Details

sample92.0ms

Algorithm

intervals

Results

30.0ms	136×	body	160	valid
28.0ms	225×	body	80	nan
13.0ms	120×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite41.0ms

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:

3.0ms	(pow (/ Om Omc) 2.0)
4.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
30.0ms	(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:

64.0ms	(pow (/ Om Omc) 2.0)
64.0ms	(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))))))
315.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (41.0ms)

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

prune465.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.4b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.8b	(log (exp (pow (/ Om Omc) 2.0)))
7.2b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 101

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
67.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
64.0ms	(log (exp (pow (/ Om Omc) 2.0)))
311.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	624	1169
1	1863	1079
2	5002	1061

prune485.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.7b	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.8b	(log (exp (pow (/ Om Omc) 2.0)))
6.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
69×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `times-frac`
48×	`add-cube-cbrt`
25×	`log-pow`
17×	`exp-prod`
14×	`distribute-lft-out--`
13×	`pow1` `unpow-prod-down`
9×	`associate-/l*`
7×	`difference-of-squares`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`log-prod`
2×	`flip3-+` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `flip--` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

0.0ms	(asin (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
99.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series578.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(asin (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
314.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
65.0ms	(log (exp (pow (/ Om Omc) 2.0)))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	544	2371
1	1624	2184
2	5002	2176

prune552.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.8b	(log (exp (pow (/ Om Omc) 2.0)))
13.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`log-pow`
17×	`add-cube-cbrt` `exp-prod` `*-un-lft-identity`
13×	`unpow-prod-down`
10×	`cbrt-prod`
9×	`times-frac`
6×	`pow1` `cbrt-div` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `flip3-+` `pow1/3` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`pow1/2` `rem-log-exp` `div-inv` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

4.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.0ms	(log (exp (pow (/ Om Omc) 2.0)))
1.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series807.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
67.0ms	(log (exp (pow (/ Om Omc) 2.0)))
246.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify131.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	376	684
1	1105	635
2	4979	625
3	5002	625

prune500.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

regimes526.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample2.8s

Algorithm

intervals

Results

977.0ms	3803×	body	160	valid
908.0ms	8132×	body	80	nan
466.0ms	4197×	body	80	valid