Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	277×	body	80	nan
15.0ms	123×	body	160	valid
9.0ms	133×	body	80	valid

simplify127.0ms

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: 8.5b

localize15.0ms

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)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite79.0ms

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:

37.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(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)))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
63.0ms	(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)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (46.0ms)

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

prune551.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.8b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
22×	`sqrt-prod`
9×	`pow1` `sqrt-div`
7×	`distribute-lft-out`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`sqrt-pow1` `flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `div-inv`

Counts

4 → 94

Calls

4 calls:

49.0ms	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (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))))
39.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

314.0ms	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (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))))
407.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	323	1573
1	1199	1483
2	5001	1469

prune453.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.5b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b	(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)))))))
27.3b	(cbrt (pow (/ t l) 2.0))
27.3b	(cbrt (pow (/ t l) 2.0))
27.3b	(cbrt (pow (/ t l) 2.0))

rewrite46.0ms

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))
4.0ms	(cbrt (pow (/ t l) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

323.0ms	(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)))))))
270.0ms	(cbrt (pow (/ t l) 2.0))
268.0ms	(cbrt (pow (/ t l) 2.0))
270.0ms	(cbrt (pow (/ t l) 2.0))

simplify126.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (104.0ms)

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

prune640.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.5b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
126×	`sqrt-prod`
117×	`add-sqr-sqrt`
80×	`cbrt-div`
72×	`*-un-lft-identity`
71×	`cbrt-prod`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-r/` `associate-l/`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 180

Calls

4 calls:

52.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 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))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

330.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
246.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
253.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
249.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify99.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	946	6225
1	2907	6123
2	5001	6115

prune982.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 8.5b

regimes530.0ms

Accuracy

0% (0.1b remaining)

Error of 9.9b against oracle of 9.9b and baseline of 9.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

480.0ms	7831×	body	80	nan
478.0ms	3810×	body	160	valid
260.0ms	4190×	body	80	valid