Details

sample79.0ms

Algorithm

intervals

Results

25.0ms	223×	body	80	nan
20.0ms	125×	body	160	valid
13.0ms	131×	body	80	valid

simplify124.0ms

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: 8.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.3b	(pow (/ Om Omc) 2.0)
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite75.0ms

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:

39.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
27.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
59.0ms	(pow (/ Om Omc) 2.0)
23.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
309.0ms	(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 (43.0ms)

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

prune549.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.3b	(pow (/ Om Omc) 2.0)
0.8b	(asin (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.0b	(sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`times-frac`
28×	`*-un-lft-identity`
27×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`unpow-prod-down`
11×	`add-exp-log`
8×	`pow1`
6×	`add-cbrt-cube`
4×	`associate-/r/` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `sqrt-pow1` `div-exp` `associate-/r` `div-inv` `associate-/l`
2×	`pow-flip` `flip3-+` `pow-exp` `flip-+` `inv-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `asin-acos` `pow-pow` `frac-2neg` `pow1/2` `sqrt-div` `1-exp` `clear-num` `sqr-pow`

Counts

4 → 99

Calls

4 calls:

4.0ms	(/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
60.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
337.0ms	(sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	503	972
1	1862	881
2	5002	845

prune381.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

localize18.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
126×	`sqrt-prod`
117×	`add-sqr-sqrt`
80×	`cbrt-div`
72×	`*-un-lft-identity`
71×	`cbrt-prod`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-r/` `associate-l/`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 180

Calls

4 calls:

48.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
1.0ms	(cbrt (+ 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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

308.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
237.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
230.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
235.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify102.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	946	6224
1	2907	6123
2	5001	6115

prune961.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.0b

localize21.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
14.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.5b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

20×	`sqrt-prod`
19×	`add-sqr-sqrt`
18×	`cbrt-div`
11×	`*-un-lft-identity`
10×	`times-frac`
9×	`cbrt-prod` `add-cube-cbrt` `flip3-+` `flip-+`
8×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`pow1/3`
2×	`unpow-prod-down` `rem-sqrt-square` `associate-r/` `associate-l/`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(cbrt (+ 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:

342.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
241.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
236.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
240.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	339	1227
1	799	1176
2	2819	1164
3	5002	1163

prune441.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 8.0b

regimes451.0ms

Accuracy

0% (0.1b remaining)

Error of 9.7b against oracle of 9.7b and baseline of 9.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

765.0ms	7817×	body	80	nan
603.0ms	3810×	body	160	valid
407.0ms	4190×	body	80	valid