Details

sample58.0ms

Algorithm

intervals

Results

14.0ms	239×	body	80	nan
13.0ms	110×	body	160	valid
9.0ms	146×	body	80	valid

simplify124.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite46.0ms

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

series462.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ t l) 2.0)
66.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
316.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

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

prune448.0ms

Filtered

118 candidates to 92 candidates (78.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0b	(log (exp (pow (/ Om Omc) 2.0)))
10.6b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 101

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms	(log (exp (pow (/ Om Omc) 2.0)))
74.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
64.0ms	(log (exp (pow (/ Om Omc) 2.0)))
321.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	519	1161
1	1515	1073
2	5001	1055

prune458.0ms

Filtered

113 candidates to 87 candidates (77.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.2b	(pow (/ t l) 2.0)
0.9b	(asin (* (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) 1)) (sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.6b	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
96×	`times-frac`
70×	`sqrt-prod`
59×	`*-un-lft-identity`
56×	`difference-of-squares`
45×	`add-cube-cbrt`
41×	`unpow-prod-down`
15×	`sqr-pow`
12×	`associate-/l*`
9×	`add-exp-log`
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 → 158

Calls

4 calls:

52.0ms	(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (* (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) 1)) (sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
37.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
64.0ms	(pow (/ t l) 2.0)
35.0ms	(asin (* (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) 1)) (sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
272.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	685	3000
1	2244	2871
2	5003	2856

prune722.0ms

Filtered

170 candidates to 114 candidates (67.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize25.0ms

Local error

Found 4 expressions with local error:

10.6b	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 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))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
70×	`times-frac`
54×	`sqrt-prod`
51×	`cbrt-prod` `unpow-prod-down`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
24×	`difference-of-squares`
9×	`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 → 129

Calls

4 calls:

39.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
4.0ms	(cbrt (pow (/ t l) 2.0))
4.0ms	(cbrt (pow (/ t l) 2.0))
3.0ms	(cbrt (pow (/ t l) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

284.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
263.0ms	(cbrt (pow (/ t l) 2.0))
265.0ms	(cbrt (pow (/ t l) 2.0))
271.0ms	(cbrt (pow (/ t l) 2.0))

simplify112.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	550	2890
1	1276	2815
2	4408	2775
3	5001	2766

prune751.0ms

Filtered

141 candidates to 103 candidates (73.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.4b

regimes673.0ms

Accuracy

0% (0.2b remaining)

Error of 10.3b against oracle of 10.1b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

472.0ms	7979×	body	80	nan
443.0ms	3765×	body	160	valid
246.0ms	4235×	body	80	valid