Details

sample86.0ms

Algorithm

intervals

Results

25.0ms	124×	body	160	valid
24.0ms	233×	body	80	nan
14.0ms	132×	body	80	valid

simplify120.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite38.0ms

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)
3.0ms	(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))))))
27.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
12.0ms	(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))))))
154.0ms	(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 (41.0ms)

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

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.5b	(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)
5.0ms	(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))))))
27.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
14.0ms	(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))))))
152.0ms	(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

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.4b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.6b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite51.0ms

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)
38.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms	(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))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ Om Omc) 2.0)
153.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
53.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (41.0ms)

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

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.6b	(asin (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.6b	(log (exp (pow (/ Om Omc) 2.0)))
11.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

95.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms	(asin (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0ms	(asin (/ (sqrt (- 1.0 (log (exp (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
53.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	563	2444
1	1676	2256
2	5001	2247

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.2b

regimes2.0s

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	20	12
1	20	12

end0.0ms

sample2.5s

Algorithm

intervals

Results

823.0ms	7995×	body	80	nan
783.0ms	3806×	body	160	valid
430.0ms	4194×	body	80	valid