Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	125×	body	160	valid
15.0ms	253×	body	80	nan
8.0ms	131×	body	80	valid

simplify122.0ms

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: 10.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(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))))))
9.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite59.0ms

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:

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

series438.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (/ Om Omc) 2.0)
59.0ms	(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))))))
308.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

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

prune448.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.6b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 151

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
62.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow (/ t l) 2.0)
21.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
304.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
173.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	619	2493
1	1983	2321
2	5001	2311

prune553.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
0.6b	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

150×	`add-sqr-sqrt`
105×	`unpow-prod-down`
101×	`sqrt-prod`
80×	`difference-of-squares`
77×	`times-frac`
60×	`cube-prod`
52×	`associate-/l*`
45×	`sqr-pow`
37×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`sqrt-div`
12×	`add-exp-log`
10×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow` `div-exp`
2×	`difference-cubes` `cbrt-undiv` `associate-r/` `associate-l/` `pow-exp` `div-inv` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-unprod` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod`

Counts

4 → 181

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
219.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (/ t l) 2.0)
46.0ms	(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0))))))))
885.0ms	(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (+ (* 1.0 1.0) (+ (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0)) (* 1.0 (pow (/ Om Omc) 2.0)))))))
172.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify118.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	992	4667
1	3595	4497
2	5003	4497

prune888.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.0b

localize19.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.0b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

9.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series941.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
369.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
173.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
169.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	201	720
1	658	700
2	2858	696
3	5002	688

prune372.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.0b

regimes716.0ms

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	18	10
1	18	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

481.0ms	8091×	body	80	nan
443.0ms	3762×	body	160	valid
256.0ms	4238×	body	80	valid