Details

sample115.0ms

Algorithm

intervals

Results

29.0ms	273×	body	80	nan
26.0ms	124×	body	160	valid
15.0ms	132×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite218.0ms

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×	`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 → 138

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
122.0ms	(/ (- 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))))))
81.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series993.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(pow (/ Om Omc) 2.0)
366.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
24.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
491.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.8s

Counts

150 → 150

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	316	3783
1	649	3663
2	1541	3335
3	4790	3323
done	5000	3323

prune915.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.5b	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
9.0b	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

rewrite156.0ms

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×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num` `flip--`

Counts

4 → 107

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
132.0ms	(/ (- 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))))))
3.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (/ Om Omc) 2.0)
270.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
17.0ms	(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)))))

simplify2.2s

Counts

119 → 119

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	253	2588
1	511	2426
2	1162	2288
3	3399	2273
done	5001	2268

prune767.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
9.0b	(sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
9.4b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
9.4b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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 (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
1.0ms	(sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
1.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
2.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series872.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(asin (sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
485.0ms	(sqrt (expm1 (log1p (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
167.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
201.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.1s

Counts

67 → 67

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	105	1590
1	171	1397
2	307	1237
3	787	951
4	2045	930
done	5000	922

prune364.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

localize39.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (expm1 (log1p (* (/ 1 (* (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
9.4b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
13.9b	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
13.9b	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(sqrt (expm1 (log1p (* (/ 1 (* (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
2.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.1s	(sqrt (expm1 (log1p (* (/ 1 (* (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
150.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
205.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
187.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	103	1543
1	177	1367
2	357	1230
3	974	1224
4	2986	1194
done	5001	1182

prune819.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

regimes642.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.3b and baseline of 10.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	20
done	17	20

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	8083×	body	80	nan
922.0ms	3695×	body	160	valid
609.0ms	4305×	body	80	valid