Details

sample72.0ms

Algorithm

intervals

Results

22.0ms	262×	body	80	nan
16.0ms	113×	body	160	valid
11.0ms	143×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(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))))))
11.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite26.0ms

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:

4.0ms	(pow (/ Om Omc) 2.0)
4.0ms	(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)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ Om Omc) 2.0)
62.0ms	(pow (/ t l) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
324.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (43.0ms)

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

prune499.0ms

Filtered

126 candidates to 100 candidates (79.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

5.0ms	(pow (/ Om Omc) 2.0)
5.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0ms	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ Om Omc) 2.0)
59.0ms	(pow (/ t l) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
336.0ms	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	631	1213
1	1903	1132
2	5002	1120

prune511.0ms

Filtered

117 candidates to 91 candidates (77.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.5b	(asin (/ (sqrt (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.6b	(/ (sqrt (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.6b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

65×	`sqrt-prod`
60×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
57×	`times-frac`
45×	`add-cube-cbrt`
13×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
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--` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (/ (sqrt (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.0ms	(/ (sqrt (- 1.0 (expm1 (log1p (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))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ t l) 2.0)
16.0ms	(asin (/ (sqrt (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
341.0ms	(/ (sqrt (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
177.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	601	2344
1	1992	2174
2	5002	2166

prune591.0ms

Filtered

150 candidates to 99 candidates (66.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 11.5b

localize22.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.1b	(sqrt (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.0b	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

136×	`sqrt-prod`
80×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
64×	`times-frac`
42×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
8×	`associate-/r/`
6×	`pow1/2` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 152

Calls

4 calls:

8.0ms	(sqrt (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0ms	(sqrt (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0ms	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0ms	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

294.0ms	(sqrt (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
294.0ms	(sqrt (sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
345.0ms	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
354.0ms	(sqrt (/ (- 1.0 (expm1 (log1p (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	324	2924
1	689	2832
2	1953	2812
3	5001	2788

prune875.0ms

Filtered

164 candidates to 124 candidates (75.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 11.5b

regimes611.0ms

Accuracy

0% (0.1b remaining)

Error of 9.9b against oracle of 9.8b and baseline of 9.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.9s

Algorithm

intervals

Results

556.0ms	3826×	body	160	valid
541.0ms	7843×	body	80	nan
295.0ms	4174×	body	80	valid