Details

sample107.0ms

Algorithm

intervals

Results

22.0ms	245×	body	80	nan
20.0ms	115×	body	160	valid
12.0ms	141×	body	80	valid

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	49	10
2	101	10
3	279	10
4	1029	10
5	4384	10
6	5002	10

prune156.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 10.8b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
9.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite34.0ms

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×	`associate-/r/` `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 → 130

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
11.0ms	(/ (- 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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
93.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
134.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	649	1889
1	2079	1797
2	5001	1774

prune399.0ms

Filtered

142 candidates to 114 candidates (19.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 10.8b

Counts

143 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.7b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.8b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

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` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `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 → 151

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
14.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
134.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	689	2519
1	2333	2350
2	5001	2330

prune408.0ms

Filtered

163 candidates to 106 candidates (35.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	162	8	170

Merged error: 10.7b

Counts

170 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

9.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.3b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
63.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	262	796
1	822	778
2	3917	772
3	5002	764

prune303.0ms

Filtered

84 candidates to 64 candidates (23.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Merged error: 10.7b

Counts

92 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.3b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
17.1b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.1b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
92×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
33×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
6×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 133

Calls

4 calls:

1.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
13.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
141.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
143.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
143.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify125.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	532	2819
1	1231	2727
2	4288	2718
3	5001	2695

prune695.0ms

Filtered

145 candidates to 125 candidates (13.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	145	8	153

Merged error: 10.7b

Counts

153 → 8

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.5s

Algorithm

intervals

Results

707.0ms	7789×	body	80	nan
694.0ms	3727×	body	160	valid
398.0ms	4273×	body	80	valid

Details

sample107.0ms

simplify127.0ms

prune156.0ms

localize14.0ms

rewrite34.0ms

series254.0ms

simplify63.0ms

prune399.0ms

localize15.0ms

rewrite30.0ms

series206.0ms

simplify70.0ms

prune408.0ms

localize18.0ms

rewrite12.0ms

series220.0ms

simplify111.0ms

prune303.0ms

localize18.0ms

rewrite43.0ms

series453.0ms

simplify125.0ms

prune695.0ms

regimes1.2s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

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