Details

analyze1.4s

Algorithm: search

sample67.0ms

Algorithm

intervals

Results

21.0ms	115×	body	160	valid
16.0ms	169×	body	80	nan
13.0ms	141×	body	80	valid

simplify127.0ms

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: 11.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.7b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite36.0ms

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:

5.0ms	(pow (/ t l) 2.0)
12.0ms	(/ (- 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))))))
14.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (/ t l) 2.0)
93.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
135.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

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

prune411.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Merged error: 11.8b

Counts

143 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
10.2b	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-div` `sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`frac-times` `asin-acos` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 52

Calls

4 calls:

1.0ms	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
20.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 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))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
138.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
50.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify114.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	340	833
1	1025	771
2	4848	765
3	5001	765

prune222.0ms

Filtered

53 candidates to 64 candidates (-20.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	64	8	72

Merged error: 11.8b

Counts

72 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

120×	`sqrt-prod`
104×	`add-sqr-sqrt`
78×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
10×	`pow1` `rem-sqrt-square` `sqrt-div`
9×	`sqrt-pow1`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow-flip`
2×	`div-inv`
1×	`inv-pow`

Counts

4 → 140

Calls

4 calls:

6.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms	(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))))
4.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
130.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
50.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	605	2292
1	1651	2239
2	5001	2188

prune501.0ms

Filtered

101 candidates to 152 candidates (-50.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	152	8	160

Merged error: 11.8b

Counts

160 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
16.4b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.4b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.4b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
90×	`cbrt-prod`
81×	`times-frac`
58×	`*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`difference-of-squares`
24×	`pow1`
18×	`unpow-prod-down`
15×	`cbrt-div` `sqrt-pow1`
12×	`pow1/3`
9×	`pow-prod-up` `distribute-lft-out--` `sqr-pow`
7×	`sqrt-div`
6×	`pow-plus` `associate-/r/`
5×	`frac-times` `pow-prod-down` `associate-*l/`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-*r/` `pow-sqr` `flip-+` `div-inv`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 148

Calls

4 calls:

44.0ms	(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (* (* (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
147.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
145.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
147.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	418	2874
1	1052	2786
2	5001	2729

prune845.0ms

Filtered

128 candidates to 160 candidates (-25.0%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	160	8	168

Merged error: 11.8b

Counts

168 → 8

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

analyze1.4s

Algorithm: search

sample1.9s

Algorithm

intervals

Results

717.0ms	3883×	body	160	valid
455.0ms	4749×	body	80	nan
386.0ms	4117×	body	80	valid

Details

analyze1.4s

sample67.0ms

simplify127.0ms

prune5.0ms

localize14.0ms

rewrite36.0ms

series257.0ms

simplify63.0ms

prune411.0ms

localize18.0ms

rewrite27.0ms

series250.0ms

simplify114.0ms

prune222.0ms

localize19.0ms

rewrite33.0ms

series303.0ms

simplify60.0ms

prune501.0ms

localize22.0ms

rewrite82.0ms

series573.0ms

simplify64.0ms

prune845.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.4s

sample1.9s

Profiling