Details

sample101.0ms

Algorithm

intervals

Results

27.0ms	255×	body	80	nan
22.0ms	111×	body	160	valid
15.0ms	145×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1583
4	292
3	108
2	51
1	29
0	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.9b	(asin (sqrt (/ (- 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)))))

rewrite174.0ms

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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 138

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
77.0ms	(/ (- 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))))))
72.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series913.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(pow (/ t l) 2.0)
332.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
27.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
467.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2499
1	771
0	325

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.9b	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
8.8b	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
37×	`times-frac`
34×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`unpow-prod-down`
16×	`difference-of-squares`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `add-cbrt-cube`
5×	`sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `sqrt-prod`
2×	`div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `flip--`

Counts

4 → 107

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
80.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
2.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

117.0ms	(pow (/ t l) 2.0)
241.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
14.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
1.5s	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

simplify1.1s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1889
1	648
0	270

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.9b	(asin (sqrt (expm1 (log1p (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
8.8b	(sqrt (expm1 (log1p (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
9.2b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
9.2b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(asin (sqrt (expm1 (log1p (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
2.0ms	(sqrt (expm1 (log1p (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
3.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
2.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (sqrt (expm1 (log1p (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
1.5s	(sqrt (expm1 (log1p (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
168.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
155.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify611.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
3	1271
2	484
1	228
0	126

prune487.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.1b

localize65.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0))) 2.0 1.0)))))
30.3b	(cbrt (pow (/ t l) 2.0))
30.3b	(cbrt (pow (/ t l) 2.0))
30.3b	(cbrt (pow (/ t l) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`unpow-prod-down`
30×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 96

Calls

4 calls:

1.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0))) 2.0 1.0)))))
4.0ms	(cbrt (pow (/ t l) 2.0))
10.0ms	(cbrt (pow (/ t l) 2.0))
4.0ms	(cbrt (pow (/ t l) 2.0))

series3.0s

Counts

4 → 12

Calls

4 calls:

1.7s	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0))) 2.0 1.0)))))
441.0ms	(cbrt (pow (/ t l) 2.0))
442.0ms	(cbrt (pow (/ t l) 2.0))
406.0ms	(cbrt (pow (/ t l) 2.0))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	2208
2	801
1	349
0	175

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 10.1b

regimes1.3s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.1b and baseline of 10.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
0	17

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	3798×	body	160	valid
1.4s	8231×	body	80	nan
604.0ms	4202×	body	80	valid