Details

sample125.0ms

Algorithm

intervals

Results

35.0ms	263×	body	80	nan
32.0ms	114×	body	160	valid
19.0ms	142×	body	80	valid

simplify127.0ms

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

prune5.0ms

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: 12.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite34.0ms

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:

4.0ms	(pow (/ t l) 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)))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
100.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
144.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	662	1889
1	2099	1789
2	5002	1774

prune447.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 12.4b

Counts

143 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
56×	`times-frac`
54×	`sqrt-prod`
41×	`*-un-lft-identity`
31×	`cbrt-prod`
29×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
6×	`cbrt-div` `distribute-lft-out--` `sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
2×	`pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 101

Calls

4 calls:

1.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
14.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 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))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
139.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
66.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
70.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	618	2081
1	1575	1993
2	5001	1980

prune587.0ms

Filtered

100 candidates to 113 candidates (-13.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	112	10	122

Merged error: 12.4b

Counts

122 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.9b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.7b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.7b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
92×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
33×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
6×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 133

Calls

4 calls:

1.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
13.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
152.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
288.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
153.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	532	2819
1	1231	2727
2	4288	2718
3	5001	2695

prune823.0ms

Filtered

125 candidates to 145 candidates (-16.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	146	9	155

Merged error: 12.4b

Counts

155 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`pow1` `sqrt-div`
4×	`add-exp-log` `cbrt-div` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 59

Calls

4 calls:

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

series237.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
50.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
49.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
69.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	310	764
1	1000	732
2	5001	722

prune376.0ms

Filtered

64 candidates to 71 candidates (-10.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	71	9	80

Merged error: 12.4b

Counts

80 → 9

regimes1.4s

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	18	10
1	18	10

end0.0ms

sample2.6s

Algorithm

intervals

Results

738.0ms	8027×	body	80	nan
699.0ms	3821×	body	160	valid
380.0ms	4179×	body	80	valid

Details

sample125.0ms

simplify127.0ms

prune5.0ms

localize14.0ms

rewrite34.0ms

series273.0ms

simplify65.0ms

prune447.0ms

localize24.0ms

rewrite25.0ms

series300.0ms

simplify55.0ms

prune587.0ms

localize18.0ms

rewrite45.0ms

series621.0ms

simplify129.0ms

prune823.0ms

localize24.0ms

rewrite12.0ms

series237.0ms

simplify38.0ms

prune376.0ms

regimes1.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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