Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	133×	body	160	valid
16.0ms	248×	body	80	nan
8.0ms	123×	body	80	valid

simplify127.0ms

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: 9.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(pow (/ Om Omc) 2.0)
1.0b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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:

3.0ms	(pow (/ t l) 2.0)
3.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
29.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ t l) 2.0)
59.0ms	(pow (/ Om Omc) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
318.0ms	(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

prune497.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(pow (/ Om Omc) 2.0)
1.0b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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:

4.0ms	(pow (/ t l) 2.0)
3.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
29.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
59.0ms	(pow (/ Om Omc) 2.0)
20.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
313.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	709	1290
1	2085	1218
2	5002	1206

prune563.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.2b

localize20.0ms

Local error

Found 4 expressions with local error:

8.1b	(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)))))))
30.1b	(cbrt (pow (/ t l) 2.0))
30.1b	(cbrt (pow (/ t l) 2.0))
30.1b	(cbrt (pow (/ t l) 2.0))

rewrite48.0ms

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:

29.0ms	(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)))))))
3.0ms	(cbrt (pow (/ t l) 2.0))
8.0ms	(cbrt (pow (/ t l) 2.0))
3.0ms	(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)))))))
268.0ms	(cbrt (pow (/ t l) 2.0))
263.0ms	(cbrt (pow (/ t l) 2.0))
268.0ms	(cbrt (pow (/ t l) 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	523	2251
1	1233	2182
2	5001	2146

prune816.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.2b

localize37.0ms

Local error

Found 4 expressions with local error:

8.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0)))) (cbrt (pow (/ t l) 2.0)))))))
22.8b	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
30.1b	(cbrt (pow (/ t l) 2.0))
30.1b	(cbrt (pow (/ t l) 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
47×	`times-frac`
43×	`cbrt-prod`
40×	`*-un-lft-identity`
37×	`unpow-prod-down`
34×	`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 → 117

Calls

4 calls:

30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0)))) (cbrt (pow (/ t l) 2.0)))))))
2.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
3.0ms	(cbrt (pow (/ t l) 2.0))
3.0ms	(cbrt (pow (/ t l) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

312.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0)))) (cbrt (pow (/ t l) 2.0)))))))
258.0ms	(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
256.0ms	(cbrt (pow (/ t l) 2.0))
256.0ms	(cbrt (pow (/ t l) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	647	3209
1	1475	3104
2	5002	3044

prune898.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.2b

regimes656.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.7s

Algorithm

intervals

Results

522.0ms	8093×	body	80	nan
479.0ms	3825×	body	160	valid
273.0ms	4175×	body	80	valid