Details

sample76.0ms

Algorithm

intervals

Results

21.0ms	241×	body	80	nan
20.0ms	113×	body	160	valid
13.0ms	143×	body	80	valid

simplify129.0ms

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

prune3.0ms

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: 11.0b

Counts

2 → 1

localize18.0ms

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))))))
10.0b	(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)))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ t l) 2.0)
206.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
453.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	648	1882
1	2047	1787
2	5001	1774

prune510.0ms

Filtered

142 candidates to 114 candidates (80.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	133	9	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	10	143

Merged error: 10.9b

Counts

143 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.7b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite32.0ms

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

series570.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
16.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
310.0ms	(/ (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))))

simplify66.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	619	2493
1	1983	2321
2	5001	2311

prune474.0ms

Filtered

163 candidates to 106 candidates (65.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	163	10	173

Merged error: 10.9b

Counts

173 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.4b	(sqrt (pow (/ Om Omc) 2.0))
18.4b	(sqrt (pow (/ Om Omc) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`flip3-+` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

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

series880.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
259.0ms	(sqrt (pow (/ Om Omc) 2.0))
259.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	366	816
1	964	796
2	3826	796
3	5002	796

prune526.0ms

Filtered

102 candidates to 84 candidates (82.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	102	10	112

Merged error: 10.9b

Counts

112 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite13.0ms

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:

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

series833.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
239.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
176.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
177.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	201	720
1	658	700
2	2858	696
3	5002	688

prune323.0ms

Filtered

84 candidates to 64 candidates (76.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	84	10	94

Merged error: 10.9b

Counts

94 → 10

regimes717.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b 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

sample2.2s

Algorithm

intervals

Results

727.0ms	8152×	body	80	nan
672.0ms	3871×	body	160	valid
364.0ms	4129×	body	80	valid

Details

sample76.0ms

simplify129.0ms

prune3.0ms

localize18.0ms

rewrite34.0ms

series738.0ms

simplify69.0ms

prune510.0ms

localize15.0ms

rewrite32.0ms

series570.0ms

simplify66.0ms

prune474.0ms

localize22.0ms

rewrite16.0ms

series880.0ms

simplify89.0ms

prune526.0ms

localize18.0ms

rewrite13.0ms

series833.0ms

simplify86.0ms

prune323.0ms

regimes717.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling