Details

sample146.0ms

Algorithm

intervals

Results

54.0ms	221×	body	80	nan
31.0ms	125×	body	160	valid
17.0ms	131×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	108	18
4	292	18
5	1585	18
done	5000	18

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ t l) 2.0)
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
28×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 112

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
6.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
57.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(pow (/ Om Omc) 2.0)
97.0ms	(pow (/ t l) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
423.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.1s

Counts

124 → 124

Iterations

Useful iterations: 2 (396.0ms)

Iter	Nodes	Cost
0	319	2298
1	740	2196
2	1840	2088
done	5000	2088

prune788.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt Om)
0.7b	(cbrt Om)
0.7b	(cbrt Om)
9.7b	(sqrt (/ (- 1.0 (* (pow (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) 2.0) (pow (/ (cbrt Om) (cbrt Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
10×	`times-frac`
9×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 66

Calls

4 calls:

2.0ms	(cbrt Om)
2.0ms	(cbrt Om)
2.0ms	(cbrt Om)
18.0ms	(sqrt (/ (- 1.0 (* (pow (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) 2.0) (pow (/ (cbrt Om) (cbrt Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt Om)
249.0ms	(cbrt Om)
268.0ms	(cbrt Om)
493.0ms	(sqrt (/ (- 1.0 (* (pow (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) 2.0) (pow (/ (cbrt Om) (cbrt Omc)) 2.0))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.2s

Counts

78 → 78

Iterations

Useful iterations: 3 (470.0ms)

Iter	Nodes	Cost
0	117	1573
1	213	1481
2	575	1297
3	2151	1288
done	5000	1288

prune702.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.8b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
15.0b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
15.0b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
183×	`cbrt-prod`
149×	`times-frac`
105×	`*-un-lft-identity`
79×	`add-cube-cbrt`
70×	`sqrt-prod`
52×	`difference-of-squares`
26×	`unpow-prod-down`
13×	`distribute-lft-out--` `sqr-pow`
11×	`associate-/l*`
6×	`add-exp-log` `associate-/r*`
5×	`pow1` `rem-sqrt-square`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `pow1/3` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `flip--`

Counts

4 → 212

Calls

4 calls:

69.0ms	(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
72.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

571.0ms	(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
586.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
240.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
202.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.6s

Counts

224 → 224

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	347	7170
1	521	6950
2	1207	6808
3	3577	6793
done	5000	6766

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
1.8b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
15.4b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
15.4b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
86×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
31×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `pow1/3` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 135

Calls

4 calls:

2.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
56.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
28.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
19.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

35.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
420.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
420.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
483.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.1s

Counts

147 → 147

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	251	4840
1	403	4725
2	807	4553
3	2136	4489
done	5002	4480

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.1b

regimes697.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	34
1	23	34
done	23	34

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	7869×	body	80	nan
931.0ms	3713×	body	160	valid
503.0ms	4287×	body	80	valid