Details

analyze1.4s

Algorithm: search

sample70.0ms

Algorithm

intervals

Results

24.0ms	129×	body	160	valid
17.0ms	175×	body	80	nan
12.0ms	127×	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: 10.1b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(/ (- 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))))))
9.4b	(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:

5.0ms	(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)))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
96.0ms	(/ (- 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))))))
137.0ms	(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 (45.0ms)

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

prune419.0ms

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: 10.1b

Counts

143 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

5.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
5.8b	(sqrt (/ 1 (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))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

120×	`sqrt-prod`
104×	`add-sqr-sqrt`
78×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
10×	`pow1` `rem-sqrt-square` `sqrt-div`
9×	`sqrt-pow1`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow-flip`
2×	`div-inv`
1×	`inv-pow`

Counts

4 → 140

Calls

4 calls:

15.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.0ms	(sqrt (/ 1 (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))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
78.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
52.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	605	2292
1	1651	2239
2	5001	2188

prune509.0ms

Filtered

101 candidates to 152 candidates (-50.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	152	9	161

Merged error: 10.1b

Counts

161 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
29.5b	(cbrt (pow (/ t l) 2.0))
29.5b	(cbrt (pow (/ t l) 2.0))
29.5b	(cbrt (pow (/ t l) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
55×	`times-frac`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`pow1/3` `distribute-lft-out--`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 117

Calls

4 calls:

12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
4.0ms	(cbrt (pow (/ t l) 2.0))
4.0ms	(cbrt (pow (/ t l) 2.0))
4.0ms	(cbrt (pow (/ t l) 2.0))

series425.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
194.0ms	(cbrt (pow (/ t l) 2.0))
47.0ms	(cbrt (pow (/ t l) 2.0))
49.0ms	(cbrt (pow (/ t l) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	544	2085
1	1305	2015
2	5001	1967

prune572.0ms

Filtered

112 candidates to 129 candidates (-15.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	129	9	138

Merged error: 10.1b

Counts

138 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.2b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.6b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.6b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

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

series313.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
147.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
73.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	654	2729
1	1687	2628
2	5001	2614

prune753.0ms

Filtered

120 candidates to 133 candidates (-10.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	132	10	142

Merged error: 10.1b

Counts

142 → 10

regimes1.4s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

analyze1.4s

Algorithm: search

sample2.0s

Algorithm

intervals

Results

753.0ms	3894×	body	160	valid
500.0ms	4944×	body	80	nan
403.0ms	4106×	body	80	valid

Details

analyze1.4s

sample70.0ms

simplify127.0ms

prune5.0ms

localize18.0ms

rewrite34.0ms

series262.0ms

simplify65.0ms

prune419.0ms

localize23.0ms

rewrite32.0ms

series309.0ms

simplify60.0ms

prune509.0ms

localize19.0ms

rewrite29.0ms

series425.0ms

simplify51.0ms

prune572.0ms

localize23.0ms

rewrite29.0ms

series313.0ms

simplify64.0ms

prune753.0ms

regimes1.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.4s

sample2.0s

Profiling