Details

sample96.0ms

Algorithm

intervals

Results

25.0ms	274×	body	80	nan
22.0ms	120×	body	160	valid
13.0ms	136×	body	80	valid

simplify117.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite120.0ms

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)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
62.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
45.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(pow (/ Om Omc) 2.0)
22.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
250.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
382.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Counts: 142 → 142

prune625.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize33.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
15.2b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.2b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.2b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
90×	`cbrt-prod`
81×	`times-frac`
58×	`*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`difference-of-squares`
24×	`pow1`
18×	`unpow-prod-down`
15×	`cbrt-div` `sqrt-pow1`
12×	`pow1/3`
9×	`pow-prod-up` `distribute-lft-out--` `sqr-pow`
7×	`sqrt-div`
6×	`pow-plus` `associate-/r/`
5×	`frac-times` `pow-prod-down` `associate-*l/`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-*r/` `pow-sqr` `flip-+` `div-inv`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 148

Calls

4 calls:

213.0ms	(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
21.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
25.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
23.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

374.0ms	(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
697.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
409.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
401.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Counts: 160 → 160

prune865.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.6b

localize35.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (* (* (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
15.2b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.2b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
63×	`cbrt-prod`
54×	`times-frac`
41×	`*-un-lft-identity`
29×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down` `cbrt-div`
10×	`pow1`
7×	`sqrt-div`
6×	`distribute-lft-out--` `sqr-pow`
5×	`frac-times` `associate-*l/`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `pow1/3` `associate-*r/` `pow-prod-down` `flip-+`
2×	`div-inv`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 110

Calls

4 calls:

227.0ms	(sqrt (* (* (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
21.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
26.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

382.0ms	(sqrt (* (* (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
398.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
393.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
274.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify127.0ms

Counts: 122 → 122

prune745.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.6b

localize39.0ms

Local error

Found 4 expressions with local error:

9.5b	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
16×	`sqrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`cbrt-prod` `add-cube-cbrt` `flip3-+` `flip-+`
8×	`associate-/r/`
5×	`pow1` `times-frac`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out`

Counts

4 → 67

Calls

4 calls:

60.0ms	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

461.0ms	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
283.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
273.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
283.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify111.0ms

Counts: 79 → 79

prune497.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 9.6b

regimes773.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	3781×	body	160	valid
758.0ms	8020×	body	80	nan
380.0ms	4219×	body	80	valid