Details

sample84.0ms

Algorithm

intervals

Results

28.0ms	266×	body	80	nan
19.0ms	108×	body	160	valid
13.0ms	148×	body	80	valid

simplify131.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 12.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite45.0ms

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:

5.0ms	(pow (/ Om Omc) 2.0)
21.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ Om Omc) 2.0)
205.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
455.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	650	1948
1	2076	1846
2	5001	1827

prune525.0ms

Filtered

150 candidates to 123 candidates (82.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	144	6	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	6	151

Merged error: 12.2b

Counts

151 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite43.0ms

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:

5.0ms	(pow (/ Om Omc) 2.0)
19.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ Om Omc) 2.0)
206.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
305.0ms	(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 (47.0ms)

Iter	Nodes	Cost
0	650	1948
1	2076	1846
2	5001	1827

prune590.0ms

Filtered

150 candidates to 123 candidates (82.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	149	7	156

Merged error: 12.2b

Counts

156 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

10.7b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
17.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
21×	`add-sqr-sqrt`
18×	`cbrt-div`
14×	`times-frac`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`cbrt-prod` `flip3-+` `flip-+`
8×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`rem-sqrt-square` `pow1/3`
2×	`unpow-prod-down` `associate-r/` `associate-l/`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

18.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 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))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

447.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
244.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
244.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
245.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify100.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	375	1422
1	863	1367
2	3129	1355
3	5001	1352

prune503.0ms

Filtered

95 candidates to 85 candidates (89.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Merged error: 12.2b

Counts

102 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.1b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
17.6b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.6b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
92×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
33×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
6×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 141

Calls

4 calls:

1.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
14.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

37.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
332.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
344.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
339.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify136.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	544	2927
1	1275	2835
2	4488	2820
3	5001	2820

prune726.0ms

Filtered

153 candidates to 134 candidates (87.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	153	7	160

Merged error: 12.2b

Counts

160 → 7

regimes628.0ms

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	20	12
1	20	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

716.0ms	7876×	body	80	nan
694.0ms	3818×	body	160	valid
379.0ms	4182×	body	80	valid