Details

sample76.0ms

Algorithm

intervals

Results

23.0ms	128×	body	160	valid
20.0ms	216×	body	80	nan
11.0ms	128×	body	80	valid

simplify133.0ms

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

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: 9.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(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))))))
8.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 106

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
5.0ms	(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))))))
17.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ Om Omc) 2.0)
65.0ms	(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))))))
317.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	695	1235
1	2043	1164
2	5002	1152

prune404.0ms

Filtered

118 candidates to 92 candidates (78.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Merged error: 9.2b

Counts

119 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

6.7b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.7b	(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

129×	`sqrt-prod`
106×	`add-sqr-sqrt`
84×	`times-frac`
56×	`*-un-lft-identity`
50×	`cbrt-prod`
44×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
10×	`rem-sqrt-square` `sqrt-div`
8×	`pow1`
6×	`distribute-lft-out--` `sqr-pow`
4×	`add-exp-log` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`div-inv`

Counts

4 → 142

Calls

4 calls:

18.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
21.0ms	(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 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))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

433.0ms	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
434.0ms	(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
312.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
176.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify139.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	524	2804
1	1238	2751
2	4721	2724
3	5001	2724

prune658.0ms

Filtered

154 candidates to 110 candidates (71.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	154	6	160

Merged error: 9.2b

Counts

160 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(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))))))))
1.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite27.0ms

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))))))))
16.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series856.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(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))))))))
338.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
246.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
242.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	545	2043
1	1354	1953
2	5001	1942

prune579.0ms

Filtered

113 candidates to 100 candidates (88.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	113	6	119

Merged error: 9.2b

Counts

119 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.2b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
66×	`sqrt-prod`
56×	`times-frac`
42×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
8×	`pow1`
6×	`rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r/` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

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

series699.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
45.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
305.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
307.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	388	1928
1	920	1854
2	3298	1846
3	5001	1822

prune564.0ms

Filtered

122 candidates to 100 candidates (82.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	119	9	128

Merged error: 9.2b

Counts

128 → 9

regimes743.0ms

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

sample2.2s

Algorithm

intervals

Results

701.0ms	7862×	body	80	nan
688.0ms	3801×	body	160	valid
380.0ms	4199×	body	80	valid

Details

sample76.0ms

simplify133.0ms

prune4.0ms

localize15.0ms

rewrite31.0ms

series465.0ms

simplify57.0ms

prune404.0ms

localize22.0ms

rewrite55.0ms

series1.4s

simplify139.0ms

prune658.0ms

localize23.0ms

rewrite27.0ms

series856.0ms

simplify55.0ms

prune579.0ms

localize18.0ms

rewrite35.0ms

series699.0ms

simplify96.0ms

prune564.0ms

regimes743.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling