Details

sample66.0ms

Algorithm

intervals

Results

19.0ms	116×	body	160	valid
17.0ms	252×	body	80	nan
10.0ms	140×	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: 12.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite26.0ms

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 (/ t l) 2.0)
4.0ms	(pow (/ Om Omc) 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)))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ t l) 2.0)
65.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
324.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	695	1236
1	2041	1164
2	5001	1152

prune466.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.3b	(pow (/ Om Omc) 2.0)
0.5b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
12.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

15.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (fabs (/ (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))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
61.0ms	(pow (/ Om Omc) 2.0)
21.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	609	2507
1	1958	2333
2	5001	2323

prune758.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.6b

localize19.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (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))))

series868.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
253.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify91.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	201	720
1	658	700
2	2858	696
3	5002	688

prune436.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.6b

localize20.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (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))))

series863.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
250.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
179.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	201	720
1	658	700
2	2858	696
3	5002	688

prune414.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.6b

regimes641.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

534.0ms	7672×	body	80	nan
515.0ms	3751×	body	160	valid
289.0ms	4249×	body	80	valid