Details

sample161.0ms

Algorithm

intervals

Results

40.0ms	143×	body	80	valid
35.0ms	244×	body	80	nan
31.0ms	113×	body	160	valid

simplify2.1s

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite164.0ms

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:

6.0ms	(pow (/ Om Omc) 2.0)
83.0ms	(/ (- 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))))))
68.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series971.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(pow (/ Om Omc) 2.0)
329.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
43.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
490.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify905.0ms

Counts: 142 → 142

prune799.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
10.1b	(sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite250.0ms

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:

1.0ms	(asin (sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
238.0ms	(sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

29.0ms	(asin (sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
515.0ms	(sqrt (* (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
260.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
254.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.3s

Counts: 64 → 64

prune505.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.3b

localize38.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.3b	(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

129×	`sqrt-prod`
106×	`add-sqr-sqrt`
84×	`times-frac`
56×	`*-un-lft-identity`
50×	`cbrt-prod`
44×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
10×	`rem-sqrt-square` `sqrt-div`
8×	`pow1`
6×	`distribute-lft-out--` `sqr-pow`
4×	`add-exp-log` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`div-inv`

Counts

4 → 142

Calls

4 calls:

77.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
47.0ms	(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.9s

Counts

4 → 12

Calls

4 calls:

689.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
687.0ms	(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
199.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
286.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.5s

Counts: 154 → 154

prune1.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 11.3b

localize38.0ms

Local error

Found 4 expressions with local error:

10.1b	(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))))))
17.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite189.0ms

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:

152.0ms	(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))))))
6.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.6s

Counts

4 → 12

Calls

4 calls:

515.0ms	(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))))))
370.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
409.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
338.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.2s

Counts: 192 → 192

prune1.4s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 11.3b

regimes793.0ms

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.5b and baseline of 10.6b

bsearch0.0ms

simplify2.1s

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	7799×	body	80	nan
1.0s	3801×	body	160	valid
543.0ms	4199×	body	80	valid