Details

sample70.0ms

Algorithm

intervals

Results

20.0ms	111×	body	160	valid
18.0ms	251×	body	80	nan
10.0ms	145×	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: 9.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(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))))))
8.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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:

3.0ms	(pow (/ Om Omc) 2.0)
4.0ms	(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))))))
28.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ Om Omc) 2.0)
65.0ms	(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))))))
323.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	709	1290
1	2085	1218
2	5002	1206

prune502.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.4b	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`times-frac`
29×	`add-cube-cbrt`
26×	`unpow-prod-down`
21×	`sqrt-prod`
10×	`add-exp-log`
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--` `difference-of-squares`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/` `sqr-pow`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 105

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
3.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0ms	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series483.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
60.0ms	(pow (/ t l) 2.0)
20.0ms	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
338.0ms	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	631	1213
1	1903	1132
2	5002	1120

prune522.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

65×	`sqrt-prod`
60×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`times-frac`
45×	`add-cube-cbrt`
13×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
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--` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
15.0ms	(/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms	(asin (/ (sqrt (- 1.0 (log1p (expm1 (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))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
341.0ms	(/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.0ms	(asin (/ (sqrt (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify65.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	601	2344
1	1992	2174
2	5002	2166

prune612.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (/ (/ (sqrt (- 1.0 (log1p (expm1 (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)))))))
1.7b	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`asin-acos` `pow1/2`

Counts

4 → 62

Calls

4 calls:

0.0ms	(asin (/ (/ (sqrt (- 1.0 (log1p (expm1 (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)))))))
3.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series887.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(asin (/ (/ (sqrt (- 1.0 (log1p (expm1 (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)))))))
369.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
241.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
248.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify129.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	322	941
1	1002	865
2	4550	856
3	5001	856

prune471.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.3b

regimes726.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

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

583.0ms	8170×	body	80	nan
565.0ms	3852×	body	160	valid
307.0ms	4148×	body	80	valid