Details

sample58.0ms

Algorithm

intervals

Results

13.0ms	117×	body	160	valid
12.0ms	214×	body	80	nan
8.0ms	139×	body	80	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize14.0ms

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×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `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 → 114

Calls

4 calls:

6.0ms	(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))))))
43.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ t l) 2.0)
56.0ms	(pow (/ Om Omc) 2.0)
22.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
315.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	709	1289
1	2087	1218
2	5001	1206

prune498.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (* (sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) 1)) (sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.2b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
64×	`sqrt-prod`
56×	`times-frac`
44×	`*-un-lft-identity`
38×	`add-cube-cbrt`
32×	`unpow-prod-down`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 124

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (* (sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) 1)) (sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
44.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ Om Omc) 2.0)
54.0ms	(pow (/ Om Omc) 2.0)
21.0ms	(asin (* (sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) 1)) (sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
548.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	582	1699
1	1696	1602
2	5002	1584

prune639.0ms

Pruning

7 alts after pruning (6 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))

rewrite61.0ms

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 125

Calls

4 calls:

42.0ms	(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))
5.0ms	(cbrt (pow (/ t l) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

316.0ms	(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)))))))
258.0ms	(cbrt (pow (/ t l) 2.0))
254.0ms	(cbrt (pow (/ t l) 2.0))
253.0ms	(cbrt (pow (/ t l) 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	523	2252
1	1233	2182
2	5001	2146

prune678.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.0b

localize18.0ms

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)))))

rewrite91.0ms

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 141

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))))))))
41.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
22.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
20.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

37.0ms	(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))))))))
339.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
334.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
334.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify132.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	544	2927
1	1275	2835
2	4488	2820
3	5001	2820

prune831.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.0b

regimes603.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	18
1	26	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

470.0ms	7966×	body	80	nan
434.0ms	3802×	body	160	valid
251.0ms	4198×	body	80	valid