Details

sample58.0ms

Algorithm

intervals

Results

16.0ms	214×	body	80	nan
15.0ms	126×	body	160	valid
7.0ms	130×	body	80	valid

simplify130.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

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 (/ t l) 2.0)
0.3b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite86.0ms

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:

46.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(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))))))
31.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(pow (/ t l) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
327.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	664	1948
1	2106	1846
2	5001	1828

prune607.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
9.2b	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
8×	`add-sqr-sqrt` `sqrt-pow1`
7×	`sqrt-div` `sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `pow1/2`
2×	`flip3-+` `flip-+`
1×	`pow2` `frac-times` `asin-acos` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`

Counts

4 → 65

Calls

4 calls:

0.0ms	(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
41.0ms	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (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))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series852.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
321.0ms	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
328.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify106.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	274	996
1	796	916
2	3430	914
3	5001	914

prune353.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.1b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
91×	`cbrt-prod`
76×	`times-frac`
72×	`sqrt-prod`
53×	`*-un-lft-identity`
41×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
6×	`cbrt-div` `distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 129

Calls

4 calls:

0.0ms	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
36.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (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))))

series879.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
348.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
247.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
250.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	597	2787
1	1525	2682
2	5001	2672

prune872.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.8b

localize22.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

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

series743.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
187.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	148	636
1	467	616
2	1887	616
3	5001	612

prune498.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.8b

regimes485.0ms

Accuracy

0% (0.0b remaining)

Error of 10.9b against oracle of 10.9b and baseline of 10.9b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

470.0ms	7961×	body	80	nan
445.0ms	3790×	body	160	valid
252.0ms	4210×	body	80	valid