Details

sample95.0ms

Algorithm

intervals

Results

25.0ms	128×	body	160	valid
21.0ms	215×	body	80	nan
13.0ms	128×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite130.0ms

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:

13.0ms	(pow (/ Om Omc) 2.0)
13.0ms	(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))))))
92.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow (/ Om Omc) 2.0)
121.0ms	(pow (/ t l) 2.0)
28.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
514.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.7s

Counts

126 → 126

Iterations

Useful iterations: 3 (1.3s)

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

prune834.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.5b

localize27.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
55×	`times-frac`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 125

Calls

4 calls:

62.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
5.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

489.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
447.0ms	(cbrt (pow (/ t l) 2.0))
406.0ms	(cbrt (pow (/ t l) 2.0))
382.0ms	(cbrt (pow (/ t l) 2.0))

simplify2.0s

Counts

137 → 137

Iterations

Useful iterations: 3 (888.0ms)

Iter	Nodes	Cost
0	273	4113
1	523	3960
2	1057	2941
3	2803	2720
done	5001	2720

prune947.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.5b

localize42.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
20.1b	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
47×	`times-frac`
43×	`cbrt-prod`
40×	`*-un-lft-identity`
37×	`unpow-prod-down`
34×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 117

Calls

4 calls:

56.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
6.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
7.0ms	(cbrt (pow (/ t l) 2.0))
22.0ms	(cbrt (pow (/ t l) 2.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

450.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
472.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
475.0ms	(cbrt (pow (/ t l) 2.0))
467.0ms	(cbrt (pow (/ t l) 2.0))

simplify2.5s

Counts

129 → 129

Iterations

Useful iterations: 3 (1000.0ms)

Iter	Nodes	Cost
0	329	5470
1	645	5275
2	1318	5034
3	4220	5000
done	5000	5000

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.5b

localize72.0ms

Local error

Found 4 expressions with local error:

12.6b	(cbrt (pow (/ t l) (/ 2.0 2)))
12.6b	(cbrt (pow (/ t l) (/ 2.0 2)))
20.1b	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
26.9b	(cbrt (pow (/ t l) 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-prod`
44×	`unpow-prod-down`
30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`

Counts

4 → 100

Calls

4 calls:

6.0ms	(cbrt (pow (/ t l) (/ 2.0 2)))
9.0ms	(cbrt (pow (/ t l) (/ 2.0 2)))
11.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
10.0ms	(cbrt (pow (/ t l) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

451.0ms	(cbrt (pow (/ t l) (/ 2.0 2)))
384.0ms	(cbrt (pow (/ t l) (/ 2.0 2)))
461.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
491.0ms	(cbrt (pow (/ t l) 2.0))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: 3 (593.0ms)

Iter	Nodes	Cost
0	235	2286
1	437	2227
2	845	2143
3	1998	2131
done	5001	2131

prune1.5s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 9.5b

regimes1.1s

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

1.5s	3788×	body	160	valid
1.2s	7919×	body	80	nan
562.0ms	4212×	body	80	valid