Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	263×	body	80	nan
17.0ms	124×	body	160	valid
9.0ms	132×	body	80	valid

simplify134.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 9.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite48.0ms

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:

5.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
19.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series613.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ Om Omc) 2.0)
216.0ms	(/ (- 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))))))
322.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (45.0ms)

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

prune754.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.6b	(asin (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
8.7b	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
46×	`times-frac`
40×	`*-un-lft-identity`
33×	`sqrt-prod`
32×	`add-cube-cbrt`
21×	`unpow-prod-down`
16×	`difference-of-squares`
11×	`sqrt-div` `associate-/l*`
9×	`add-exp-log`
8×	`pow1`
6×	`add-cbrt-cube`
5×	`sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `flip3--` `associate-/r*` `flip--`
2×	`frac-times` `sqrt-pow1` `div-exp` `associate-*l/` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `asin-acos` `pow-pow` `frac-2neg` `pow1/2` `associate-*r/` `pow-prod-down` `clear-num`

Counts

4 → 121

Calls

4 calls:

7.0ms	(pow (/ Om Omc) 2.0)
12.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(asin (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
22.0ms	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ Om Omc) 2.0)
210.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))
12.0ms	(asin (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
259.0ms	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	494	1673
1	1371	1582
2	5001	1582

prune606.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.5b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.6b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite34.0ms

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×	`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--`

Counts

4 → 159

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (/ (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))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ Om Omc) 2.0)
318.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms	(asin (/ (sqrt (- 1.0 (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))))

simplify66.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	624	2554
1	2015	2381
2	5002	2370

prune626.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize23.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
8.5b	(sqrt (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
8.7b	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))
8.7b	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-div`
18×	`pow1`
16×	`sqrt-pow1`
12×	`sqrt-prod`
8×	`add-sqr-sqrt` `frac-times` `flip3--` `associate-*l/` `flip--`
6×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
4×	`add-exp-log` `expm1-log1p-u` `associate-*r/` `pow-prod-down` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`

Counts

4 → 84

Calls

4 calls:

25.0ms	(sqrt (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
23.0ms	(sqrt (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
22.0ms	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))
22.0ms	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

310.0ms	(sqrt (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
313.0ms	(sqrt (sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))
256.0ms	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))
267.0ms	(sqrt (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	211	1428
1	499	1370
2	1814	1370
3	5001	1358

prune517.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

regimes700.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	32
1	20	32

end0.0ms

sample1.9s

Algorithm

intervals

Results

568.0ms	8082×	body	80	nan
541.0ms	3856×	body	160	valid
293.0ms	4144×	body	80	valid