Details

sample63.0ms

Algorithm

intervals

Results

15.0ms	263×	body	80	nan
15.0ms	124×	body	160	valid
11.0ms	132×	body	80	valid

simplify129.0ms

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: 9.7b

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)))))

rewrite94.0ms

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:

4.0ms	(pow (/ Om Omc) 2.0)
54.0ms	(/ (- 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))))))
30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ Om Omc) 2.0)
210.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
21.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
321.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	650	1949
1	2075	1846
2	5001	1827

prune621.0ms

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	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.7b	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
53.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms	(asin (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
17.0ms	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series629.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ Om Omc) 2.0)
220.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms	(asin (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
327.0ms	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	593	1335
1	2127	1249
2	5001	1244

prune492.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(asin (sqrt (* 1 (* (/ (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)))))))))
8.7b	(sqrt (* 1 (* (/ (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))))))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

0.0ms	(asin (sqrt (* 1 (* (/ (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)))))))))
128.0ms	(sqrt (* 1 (* (/ (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))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(asin (sqrt (* 1 (* (/ (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)))))))))
317.0ms	(sqrt (* 1 (* (/ (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))))))))
324.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	278	1022
1	861	928
2	3755	925
3	5001	901

prune369.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.7b

localize19.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.5b	(sqrt (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.7b	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`sqrt-pow1`
12×	`sqrt-prod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2` `sqrt-div`
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 → 68

Calls

4 calls:

18.0ms	(sqrt (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
17.0ms	(sqrt (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
17.0ms	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
20.0ms	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

340.0ms	(sqrt (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
334.0ms	(sqrt (sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
313.0ms	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
316.0ms	(sqrt (* 1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	142	772
1	375	716
2	1592	708
3	5001	696

prune349.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

regimes574.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	25	11
2	25	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

474.0ms	8082×	body	80	nan
442.0ms	3856×	body	160	valid
239.0ms	4144×	body	80	valid