Details

sample1.2s

Algorithm

intervals

Results

957.0ms	761×	body	10240	exit
131.0ms	1016×	body	80	nan
28.0ms	126×	body	160	valid
14.0ms	130×	body	80	valid

simplify123.0ms

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: 9.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite78.0ms

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:

3.0ms	(pow (/ t l) 2.0)
37.0ms	(/ (- 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))))))
31.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
215.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
323.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

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

prune580.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0)))))))
7.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0))))))
15.0b	(sqrt (/ t l))
15.0b	(sqrt (/ t l))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
56×	`sqrt-prod`
48×	`times-frac`
36×	`*-un-lft-identity`
30×	`add-cube-cbrt`
12×	`difference-of-squares`
7×	`pow1`
6×	`unpow-prod-down` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out--` `sqr-pow`
2×	`associate-/r/`
1×	`asin-acos` `flip3-+` `flip-+`

Counts

4 → 100

Calls

4 calls:

0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0)))))))
28.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0))))))
5.0ms	(sqrt (/ t l))
3.0ms	(sqrt (/ t l))

series436.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0)))))))
319.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0))))))
46.0ms	(sqrt (/ t l))
50.0ms	(sqrt (/ t l))

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	500	1627
1	1315	1527
2	5001	1520

prune545.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(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))))))))
2.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 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))))

rewrite42.0ms

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

series872.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(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))))))))
349.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
244.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
248.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune638.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.8b	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
22×	`sqrt-prod`
9×	`pow1` `sqrt-div`
7×	`distribute-lft-out`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`sqrt-pow1` `flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `div-inv`

Counts

4 → 94

Calls

4 calls:

51.0ms	(/ (+ (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))))
39.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

320.0ms	(/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
425.0ms	(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	323	1577
1	1199	1483
2	5001	1469

prune447.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.1b

regimes795.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	15
1	20	15

end0.0ms

sample36.5s

Algorithm

intervals

Results

29.3s	24096×	body	10240	exit
3.9s	31747×	body	80	nan
727.0ms	3859×	body	160	valid
450.0ms	4141×	body	80	valid