Details

sample85.0ms

Algorithm

intervals

Results

24.0ms	291×	body	80	nan
19.0ms	109×	body	160	valid
12.0ms	147×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1551
4	277
3	101
2	49
1	29
0	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`difference-of-squares`
27×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*` `sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 130

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
78.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

78.0ms	(pow (/ t l) 2.0)
357.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
36.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
532.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	2435
1	755
0	317

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.3b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

658×	`times-frac`
647×	`sqrt-prod`
560×	`add-sqr-sqrt`
325×	`*-un-lft-identity`
253×	`add-cube-cbrt`
144×	`difference-of-squares`
72×	`unpow-prod-down`
36×	`distribute-lft-out--` `sqr-pow`
19×	`sqrt-div`
14×	`associate-/r/`
9×	`rem-sqrt-square` `flip3-+` `flip-+`
7×	`pow1` `div-inv`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`asin-acos`

Counts

4 → 385

Calls

4 calls:

0.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
4.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
119.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

23.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
278.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
253.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
484.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify2.3s

Counts

397 → 397

Iterations

Iter	Nodes
done	5001
1	1543
0	873

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.2b

localize81.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.3b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.3b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.5b	(sqrt (/ (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

405×	`times-frac`
395×	`sqrt-prod`
237×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
200×	`add-cube-cbrt`
172×	`cbrt-prod`
27×	`sqrt-div`
20×	`associate-/r/`
16×	`rem-sqrt-square`
13×	`flip3-+` `flip-+`
10×	`div-inv`
8×	`cbrt-div`
6×	`pow1`
5×	`pow1/3`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-pow1`
2×	`pow-div`
1×	`pow1/2` `pow-flip` `inv-pow`

Counts

4 → 298

Calls

4 calls:

6.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
86.0ms	(sqrt (/ (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

469.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
351.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
369.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
324.0ms	(sqrt (/ (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify2.1s

Counts

310 → 310

Iterations

Iter	Nodes
done	5000
2	2776
1	1121
0	610

prune3.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.2b

localize73.0ms

Local error

Found 4 expressions with local error:

9.3b	(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)))))))
29.3b	(cbrt (pow (/ t l) 2.0))
29.3b	(cbrt (pow (/ t l) 2.0))
29.3b	(cbrt (pow (/ t l) 2.0))

rewrite90.0ms

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-cbrt-cube` `add-exp-log` `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:

61.0ms	(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)))))))
7.0ms	(cbrt (pow (/ t l) 2.0))
7.0ms	(cbrt (pow (/ t l) 2.0))
7.0ms	(cbrt (pow (/ t l) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

510.0ms	(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)))))))
406.0ms	(cbrt (pow (/ t l) 2.0))
426.0ms	(cbrt (pow (/ t l) 2.0))
440.0ms	(cbrt (pow (/ t l) 2.0))

simplify7.0s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
3	4374
2	1314
1	522
0	269

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.2b

regimes1.8s

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	7925×	body	80	nan
1.1s	4225×	body	80	valid
992.0ms	3775×	body	160	valid