Details

sample61.0ms

Algorithm

intervals

Results

14.0ms	122×	body	160	valid
14.0ms	249×	body	80	nan
11.0ms	134×	body	80	valid

simplify145.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite41.0ms

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×	`pow-exp` `add-cbrt-cube` `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 → 106

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
4.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
30.0ms	(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:

63.0ms	(pow (/ t l) 2.0)
63.0ms	(pow (/ Om Omc) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
313.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	695	1235
1	2043	1164
2	5002	1152

prune454.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
0.7b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`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 → 151

Calls

4 calls:

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

series578.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ Om Omc) 2.0)
20.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
314.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify73.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	609	2508
1	1957	2333
2	5001	2323

prune590.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.8b

localize22.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.6b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

320×	`sqrt-prod`
192×	`add-sqr-sqrt`
152×	`times-frac`
100×	`*-un-lft-identity`
76×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`unpow-prod-down`
12×	`rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
10×	`sqrt-div`
8×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`div-inv`

Counts

4 → 204

Calls

4 calls:

36.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
34.0ms	(sqrt (/ (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))))

series1.1s

Counts

4 → 12

Calls

4 calls:

343.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
345.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify152.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	457	4306
1	1108	4238
2	4822	4160
3	5001	4160

prune905.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.8b

localize19.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
30.3b	(cbrt (pow (/ t l) 2.0))
30.3b	(cbrt (pow (/ t l) 2.0))
30.3b	(cbrt (pow (/ t l) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
55×	`times-frac`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 117

Calls

4 calls:

30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
3.0ms	(cbrt (pow (/ t l) 2.0))
3.0ms	(cbrt (pow (/ t l) 2.0))
3.0ms	(cbrt (pow (/ t l) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

319.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
273.0ms	(cbrt (pow (/ t l) 2.0))
273.0ms	(cbrt (pow (/ t l) 2.0))
270.0ms	(cbrt (pow (/ t l) 2.0))

simplify134.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	516	2189
1	1205	2120
2	4830	2084
3	5001	2075

prune626.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 10.8b

regimes835.0ms

Accuracy

0% (0.1b remaining)

Error of 10.9b against oracle of 10.8b and baseline of 10.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

459.0ms	7890×	body	80	nan
432.0ms	3714×	body	160	valid
260.0ms	4286×	body	80	valid