Details

sample62.0ms

Algorithm

intervals

Results

15.0ms	232×	body	80	nan
15.0ms	116×	body	160	valid
12.0ms	140×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	242	19
5	729	19
6	2670	19
done	5000	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize15.0ms

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))))
1.0b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite78.0ms

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:

3.0ms	(pow (/ Om Omc) 2.0)
40.0ms	(/ (- 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))))))
28.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ Om Omc) 2.0)
209.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
319.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.6s

Counts

142 → 142

Iterations

Useful iterations: 3 (740.0ms)

Iter	Nodes	Cost
0	308	3657
1	636	3542
2	1499	3367
3	4827	3355
done	5000	3355

prune545.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(asin (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))))))))
10.7b	(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)))))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

0.0ms	(asin (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))))))))
40.0ms	(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)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(asin (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))))))))
405.0ms	(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)))))))
173.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
173.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.0s

Counts

64 → 64

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	124	1871
1	252	1741
2	706	1378
3	2853	1378
done	5000	1378

prune325.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.0b

localize25.0ms

Local error

Found 4 expressions with local error:

10.7b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (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)))))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

74.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (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)))))))
3.0ms	(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))))

series936.0ms

Counts

4 → 12

Calls

4 calls:

407.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (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)))))))
178.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
178.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
173.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.0s

Counts

71 → 71

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	95	1763
1	206	1429
2	600	1240
3	2373	1240
done	5000	1240

prune384.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.0b

localize28.0ms

Local error

Found 4 expressions with local error:

10.7b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 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)))))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

51.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 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)))))))
3.0ms	(sqrt (+ 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))))

series1.2s

Counts

4 → 12

Calls

4 calls:

535.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (cbrt (+ 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)))))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
238.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.3s

Counts

67 → 67

Iterations

Useful iterations: 3 (407.0ms)

Iter	Nodes	Cost
0	144	1839
1	312	1706
2	951	1589
3	4411	1579
done	5000	1579

prune407.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 12.0b

regimes667.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 10.0b and baseline of 10.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	18	19
done	18	19

end0.0ms

sample1.7s

Algorithm

intervals

Results

504.0ms	8094×	body	80	nan
479.0ms	3849×	body	160	valid
262.0ms	4151×	body	80	valid