Details

sample76.0ms

Algorithm

intervals

Results

21.0ms	121×	body	160	valid
21.0ms	246×	body	80	nan
12.0ms	135×	body	80	valid

simplify124.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 12.2b

Counts

2 → 1

localize20.0ms

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))))
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite38.0ms

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:

5.0ms	(pow (/ Om Omc) 2.0)
13.0ms	(/ (- 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))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series608.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (/ Om Omc) 2.0)
212.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
322.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	634	1882
1	2017	1787
2	5001	1774

prune621.0ms

Filtered

142 candidates to 114 candidates (80.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Merged error: 12.2b

Counts

143 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.2b	(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
13×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1`
6×	`sqrt-div` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `div-exp` `associate-/r` `associate-/l`
2×	`frac-times` `flip3--` `sqrt-pow1` `associate-*l/` `pow-exp` `associate-/r/` `flip--` `div-inv`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `asin-acos` `pow-flip` `pow-pow` `frac-2neg` `flip3-+` `pow1/2` `1-exp` `associate-*r/` `pow-prod-down` `clear-num` `sqrt-prod` `un-div-inv` `flip-+` `inv-pow` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
5.0ms	(/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(asin (sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
13.0ms	(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
145.0ms	(/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
20.0ms	(asin (sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
305.0ms	(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	503	853
1	1933	784
2	5003	769

prune282.0ms

Filtered

98 candidates to 69 candidates (70.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	98	7	105

Merged error: 12.2b

Counts

105 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.2b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

190×	`sqrt-prod`
164×	`add-sqr-sqrt`
112×	`times-frac`
78×	`*-un-lft-identity`
54×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`unpow-prod-down`
12×	`distribute-lft-out--` `sqr-pow`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
8×	`associate-/r/`
6×	`pow1/2` `sqrt-div`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`

Counts

4 → 180

Calls

4 calls:

17.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms	(sqrt (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)))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

341.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
335.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
309.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
308.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	414	3308
1	911	3236
2	3359	3216
3	5002	3182

prune811.0ms

Filtered

192 candidates to 154 candidates (80.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	192	7	199

Merged error: 12.2b

Counts

199 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

11.2b	(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (* (* (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
17.3b	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.3b	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.3b	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

45×	`cbrt-prod`
39×	`cbrt-div`
29×	`frac-times`
27×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
23×	`sqrt-div`
17×	`associate-*l/`
16×	`associate-*r/`
14×	`pow1`
8×	`flip3--` `flip--`
6×	`pow-prod-down` `associate-/r/`
4×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 108

Calls

4 calls:

27.0ms	(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (* (* (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
4.0ms	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

317.0ms	(sqrt (* (- 1.0 (pow (/ Om Omc) 2.0)) (* (* (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
265.0ms	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
272.0ms	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
287.0ms	(cbrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	410	2046
1	1249	1981
2	5002	1926

prune423.0ms

Filtered

120 candidates to 85 candidates (70.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	119	8	127

Merged error: 12.2b

Counts

127 → 8

regimes735.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

723.0ms	8123×	body	80	nan
673.0ms	3803×	body	160	valid
370.0ms	4197×	body	80	valid