Details

sample59.0ms

Algorithm

intervals

Results

16.0ms	110×	body	160	valid
13.0ms	239×	body	80	nan
9.0ms	146×	body	80	valid

simplify125.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.6b	(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)
6.0ms	(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)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ t l) 2.0)
63.0ms	(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))))))
304.0ms	(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

prune495.0ms

Filtered

126 candidates to 100 candidates (79.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0b	(log (exp (pow (/ Om Omc) 2.0)))
10.6b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0ms	(log (exp (pow (/ Om Omc) 2.0)))
67.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ Om Omc) 2.0)
21.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
57.0ms	(log (exp (pow (/ Om Omc) 2.0)))
313.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	533	1222
1	1557	1135
2	5001	1117

prune516.0ms

Filtered

121 candidates to 95 candidates (78.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.9b	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0b	(log (exp (pow (/ Om Omc) 2.0)))
10.6b	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
31×	`add-cube-cbrt`
26×	`unpow-prod-down`
24×	`sqrt-prod`
21×	`log-pow`
17×	`exp-prod`
10×	`pow1`
7×	`add-exp-log`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod` `div-inv` `difference-of-squares`
2×	`rem-sqrt-square` `pow-exp` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `flip-+`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(log (exp (pow (/ Om Omc) 2.0)))
67.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
60.0ms	(log (exp (pow (/ Om Omc) 2.0)))
313.0ms	(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	533	1222
1	1557	1135
2	5001	1117

prune578.0ms

Filtered

121 candidates to 95 candidates (78.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.2b	(pow (/ t l) 2.0)
0.9b	(asin (* (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) 1)) (sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.6b	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
96×	`times-frac`
70×	`sqrt-prod`
59×	`*-un-lft-identity`
56×	`difference-of-squares`
45×	`add-cube-cbrt`
41×	`unpow-prod-down`
15×	`sqr-pow`
12×	`associate-/l*`
9×	`add-exp-log`
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 → 166

Calls

4 calls:

61.0ms	(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(pow (/ t l) 2.0)
0.0ms	(asin (* (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) 1)) (sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
33.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
59.0ms	(pow (/ t l) 2.0)
39.0ms	(asin (* (sqrt (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) 1)) (sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
266.0ms	(sqrt (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	703	3094
1	2320	2957
2	5001	2938

prune746.0ms

Filtered

178 candidates to 123 candidates (69.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.4b

regimes809.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.1b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	14
1	22	14

end0.0ms

sample1.6s

Algorithm

intervals

Results

446.0ms	7979×	body	80	nan
425.0ms	3765×	body	160	valid
250.0ms	4235×	body	80	valid