Details

sample59.0ms

Algorithm

intervals

Results

17.0ms	118×	body	160	valid
13.0ms	191×	body	80	nan
10.0ms	138×	body	80	valid

simplify127.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(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))))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite27.0ms

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:

4.0ms	(pow (/ Om Omc) 2.0)
5.0ms	(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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ Om Omc) 2.0)
64.0ms	(pow (/ t l) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
323.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	695	1235
1	2043	1164
2	5002	1152

prune612.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.7b	(log (exp (pow (/ Om Omc) 2.0)))
8.9b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 101

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0ms	(log (exp (pow (/ Om Omc) 2.0)))
14.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
63.0ms	(log (exp (pow (/ Om Omc) 2.0)))
315.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	624	1169
1	1863	1079
2	5002	1061

prune487.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ t l) 2.0)
0.7b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`unpow-prod-down`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `div-exp` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 79

Calls

4 calls:

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

series333.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ Om Omc) 2.0)
67.0ms	(pow (/ t l) 2.0)
17.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	543	644
1	1769	596
2	5001	596

prune374.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.6b

localize26.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.3b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
64×	`add-sqr-sqrt`
60×	`times-frac`
58×	`*-un-lft-identity`
38×	`add-cube-cbrt`
16×	`pow1`
12×	`distribute-lft-out--`
10×	`rem-sqrt-square` `sqrt-div`
9×	`sqrt-pow1`
6×	`log-pow` `difference-of-squares`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow-flip`
2×	`div-inv`
1×	`inv-pow`

Counts

4 → 128

Calls

4 calls:

6.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
17.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series981.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
348.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	434	2027
1	1224	1968
2	5002	1917

prune598.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.6b

regimes564.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

564.0ms	7952×	body	80	nan
545.0ms	3864×	body	160	valid
296.0ms	4136×	body	80	valid