Details

analyze1.5s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

sample69.0ms

Algorithm

intervals

Results

23.0ms	123×	body	160	valid
16.0ms	166×	body	80	nan
13.0ms	133×	body	80	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4745	19
1	4745	19

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: 8.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite39.0ms

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)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
14.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
93.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
134.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4953	3362
1	4953	3362

prune475.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	131	11	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	11	143

Merged error: 8.5b

Counts

143 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 151

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.0ms	(/ (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))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
14.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
131.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
50.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify81.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5030	4133

prune446.0ms

Filtered

107 candidates to 163 candidates (-52.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	163	11	174

Merged error: 8.5b

Counts

174 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

6.2b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.2b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(sqrt (sqrt (+ 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))))

series219.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
64.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
45.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5060	1262

prune326.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	84	11	95

Merged error: 8.5b

Counts

95 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

7.5b	(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))))))
15.5b	(cbrt (/ t l))
15.5b	(cbrt (/ t l))
15.5b	(cbrt (/ t l))

rewrite26.0ms

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` `add-cbrt-cube` `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 → 108

Calls

4 calls:

14.0ms	(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))))))
2.0ms	(cbrt (/ t l))
2.0ms	(cbrt (/ t l))
2.0ms	(cbrt (/ t l))

series175.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(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))))))
13.0ms	(cbrt (/ t l))
12.0ms	(cbrt (/ t l))
15.0ms	(cbrt (/ t l))

simplify77.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4930	2800
1	4930	2800

prune323.0ms

Filtered

100 candidates to 120 candidates (-20.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	119	12	131

Merged error: 8.5b

Counts

131 → 12

regimes1.8s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	20
1	29	20

end0.0ms

sample2.0s

Algorithm

intervals

Results

720.0ms	3803×	body	160	valid
454.0ms	4664×	body	80	nan
415.0ms	4197×	body	80	valid

Details

analyze1.5s

sample69.0ms

simplify41.0ms

prune5.0ms

localize15.0ms

rewrite39.0ms

series253.0ms

simplify79.0ms

prune475.0ms

localize16.0ms

rewrite31.0ms

series208.0ms

simplify81.0ms

prune446.0ms

localize19.0ms

rewrite16.0ms

series219.0ms

simplify37.0ms

prune326.0ms

localize21.0ms

rewrite26.0ms

series175.0ms

simplify77.0ms

prune323.0ms

regimes1.8s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

Profiling