Details

sample170.0ms

Algorithm

intervals

Results

58.0ms	129×	body	160	valid
39.0ms	286×	body	80	nan
17.0ms	127×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	265	19
5	798	19
6	3016	19
done	5001	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.3b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite227.0ms

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:

13.0ms	(pow (/ Om Omc) 2.0)
105.0ms	(/ (- 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))))))
96.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

105.0ms	(pow (/ Om Omc) 2.0)
338.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
33.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
931.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.0s

Counts

142 → 142

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	308	3657
1	633	3542
2	1483	3367
3	4467	3355
done	5001	3352

prune880.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`sqrt-prod`
18×	`times-frac`
11×	`pow1`
9×	`sqrt-div`
8×	`add-exp-log`
6×	`associate-/r*` `add-cbrt-cube`
5×	`sqrt-pow1`
4×	`pow1/2` `add-log-exp`
3×	`pow-flip` `flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `div-inv` `inv-pow`

Counts

4 → 91

Calls

4 calls:

25.0ms	(/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
74.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

300.0ms	(/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
243.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
221.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
556.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify1.8s

Counts

103 → 103

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	146	2105
1	290	1821
2	686	1634
3	2397	1634
done	5001	1634

prune549.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))))
0.3b	(asin (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))))))
9.4b	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))))))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

726×	`times-frac`
680×	`add-sqr-sqrt`
466×	`*-un-lft-identity`
281×	`sqrt-prod`
242×	`add-cube-cbrt`
216×	`difference-of-squares`
121×	`unpow-prod-down`
85×	`distribute-lft-out`
55×	`sqr-pow`
42×	`associate-/r*`
27×	`distribute-lft-out--`
20×	`associate-/r/`
12×	`add-exp-log` `div-inv`
9×	`flip3--` `add-cbrt-cube` `flip--`
6×	`pow1`
4×	`div-exp` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `pow-unpow`
2×	`pow-exp` `associate-/l/`
1×	`pow-to-exp` `asin-acos` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `clear-num` `flip-+`

Counts

4 → 453

Calls

4 calls:

9.0ms	(pow (/ t l) 2.0)
228.0ms	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))))
1.0ms	(asin (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))))))
179.0ms	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

92.0ms	(pow (/ t l) 2.0)
449.0ms	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))))
58.0ms	(asin (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2)))))))
584.0ms	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))))))

simplify2.1s

Counts

465 → 465

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	622	26423
1	1155	25316
2	3760	24143
done	5000	23986

prune2.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.1b

localize27.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (* (* (sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

21×	`sqrt-div`
13×	`pow1`
10×	`add-sqr-sqrt` `sqrt-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1`
5×	`frac-times` `associate-*l/`
4×	`add-exp-log` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `associate-*r/` `pow-prod-down` `flip-+`

Counts

4 → 64

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
190.0ms	(sqrt (* (* (sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

270.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
249.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
259.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
525.0ms	(sqrt (* (* (sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify1.6s

Counts

76 → 76

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	112	1842
1	243	1470
2	644	1371
3	2516	1257
done	5000	1239

prune587.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.1b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	33
1	25	33
done	25	33

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3861×	body	160	valid
1.1s	8023×	body	80	nan
672.0ms	4139×	body	80	valid