Details

sample97.0ms

Algorithm

intervals

Results

31.0ms	273×	body	80	nan
24.0ms	107×	body	160	valid
17.0ms	149×	body	80	valid

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite91.0ms

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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `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 → 138

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
50.0ms	(/ (- 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))))))
32.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(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))))))
468.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	664	1948
1	2106	1846
2	5001	1828

prune628.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
10.8b	(sqrt (expm1 (log1p (/ (- 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`
37×	`times-frac`
34×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`unpow-prod-down`
16×	`difference-of-squares`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `add-cbrt-cube`
5×	`sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `sqrt-prod`
2×	`div-exp` `pow-exp` `associate-/r/` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `clear-num` `flip--` `flip-+`

Counts

4 → 109

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
50.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms	(asin (sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

60.0ms	(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 (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
978.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	663	1424
1	2171	1328
2	5001	1322

prune556.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.5b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.6b	(asin (sqrt (expm1 (log1p (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
10.8b	(sqrt (expm1 (log1p (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
46×	`times-frac`
41×	`*-un-lft-identity`
35×	`sqrt-prod`
33×	`add-cube-cbrt`
21×	`unpow-prod-down`
16×	`difference-of-squares`
11×	`associate-/l*`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
5×	`sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `associate-/r*`
2×	`sqrt-div` `div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 118

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
37.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.0ms	(asin (sqrt (expm1 (log1p (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
1.0ms	(sqrt (expm1 (log1p (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ t l) 2.0)
209.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))
16.0ms	(asin (sqrt (expm1 (log1p (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
943.0ms	(sqrt (expm1 (log1p (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fma (pow (/ t l) 2.0) 2.0 1.0))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	529	1701
1	1477	1608
2	5001	1608

prune628.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.1b

localize25.0ms

Local error

Found 4 expressions with local error:

10.8b	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))))
31.4b	(cbrt (pow (/ t l) 2.0))
31.4b	(cbrt (pow (/ t l) 2.0))
31.4b	(cbrt (pow (/ t l) 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`unpow-prod-down`
30×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 96

Calls

4 calls:

1.0ms	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))))
3.0ms	(cbrt (pow (/ t l) 2.0))
3.0ms	(cbrt (pow (/ t l) 2.0))
3.0ms	(cbrt (pow (/ t l) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.0s	(sqrt (expm1 (log1p (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))))
271.0ms	(cbrt (pow (/ t l) 2.0))
271.0ms	(cbrt (pow (/ t l) 2.0))
270.0ms	(cbrt (pow (/ t l) 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	345	1183
1	766	1142
2	2888	1136
3	5001	1127

prune590.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.1b

regimes732.0ms

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	17
1	20	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

916.0ms	8082×	body	80	nan
873.0ms	3798×	body	160	valid
477.0ms	4202×	body	80	valid