Details

sample64.0ms

Algorithm

intervals

Results

17.0ms	127×	body	160	valid
17.0ms	241×	body	80	nan
9.0ms	129×	body	80	valid

simplify126.0ms

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: 10.7b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite41.0ms

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:

5.0ms	(pow (/ t l) 2.0)
17.0ms	(/ (- 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)))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
215.0ms	(/ (- 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))))))
327.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	664	1948
1	2106	1846
2	5001	1828

prune775.0ms

Filtered

150 candidates to 123 candidates (82.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	9	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	9	151

Merged error: 10.6b

Counts

151 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.4b	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

215×	`add-sqr-sqrt`
151×	`unpow-prod-down`
131×	`times-frac`
120×	`difference-of-squares`
90×	`cube-prod`
67×	`sqr-pow`
61×	`sqrt-prod`
49×	`associate-/l*`
46×	`*-un-lft-identity`
16×	`add-cube-cbrt` `associate-/r/`
15×	`distribute-lft-out--`
12×	`add-exp-log` `flip3-+` `flip-+`
9×	`add-cbrt-cube`
8×	`frac-times`
6×	`pow1`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `add-log-exp`
3×	`difference-cubes` `pow-unpow` `div-exp` `div-inv`
2×	`cbrt-undiv` `pow-exp` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod`

Counts

4 → 240

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
87.0ms	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
54.0ms	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
722.0ms	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
42.0ms	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
903.0ms	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1173	5721
1	5002	5421

prune1.0s

Filtered

252 candidates to 154 candidates (61.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	247	5	252
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	254	7	261

Merged error: 10.6b

Counts

261 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.2b	(pow (/ t l) 2.0)
0.7b	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.9b	(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

405×	`add-sqr-sqrt`
299×	`sqrt-prod`
257×	`times-frac`
243×	`unpow-prod-down`
200×	`difference-of-squares`
150×	`cube-prod`
125×	`*-un-lft-identity`
111×	`sqr-pow`
75×	`add-cube-cbrt`
52×	`associate-/l*`
25×	`distribute-lft-out--`
18×	`sqrt-div`
12×	`flip3-+` `flip-+`
9×	`add-exp-log`
8×	`pow1` `frac-times` `associate-/r/`
6×	`add-cbrt-cube`
5×	`difference-cubes`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`sqrt-pow1` `div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `pow1/2` `pow-prod-down` `clear-num` `flip--`

Counts

4 → 350

Calls

4 calls:

62.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
18.0ms	(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

924.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
65.0ms	(pow (/ t l) 2.0)
40.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
477.0ms	(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify208.0ms

Algorithm

egg-herbie

Counts

362 → 362

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1200	11831
1	4579	11548
2	5001	11548

prune1.5s

Filtered

362 candidates to 201 candidates (55.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	359	3	362
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	362	7	369

Merged error: 10.6b

Counts

369 → 7

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (* (hypot (pow (sqrt (pow (/ Om Omc) 2.0)) 3/2) (pow 1.0 3/4)) (/ (sqrt (- (pow 1.0 3/2) (pow (sqrt (pow (/ Om Omc) 2.0)) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
9.9b	(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0b	(sqrt (pow (/ Om Omc) 2.0))
16.0b	(sqrt (pow (/ Om Omc) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`sqrt-prod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
8×	`rem-sqrt-square` `sqrt-div`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow1/2`
2×	`associate-r/` `associate-l/` `div-inv`
1×	`asin-acos` `pow-prod-down`

Counts

4 → 95

Calls

4 calls:

1.0ms	(asin (* (hypot (pow (sqrt (pow (/ Om Omc) 2.0)) 3/2) (pow 1.0 3/4)) (/ (sqrt (- (pow 1.0 3/2) (pow (sqrt (pow (/ Om Omc) 2.0)) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
18.0ms	(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

81.0ms	(asin (* (hypot (pow (sqrt (pow (/ Om Omc) 2.0)) 3/2) (pow 1.0 3/4)) (/ (sqrt (- (pow 1.0 3/2) (pow (sqrt (pow (/ Om Omc) 2.0)) 3))) (sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
486.0ms	(sqrt (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
277.0ms	(sqrt (pow (/ Om Omc) 2.0))
271.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	760	1596
1	2935	1511
2	5002	1510

prune890.0ms

Filtered

107 candidates to 92 candidates (86.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	107	7	114

Merged error: 10.6b

Counts

114 → 7

regimes662.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

587.0ms	8130×	body	80	nan
549.0ms	3742×	body	160	valid
311.0ms	4258×	body	80	valid