Details

sample63.0ms

Algorithm

intervals

Results

18.0ms	309×	body	80	nan
15.0ms	130×	body	160	valid
7.0ms	126×	body	80	valid

simplify125.0ms

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: 9.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite80.0ms

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×	`associate-/r/` `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 → 130

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
42.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
29.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
213.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
317.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	648	1882
1	2047	1787
2	5001	1774

prune587.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
56×	`times-frac`
54×	`sqrt-prod`
41×	`*-un-lft-identity`
31×	`cbrt-prod`
29×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
6×	`cbrt-div` `distribute-lft-out--` `sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
2×	`pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 101

Calls

4 calls:

0.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
32.0ms	(sqrt (/ (- 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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

30.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
483.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
246.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
244.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	545	2043
1	1354	1953
2	5001	1942

prune621.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
7.9b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

0.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
2.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))))
241.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
178.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
233.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify126.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	349	865
1	1056	791
2	4552	783
3	5001	781

prune406.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 9.4b

localize29.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.8b	(sqrt (pow (/ Om Omc) 2.0))
16.8b	(sqrt (pow (/ Om Omc) 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`sqrt-prod`
31×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
9×	`rem-sqrt-square`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`cbrt-prod` `sqrt-pow1` `pow1/2`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `div-inv`
1×	`pow1/3`

Counts

4 → 88

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(sqrt (pow (/ Om Omc) 2.0))
9.0ms	(sqrt (pow (/ Om Omc) 2.0))

series941.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
237.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
261.0ms	(sqrt (pow (/ Om Omc) 2.0))
260.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify118.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	417	829
1	1156	802
2	4842	798
3	5001	797

prune720.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 9.4b

regimes593.0ms

Accuracy

0% (0.0b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

478.0ms	8008×	body	80	nan
444.0ms	3733×	body	160	valid
254.0ms	4267×	body	80	valid