Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	262×	body	80	nan
16.0ms	113×	body	160	valid
10.0ms	143×	body	80	valid

simplify124.0ms

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: 11.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(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))))))
11.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite32.0ms

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:

5.0ms	(pow (/ Om Omc) 2.0)
9.0ms	(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))))))
13.0ms	(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:

59.0ms	(pow (/ Om Omc) 2.0)
63.0ms	(pow (/ t l) 2.0)
16.0ms	(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)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

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

prune628.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (sqrt (/ (- 1.0 (exp (log (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.7b	(exp (log (pow (/ Om Omc) 2.0)))
11.0b	(sqrt (/ (- 1.0 (exp (log (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
33.4b	(log (pow (/ Om Omc) 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
49×	`times-frac`
46×	`log-prod`
40×	`*-un-lft-identity`
34×	`add-cube-cbrt`
33×	`sqrt-prod`
32×	`unpow-prod-down`
29×	`exp-sum`
15×	`difference-of-squares`
8×	`add-exp-log`
5×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `exp-prod` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `log-pow`
1×	`pow-to-exp` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `flip-+` `rem-exp-log`

Counts

4 → 119

Calls

4 calls:

1.0ms	(asin (sqrt (/ (- 1.0 (exp (log (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.0ms	(exp (log (pow (/ Om Omc) 2.0)))
15.0ms	(sqrt (/ (- 1.0 (exp (log (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.0ms	(log (pow (/ Om Omc) 2.0))

series470.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(asin (sqrt (/ (- 1.0 (exp (log (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
66.0ms	(exp (log (pow (/ Om Omc) 2.0)))
316.0ms	(sqrt (/ (- 1.0 (exp (log (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
71.0ms	(log (pow (/ Om Omc) 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	677	1599
1	1705	1509
2	5001	1485

prune562.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (sqrt (- 1.0 (exp (log (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.7b	(exp (log (pow (/ Om Omc) 2.0)))
10.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
33.4b	(log (pow (/ Om Omc) 2.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

133×	`add-sqr-sqrt`
105×	`sqrt-prod`
97×	`times-frac`
76×	`*-un-lft-identity`
62×	`add-cube-cbrt` `log-prod`
45×	`exp-sum`
40×	`unpow-prod-down`
35×	`difference-of-squares`
12×	`associate-/l*`
10×	`add-exp-log`
9×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`sqrt-div` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `rem-log-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `log-pow` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 188

Calls

4 calls:

21.0ms	(/ (sqrt (- 1.0 (exp (log (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.0ms	(exp (log (pow (/ Om Omc) 2.0)))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(log (pow (/ Om Omc) 2.0))

series638.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ (sqrt (- 1.0 (exp (log (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
59.0ms	(exp (log (pow (/ Om Omc) 2.0)))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
74.0ms	(log (pow (/ Om Omc) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	673	3115
1	1905	2925
2	5001	2886

prune735.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 11.5b

localize22.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
33.4b	(log (pow (/ Om Omc) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`log-prod`
16×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
13×	`unpow-prod-down`
9×	`times-frac`
8×	`pow1` `add-exp-log` `sqrt-div`
6×	`sqrt-pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-exp`
1×	`pow-to-exp` `div-exp` `log-pow` `div-inv` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

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))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(log (pow (/ Om Omc) 2.0))

series678.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
178.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
177.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
70.0ms	(log (pow (/ Om Omc) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	442	751
1	1330	714
2	5001	714

prune515.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 11.5b

regimes352.0ms

Accuracy

0% (0.1b remaining)

Error of 9.9b against oracle of 9.8b and baseline of 9.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

548.0ms	7843×	body	80	nan
545.0ms	3826×	body	160	valid
304.0ms	4174×	body	80	valid