Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	309×	body	80	nan
16.0ms	130×	body	160	valid
7.0ms	126×	body	80	valid

simplify126.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
39.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
33.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ t l) 2.0)
216.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
331.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	648	1882
1	2047	1787
2	5001	1774

prune754.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
56×	`times-frac`
54×	`sqrt-prod`
41×	`*-un-lft-identity`
31×	`cbrt-prod`
29×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
6×	`cbrt-div` `distribute-lft-out--` `sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
2×	`pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 101

Calls

4 calls:

0.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
32.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series869.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
343.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
243.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
248.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	545	2043
1	1354	1953
2	5001	1942

prune653.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.4b

localize24.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.6b	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

188×	`sqrt-prod`
160×	`add-sqr-sqrt`
112×	`times-frac`
76×	`*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`unpow-prod-down`
12×	`sqr-pow`
10×	`sqrt-div`
8×	`pow1` `rem-sqrt-square`
6×	`distribute-lft-out` `distribute-lft-out--`
4×	`add-exp-log` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`div-inv`

Counts

4 → 164

Calls

4 calls:

35.0ms	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
42.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (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))))

series1.2s

Counts

4 → 12

Calls

4 calls:

398.0ms	(sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
408.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	549	3616
1	1346	3530
2	5001	3474

prune742.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 9.4b

localize31.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
6×	`pow1` `sqrt-div`
4×	`add-exp-log` `cbrt-div` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 59

Calls

4 calls:

2.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series875.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
188.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
247.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify111.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	243	688
1	800	654
2	3705	646
3	5002	643

prune529.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 9.4b

regimes589.0ms

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	18	10
1	18	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

482.0ms	8008×	body	80	nan
449.0ms	3733×	body	160	valid
266.0ms	4267×	body	80	valid