Details

sample68.0ms

Algorithm

intervals

Results

21.0ms	297×	body	80	nan
16.0ms	118×	body	160	valid
9.0ms	138×	body	80	valid

simplify127.0ms

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: 10.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
1.1b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 114

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
5.0ms	(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)))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ Om Omc) 2.0)
63.0ms	(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))))))
330.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	709	1289
1	2087	1218
2	5001	1206

prune609.0ms

Filtered

126 candidates to 100 candidates (79.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	11	127

Merged error: 10.0b

Counts

127 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.5b	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite69.0ms

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

Counts

4 → 188

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))))))
13.0ms	(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)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

342.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
346.0ms	(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
317.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
318.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	421	3398
1	945	3320
2	3569	3300
3	5003	3268

prune901.0ms

Filtered

200 candidates to 162 candidates (81.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	201	10	211

Merged error: 10.0b

Counts

211 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
16.0b	(cbrt (/ t l))
16.0b	(cbrt (/ t l))
16.0b	(cbrt (/ t l))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
55×	`times-frac`
43×	`*-un-lft-identity`
39×	`cbrt-prod`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `distribute-lft-out--` `sqr-pow`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 116

Calls

4 calls:

13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
5.0ms	(cbrt (/ t l))
3.0ms	(cbrt (/ t l))
3.0ms	(cbrt (/ t l))

series494.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
62.0ms	(cbrt (/ t l))
62.0ms	(cbrt (/ t l))
57.0ms	(cbrt (/ t l))

simplify145.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	410	1803
1	971	1739
2	4438	1730
3	5001	1730

prune594.0ms

Filtered

128 candidates to 111 candidates (86.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	128	10	138

Merged error: 10.0b

Counts

138 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt`
115×	`sqrt-prod`
84×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
8×	`pow1` `sqrt-div`
7×	`rem-sqrt-square`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`div-inv`

Counts

4 → 147

Calls

4 calls:

17.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 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)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

340.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
325.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	568	2528
1	1350	2464
2	5001	2438

prune810.0ms

Filtered

159 candidates to 119 candidates (74.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	159	10	169

Merged error: 10.0b

Counts

169 → 10

regimes773.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.9s

Algorithm

intervals

Results

562.0ms	8077×	body	80	nan
536.0ms	3753×	body	160	valid
308.0ms	4247×	body	80	valid