Details

sample61.0ms

Algorithm

intervals

Results

14.0ms	117×	body	160	valid
14.0ms	214×	body	80	nan
9.0ms	139×	body	80	valid

simplify125.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite60.0ms

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:

8.0ms	(pow (/ t l) 2.0)
6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
41.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (/ t l) 2.0)
64.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
321.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

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

prune478.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize21.0ms

Local error

Found 4 expressions with local error:

9.2b	(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)))))))
30.9b	(cbrt (pow (/ t l) 2.0))
30.9b	(cbrt (pow (/ t l) 2.0))
30.9b	(cbrt (pow (/ t l) 2.0))

rewrite65.0ms

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:

45.0ms	(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)))))))
5.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

320.0ms	(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)))))))
264.0ms	(cbrt (pow (/ t l) 2.0))
266.0ms	(cbrt (pow (/ t l) 2.0))
415.0ms	(cbrt (pow (/ t l) 2.0))

simplify123.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	516	2189
1	1205	2120
2	4830	2084
3	5001	2075

prune675.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.0b

localize26.0ms

Local error

Found 4 expressions with local error:

9.2b	(sqrt (/ (cbrt (- 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)))))))
30.9b	(cbrt (pow (/ t l) 2.0))
30.9b	(cbrt (pow (/ t l) 2.0))
30.9b	(cbrt (pow (/ t l) 2.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

46.0ms	(sqrt (/ (cbrt (- 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)))))))
5.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))
5.0ms	(cbrt (pow (/ t l) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

419.0ms	(sqrt (/ (cbrt (- 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)))))))
268.0ms	(cbrt (pow (/ t l) 2.0))
268.0ms	(cbrt (pow (/ t l) 2.0))
269.0ms	(cbrt (pow (/ t l) 2.0))

simplify111.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	563	2656
1	1270	2586
2	4327	2565
3	5001	2516

prune839.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(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))))))))
1.5b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.2b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.2b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite97.0ms

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))))))))
46.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
21.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
21.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

42.0ms	(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))))))))
341.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
340.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
348.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify122.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 3 (98.0ms)

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

prune833.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.0b

regimes691.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.9s

Algorithm

intervals

Results

501.0ms	7966×	body	80	nan
475.0ms	3802×	body	160	valid
270.0ms	4198×	body	80	valid