Details

sample60.0ms

Algorithm

intervals

Results

15.0ms	263×	body	80	nan
15.0ms	124×	body	160	valid
8.0ms	132×	body	80	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	49	10
2	101	10
3	279	10
4	1029	10
5	4384	10
6	5002	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite80.0ms

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×	`cbrt-undiv` `pow-to-exp` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `clear-num` `flip--`

Counts

4 → 130

Calls

4 calls:

3.0ms	(pow (/ Om Omc) 2.0)
37.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
33.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series630.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ Om Omc) 2.0)
214.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
331.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	634	1882
1	2017	1787
2	5001	1774

prune721.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(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)))))))
8.7b	(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))))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite121.0ms

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-exp-log` `add-cbrt-cube` `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)))))))
73.0ms	(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))))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(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)))))))
326.0ms	(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))))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
178.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify178.0ms

Algorithm

egg-herbie

Counts

397 → 397

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	1539	13235
1	4654	12782
2	5002	12550

prune920.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize20.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.1b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

95×	`sqrt-prod`
88×	`add-sqr-sqrt`
56×	`times-frac`
43×	`*-un-lft-identity`
31×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
11×	`sqrt-div`
9×	`pow1`
7×	`rem-sqrt-square` `sqrt-pow1`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`associate-/r/`
1×	`div-inv`

Counts

4 → 118

Calls

4 calls:

31.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series978.0ms

Counts

4 → 12

Calls

4 calls:

347.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
188.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
187.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
255.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify139.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	480	1931
1	1265	1885
2	4838	1857
3	5001	1843

prune584.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

localize22.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
136×	`sqrt-prod`
102×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
24×	`difference-of-squares`
17×	`sqrt-div`
16×	`cbrt-div`
14×	`associate-/r/`
12×	`unpow-prod-down` `associate-*r/`
10×	`flip3-+` `flip-+`
7×	`div-inv`
6×	`pow1` `cbrt-prod` `distribute-lft-out--` `sqr-pow`
4×	`add-exp-log` `rem-sqrt-square` `add-cbrt-cube` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 144

Calls

4 calls:

44.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

449.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
188.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
254.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
254.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify90.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	773	4547
1	2492	4450
2	5001	4388

prune779.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.7b

regimes729.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	19
1	22	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

480.0ms	8082×	body	80	nan
456.0ms	3856×	body	160	valid
255.0ms	4144×	body	80	valid