Details

sample134.0ms

Algorithm

intervals

Results

35.0ms	249×	body	80	nan
32.0ms	121×	body	160	valid
18.0ms	135×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	108	18
4	279	18
5	835	18
6	3116	18
done	5000	18

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ t l) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite80.0ms

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×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `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 → 114

Calls

4 calls:

10.0ms	(pow (/ Om Omc) 2.0)
11.0ms	(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))))))
54.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(pow (/ Om Omc) 2.0)
83.0ms	(pow (/ t l) 2.0)
32.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
477.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.0s

Counts

126 → 126

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	360	2490
1	707	2370
2	1477	2183
3	4091	2173
done	5000	2173

prune800.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.5b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
7.5b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`sqrt-div` `div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 155

Calls

4 calls:

7.0ms	(pow (/ t l) 2.0)
97.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
3.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series766.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(pow (/ t l) 2.0)
486.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
23.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
168.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.6s

Counts

167 → 167

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	300	4354
1	504	4027
2	941	3908
3	2154	3908
done	5000	3902

prune831.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.1b

localize23.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
7.5b	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
8.1b	(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
8.1b	(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms	(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
8.0ms	(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
117.0ms	(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
155.0ms	(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
153.0ms	(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify3.1s

Counts

84 → 84

Iterations

Useful iterations: 5 (1.4s)

Iter	Nodes	Cost
0	75	1116
1	126	960
2	219	922
3	479	922
4	1162	886
5	3099	870
done	5000	870

prune371.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (* (/ 1 (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
2.4b	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
13.4b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
13.4b	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square` `sqrt-pow1`
1×	`asin-acos` `pow1/2`

Counts

4 → 56

Calls

4 calls:

1.0ms	(asin (* (/ 1 (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
2.0ms	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series615.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(asin (* (/ 1 (fabs (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))))
202.0ms	(sqrt (cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
214.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
173.0ms	(cbrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify2.1s

Counts

68 → 68

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	113	1342
1	205	1286
2	402	1115
3	918	1109
4	2385	1082
done	5001	1070

prune495.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 8.1b

regimes1.4s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.2s	7828×	body	80	nan
1.1s	3785×	body	160	valid
1.0s	4215×	body	80	valid