Details

sample67.0ms

Algorithm

intervals

Results

15.0ms	133×	body	160	valid
15.0ms	268×	body	80	nan
7.0ms	123×	body	80	valid

simplify125.0ms

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: 9.3b

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))))
0.2b	(pow (/ Om Omc) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite123.0ms

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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `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 → 138

Calls

4 calls:

68.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(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))))))
43.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(pow (/ Om Omc) 2.0)
19.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
349.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	650	1948
1	2076	1846
2	5001	1827

prune605.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.2b	(pow (/ Om Omc) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.5b	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
40×	`times-frac`
31×	`add-cube-cbrt`
21×	`sqrt-prod`
13×	`unpow-prod-down`
9×	`add-exp-log`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-cbrt-cube`
5×	`associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `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--` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

23.0ms	(/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
364.0ms	(sqrt (/ (- 1.0 (log1p (expm1 (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	569	1761
1	1895	1621
2	5001	1592

prune707.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.5b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

658×	`times-frac`
647×	`sqrt-prod`
560×	`add-sqr-sqrt`
325×	`*-un-lft-identity`
253×	`add-cube-cbrt`
144×	`difference-of-squares`
72×	`unpow-prod-down`
36×	`distribute-lft-out--` `sqr-pow`
19×	`sqrt-div`
14×	`associate-/r/`
9×	`rem-sqrt-square` `flip3-+` `flip-+`
7×	`pow1` `div-inv`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`asin-acos`

Counts

4 → 393

Calls

4 calls:

1.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
86.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
179.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
340.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify166.0ms

Algorithm

egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	1554	13323
1	4700	12868
2	5001	12737

prune922.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize21.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.4b	(sqrt (/ (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

678×	`times-frac` `sqrt-prod`
578×	`add-sqr-sqrt`
338×	`*-un-lft-identity`
330×	`cbrt-prod`
266×	`add-cube-cbrt`
144×	`difference-of-squares`
72×	`unpow-prod-down`
36×	`distribute-lft-out--` `sqr-pow`
21×	`sqrt-div`
14×	`associate-/r/`
12×	`rem-sqrt-square`
10×	`flip3-+` `flip-+`
8×	`pow1`
7×	`div-inv`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 420

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
94.0ms	(sqrt (/ (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

184.0ms	(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))))
454.0ms	(sqrt (/ (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify156.0ms

Algorithm

egg-herbie

Counts

432 → 432

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	1287	14592
1	2572	14529
2	5002	14392

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

regimes688.0ms

Accuracy

0% (0.1b remaining)

Error of 9.9b against oracle of 9.8b and baseline of 9.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.7s

Algorithm

intervals

Results

450.0ms	7944×	body	80	nan
439.0ms	3882×	body	160	valid
243.0ms	4118×	body	80	valid