Details

sample60.0ms

Algorithm

intervals

Results

17.0ms	249×	body	80	nan
14.0ms	122×	body	160	valid
8.0ms	134×	body	80	valid

simplify126.0ms

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: 10.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite41.0ms

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×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `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 → 114

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
4.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
63.0ms	(pow (/ Om Omc) 2.0)
16.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
310.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	709	1289
1	2087	1218
2	5001	1206

prune499.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.7b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite56.0ms

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:

3.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
42.0ms	(/ (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))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ Om Omc) 2.0)
16.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
310.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
178.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

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

prune617.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `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 → 114

Calls

4 calls:

3.0ms	(pow (/ t l) 2.0)
4.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
28.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
60.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
319.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	709	1289
1	2087	1218
2	5001	1206

prune581.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.8b

localize27.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.6b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

320×	`sqrt-prod`
192×	`add-sqr-sqrt`
152×	`times-frac`
100×	`*-un-lft-identity`
76×	`add-cube-cbrt`
48×	`difference-of-squares`
24×	`unpow-prod-down`
12×	`rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
10×	`sqrt-div`
8×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`div-inv`

Counts

4 → 212

Calls

4 calls:

36.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
34.0ms	(sqrt (/ (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))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

347.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
336.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify74.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	467	4376
1	1152	4302
2	5001	4220

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.8b

regimes720.0ms

Accuracy

0% (0.1b remaining)

Error of 10.9b against oracle of 10.8b and baseline of 10.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

458.0ms	7890×	body	80	nan
423.0ms	3714×	body	160	valid
249.0ms	4286×	body	80	valid