Details

sample72.0ms

Algorithm

intervals

Results

21.0ms	122×	body	160	valid
18.0ms	250×	body	80	nan
10.0ms	134×	body	80	valid

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10

prune4.0ms

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: 10.0b

Counts

2 → 1

localize15.0ms

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))))
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite42.0ms

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:

4.0ms	(pow (/ Om Omc) 2.0)
19.0ms	(/ (- 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)))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ Om Omc) 2.0)
206.0ms	(/ (- 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))))))
314.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	650	1948
1	2076	1846
2	5001	1827

prune523.0ms

Filtered

150 candidates to 123 candidates (82.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	144	6	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	6	151

Merged error: 10.0b

Counts

151 → 6

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))))
0.4b	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
9.2b	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite26.0ms

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

Counts

4 → 109

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
16.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ Om Omc) 2.0)
213.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
963.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	633	1423
1	2104	1328
2	5001	1321

prune465.0ms

Filtered

121 candidates to 100 candidates (82.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	120	7	127

Merged error: 10.0b

Counts

127 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.4b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.5b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 159

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
310.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	624	2554
1	2015	2381
2	5002	2370

prune509.0ms

Filtered

171 candidates to 115 candidates (67.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Merged error: 10.0b

Counts

178 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.4b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite13.0ms

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` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 80

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

series855.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
239.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify89.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	213	762
1	703	740
2	3026	738
3	5002	730

prune369.0ms

Filtered

92 candidates to 72 candidates (78.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	92	7	99

Merged error: 10.0b

Counts

99 → 7

regimes598.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample2.0s

Algorithm

intervals

Results

617.0ms	8243×	body	80	nan
564.0ms	3856×	body	160	valid
299.0ms	4144×	body	80	valid