Details

sample11.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.169922%

Guaranteed chance to sample good point: 46.36188%

Results

23.0ms	126×	body	160	valid
15.0ms	131×	body	80	nan
12.0ms	130×	body	80	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	49	10
2	101	10
3	279	10
4	1029	10
5	4384	10
6	5002	10

prune5.0ms

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: 12.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.5b	(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)))))

rewrite33.0ms

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×	`associate-/r/` `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 → 130

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
11.0ms	(/ (- 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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
91.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
133.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	662	1889
1	2099	1789
2	5002	1774

prune398.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Merged error: 12.4b

Counts

143 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.5b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.5b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

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×	`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 → 151

Calls

4 calls:

4.0ms	(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))))))
16.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
13.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
132.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
45.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	693	2519
1	2331	2342
2	5001	2330

prune390.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	163	6	169

Merged error: 12.4b

Counts

169 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

5.5b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.5b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
63.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
45.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify114.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	262	796
1	822	778
2	3917	772
3	5002	764

prune291.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	84	6	90

Merged error: 12.4b

Counts

90 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

11.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.4b	(sqrt (pow (/ Om Omc) 2.0))
17.4b	(sqrt (pow (/ Om Omc) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`flip3-+` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(sqrt (pow (/ Om Omc) 2.0))
4.0ms	(sqrt (pow (/ Om Omc) 2.0))

series185.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
45.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
45.0ms	(sqrt (pow (/ Om Omc) 2.0))
47.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	448	784
1	1229	764
2	5001	758

prune457.0ms

Filtered

88 candidates to 102 candidates (-15.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	102	6	108

Merged error: 12.4b

Counts

108 → 6

regimes1.1s

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	18	10
1	18	10

end0.0ms

sample13.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.169922%

Guaranteed chance to sample good point: 46.36188%

Results

728.0ms	3764×	body	160	valid
407.0ms	4236×	body	80	valid
401.0ms	4164×	body	80	nan

Details

sample11.8s

simplify126.0ms

prune5.0ms

localize14.0ms

rewrite33.0ms

series250.0ms

simplify64.0ms

prune398.0ms

localize15.0ms

rewrite30.0ms

series203.0ms

simplify70.0ms

prune390.0ms

localize18.0ms

rewrite13.0ms

series217.0ms

simplify114.0ms

prune291.0ms

localize22.0ms

rewrite16.0ms

series185.0ms

simplify40.0ms

prune457.0ms

regimes1.1s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample13.9s

Profiling