Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	253×	body	80	nan
14.0ms	125×	body	160	valid
8.0ms	131×	body	80	valid

simplify129.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ t l) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite61.0ms

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×	`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` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 114

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
6.0ms	(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))))))
44.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ Om Omc) 2.0)
59.0ms	(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))))))
319.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	709	1289
1	2087	1218
2	5001	1206

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ t l) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (pow (/ Om Omc) 2.0) 1)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b	(sqrt (/ (- 1.0 (pow (pow (/ Om Omc) 2.0) 1)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
52×	`times-frac`
44×	`unpow-prod-down`
40×	`*-un-lft-identity`
36×	`sqrt-prod`
34×	`add-cube-cbrt`
18×	`difference-of-squares`
10×	`add-exp-log`
8×	`sqr-pow`
7×	`pow1`
6×	`pow-unpow`
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` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 120

Calls

4 calls:

7.0ms	(pow (/ Om Omc) 2.0)
6.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (pow (/ Om Omc) 2.0) 1)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
78.0ms	(sqrt (/ (- 1.0 (pow (pow (/ Om Omc) 2.0) 1)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow (/ Om Omc) 2.0)
61.0ms	(pow (/ t l) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (pow (/ Om Omc) 2.0) 1)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
321.0ms	(sqrt (/ (- 1.0 (pow (pow (/ Om Omc) 2.0) 1)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	778	1505
1	2304	1429
2	5002	1411

prune673.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(asin (fabs (/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
0.6b	(/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
115×	`sqrt-prod`
94×	`times-frac`
69×	`*-un-lft-identity`
55×	`add-cube-cbrt` `unpow-prod-down`
42×	`difference-of-squares`
15×	`sqr-pow`
13×	`associate-/l*`
9×	`add-exp-log`
7×	`distribute-lft-out--`
6×	`pow1` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 173

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
114.0ms	(/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ t l) 2.0)
19.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
316.0ms	(/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
172.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	700	3069
1	2255	2871
2	5001	2858

prune697.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(asin (fabs (/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1)))))))
0.6b	(/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1)))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
115×	`sqrt-prod`
94×	`times-frac`
69×	`*-un-lft-identity`
55×	`add-cube-cbrt` `unpow-prod-down`
42×	`difference-of-squares`
15×	`sqr-pow`
13×	`associate-/l*`
9×	`add-exp-log`
7×	`distribute-lft-out--`
6×	`pow1` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 173

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1)))))))
114.0ms	(/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1)))))
6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ t l) 2.0)
19.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1)))))))
313.0ms	(/ (sqrt (- 1.0 (pow (pow (/ Om Omc) 2.0) 1))) (sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1)))))
173.0ms	(sqrt (+ 1.0 (* 2.0 (pow (pow (/ t l) 2.0) 1))))

simplify79.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	704	3303
1	2302	3086
2	5002	3073

prune718.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.0b

regimes680.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

468.0ms	8091×	body	80	nan
440.0ms	3762×	body	160	valid
256.0ms	4238×	body	80	valid