrt-prod`
52×	`unpow-prod-down`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `div-inv` `add-log-exp` `sqr-pow`

Counts

4 → 100

Calls

4 calls:

10.0ms	(cbrt (pow (/ t l) 2.0))
9.0ms	(cbrt (pow (/ t l) 2.0))
9.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

377.0ms	(cbrt (pow (/ t l) 2.0))
425.0ms	(cbrt (pow (/ t l) 2.0))
387.0ms	(cbrt (pow (/ t l) 2.0))
316.0ms	(cbrt (pow (/ t l) 2.0))

simplify1.4s

Counts

112 → 112

Iterations

Useful iterations: 3 (201.0ms)

Iter	Nodes	Cost
0	121	1964
1	235	1912
2	432	1864
3	960	1852
4	2397	1852
done	5000	1852

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.5b

regimes810.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	18	19
done	18	19

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	7919×	body	80	nan
937.0ms	3788×	body	160	valid
504.0ms	4212×	body	80	valid