Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	265×	body	80	nan
17.0ms	126×	body	160	valid
9.0ms	130×	body	80	valid

simplify134.0ms

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

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: 10.3b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.6b	(/ (- 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))))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite35.0ms

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)
12.0ms	(/ (- 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)))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ Om Omc) 2.0)
214.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
20.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
307.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

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

prune539.0ms

Filtered

142 candidates to 114 candidates (80.3%)

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: 10.3b

Counts

143 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.6b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`unpow-prod-down`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `div-exp` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 79

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
5.0ms	(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))))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
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))))))
179.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	543	644
1	1769	596
2	5001	596

prune343.0ms

Filtered

91 candidates to 69 candidates (75.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	91	7	98

Merged error: 10.3b

Counts

98 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
126×	`sqrt-prod`
117×	`add-sqr-sqrt`
80×	`cbrt-div`
72×	`*-un-lft-identity`
71×	`cbrt-prod`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-r/` `associate-l/`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 180

Calls

4 calls:

29.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

320.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
244.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
246.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
237.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify109.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	946	6224
1	2907	6123
2	5001	6115

prune1.1s

Filtered

192 candidates to 160 candidates (83.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	191	8	199

Merged error: 10.3b

Counts

199 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

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

series983.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
246.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
245.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
249.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	144	652
1	451	604
2	1974	588
3	5001	588

prune388.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	64	8	72

Merged error: 10.3b

Counts

72 → 8

regimes695.0ms

Accuracy

0% (0.1b remaining)

Error of 9.9b against oracle of 9.8b and baseline of 9.9b

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

569.0ms	7993×	body	80	nan
541.0ms	3840×	body	160	valid
301.0ms	4160×	body	80	valid