Details

sample97.0ms

Algorithm

intervals

Results

22.0ms	271×	body	80	nan
20.0ms	129×	body	160	valid
18.0ms	127×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	51	18
3	108	18
4	292	18
5	1585	18
done	5000	18

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
28×	`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`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 112

Calls

4 calls:

7.0ms	(pow (/ Om Omc) 2.0)
7.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
76.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(pow (/ Om Omc) 2.0)
86.0ms	(pow (/ t l) 2.0)
21.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
408.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.2s

Counts

124 → 124

Iterations

Useful iterations: 2 (528.0ms)

Iter	Nodes	Cost
0	319	2298
1	740	2196
2	1840	2088
done	5000	2088

prune750.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
2.2b	(log (exp (pow (/ Om Omc) 2.0)))
9.0b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
22×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp`

Counts

4 → 107

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
22.0ms	(log (exp (pow (/ Om Omc) 2.0)))
131.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(pow (/ t l) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
94.0ms	(log (exp (pow (/ Om Omc) 2.0)))
436.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.7s

Counts

119 → 119

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	301	2146
1	633	1868
2	1502	1755
3	4830	1753
done	5001	1753

prune747.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

localize36.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0))) 1.0)))
29.1b	(cbrt (pow (/ t l) 2.0))
29.1b	(cbrt (pow (/ t l) 2.0))
29.1b	(cbrt (pow (/ t l) 2.0))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
47×	`add-sqr-sqrt` `*-un-lft-identity`
46×	`times-frac`
39×	`unpow-prod-down`
38×	`add-cube-cbrt`
22×	`sqrt-prod`
8×	`pow1`
6×	`distribute-lft-out--`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `log-pow` `difference-of-squares` `sqr-pow`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 117

Calls

4 calls:

147.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0))) 1.0)))
9.0ms	(cbrt (pow (/ t l) 2.0))
9.0ms	(cbrt (pow (/ t l) 2.0))
9.0ms	(cbrt (pow (/ t l) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

526.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0))) 1.0)))
350.0ms	(cbrt (pow (/ t l) 2.0))
355.0ms	(cbrt (pow (/ t l) 2.0))
359.0ms	(cbrt (pow (/ t l) 2.0))

simplify1.4s

Counts

129 → 129

Iterations

Useful iterations: 3 (603.0ms)

Iter	Nodes	Cost
0	208	3486
1	379	3262
2	849	2526
3	2373	2361
done	5001	2361

prune992.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.7b

localize120.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0)))) 1.0)))
20.7b	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
29.1b	(cbrt (pow (/ t l) 2.0))
29.1b	(cbrt (pow (/ t l) 2.0))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
41×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`times-frac`
32×	`add-cube-cbrt`
31×	`unpow-prod-down`
22×	`sqrt-prod`
8×	`pow1`
6×	`distribute-lft-out--`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `log-pow` `difference-of-squares` `sqr-pow`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 109

Calls

4 calls:

137.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0)))) 1.0)))
12.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
9.0ms	(cbrt (pow (/ t l) 2.0))
9.0ms	(cbrt (pow (/ t l) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

547.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (fma 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0)))) 1.0)))
343.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
318.0ms	(cbrt (pow (/ t l) 2.0))
373.0ms	(cbrt (pow (/ t l) 2.0))

simplify1.8s

Counts

121 → 121

Iterations

Useful iterations: 3 (832.0ms)

Iter	Nodes	Cost
0	263	4520
1	503	4271
2	1210	4097
3	3377	4088
done	5001	4088

prune1.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 9.7b

regimes662.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	17	20
done	17	20

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	7975×	body	80	nan
1.2s	3821×	body	160	valid
508.0ms	4179×	body	80	valid