Details

sample82.0ms

Algorithm

intervals

Results

25.0ms	276×	body	80	nan
22.0ms	120×	body	160	valid
12.0ms	136×	body	80	valid

simplify124.0ms

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: 10.1b

Counts

2 → 1

localize21.0ms

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))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(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)
17.0ms	(/ (- 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))))))
14.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
219.0ms	(/ (- 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))))))
470.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (47.0ms)

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

prune574.0ms

Filtered

150 candidates to 123 candidates (82.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	143	7	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	7	151

Merged error: 10.0b

Counts

151 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.7b	(log (exp (pow (/ Om Omc) 2.0)))
8.7b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
46×	`times-frac`
34×	`add-cube-cbrt`
25×	`log-pow`
24×	`sqrt-prod`
17×	`exp-prod`
14×	`distribute-lft-out--`
13×	`pow1` `unpow-prod-down`
7×	`difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `asin-acos` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `sqr-pow`

Counts

4 → 125

Calls

4 calls:

22.0ms	(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0ms	(log (exp (pow (/ Om Omc) 2.0)))
16.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
21.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
64.0ms	(log (exp (pow (/ Om Omc) 2.0)))
334.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	568	1833
1	1707	1685
2	5001	1648

prune507.0ms

Filtered

137 candidates to 107 candidates (78.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	137	7	144

Merged error: 10.0b

Counts

144 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite35.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 159

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
19.0ms	(/ (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))))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ Om Omc) 2.0)
333.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
187.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	624	2554
1	2015	2381
2	5002	2370

prune555.0ms

Filtered

171 candidates to 115 candidates (67.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Merged error: 10.0b

Counts

178 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

9.6b	(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)))))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.8b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

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:

19.0ms	(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)))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(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:

453.0ms	(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)))))))
255.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
249.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
250.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify95.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (81.0ms)

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

prune507.0ms

Filtered

95 candidates to 85 candidates (89.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	95	7	102

Merged error: 10.0b

Counts

102 → 7

regimes726.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

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

737.0ms	7898×	body	80	nan
713.0ms	3790×	body	160	valid
390.0ms	4210×	body	80	valid