Details

sample65.0ms

Algorithm

intervals

Results

16.0ms	120×	body	160	valid
15.0ms	267×	body	80	nan
8.0ms	136×	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: 10.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite57.0ms

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))))))
41.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
61.0ms	(pow (/ t l) 2.0)
24.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
345.0ms	(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 (43.0ms)

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

prune454.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.9b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite80.0ms

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:

7.0ms	(pow (/ t l) 2.0)
60.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (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))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series616.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ t l) 2.0)
340.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
20.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
190.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (43.0ms)

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

prune551.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite58.0ms

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

series512.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(pow (/ Om Omc) 2.0)
66.0ms	(pow (/ t l) 2.0)
19.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
349.0ms	(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 (42.0ms)

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

prune437.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (* (sqrt (pow (/ t l) 2.0)) (sqrt (pow (/ t l) 2.0))))))))
9.3b	(sqrt (+ 1.0 (* 2.0 (* (sqrt (pow (/ t l) 2.0)) (sqrt (pow (/ t l) 2.0))))))
18.7b	(sqrt (pow (/ t l) 2.0))
18.7b	(sqrt (pow (/ t l) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

37×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
9×	`rem-sqrt-square`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`sqrt-pow1` `pow1/2`
2×	`sqrt-div` `div-inv`
1×	`asin-acos` `flip3-+` `flip-+`

Counts

4 → 83

Calls

4 calls:

1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (* (sqrt (pow (/ t l) 2.0)) (sqrt (pow (/ t l) 2.0))))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (* (sqrt (pow (/ t l) 2.0)) (sqrt (pow (/ t l) 2.0))))))
8.0ms	(sqrt (pow (/ t l) 2.0))
8.0ms	(sqrt (pow (/ t l) 2.0))

series763.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (* (sqrt (pow (/ t l) 2.0)) (sqrt (pow (/ t l) 2.0))))))))
190.0ms	(sqrt (+ 1.0 (* 2.0 (* (sqrt (pow (/ t l) 2.0)) (sqrt (pow (/ t l) 2.0))))))
277.0ms	(sqrt (pow (/ t l) 2.0))
276.0ms	(sqrt (pow (/ t l) 2.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	437	1000
1	1192	947
2	5001	947

prune470.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.4b

regimes660.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	16
1	21	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

449.0ms	8125×	body	80	nan
420.0ms	3825×	body	160	valid
236.0ms	4175×	body	80	valid