Details

sample86.0ms

Algorithm

intervals

Results

25.0ms	114×	body	160	valid
20.0ms	232×	body	80	nan
13.0ms	142×	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: 12.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite38.0ms

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))))))
15.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
97.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
140.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

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

prune453.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 12.5b

Counts

143 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
1.4b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite29.0ms

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))))))
15.0ms	(/ (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))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
14.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
140.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (45.0ms)

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

prune438.0ms

Filtered

107 candidates to 163 candidates (-52.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	163	8	171

Merged error: 12.5b

Counts

171 → 8

localize149.0ms

Local error

Found 4 expressions with local error:

11.0b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
16.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
21×	`add-sqr-sqrt`
18×	`cbrt-div`
14×	`times-frac`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`cbrt-prod` `flip3-+` `flip-+`
8×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`rem-sqrt-square` `pow1/3`
2×	`unpow-prod-down` `associate-r/` `associate-l/`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

18.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
68.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
69.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify103.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	423	1410
1	970	1361
2	3666	1346
3	5001	1340

prune510.0ms

Filtered

74 candidates to 87 candidates (-17.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	87	8	95

Merged error: 12.5b

Counts

95 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

11.6b	(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)))))))
17.0b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite89.0ms

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:

46.0ms	(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)))))
12.0ms	(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)))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(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)))))))
153.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
153.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
152.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (36.0ms)

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

prune913.0ms

Filtered

127 candidates to 160 candidates (-26.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	160	8	168

Merged error: 12.5b

Counts

168 → 8

regimes1.5s

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample2.5s

Algorithm

intervals

Results

720.0ms	8067×	body	80	nan
686.0ms	3806×	body	160	valid
382.0ms	4194×	body	80	valid

Details

sample86.0ms

simplify126.0ms

prune5.0ms

localize14.0ms

rewrite38.0ms

series266.0ms

simplify65.0ms

prune453.0ms

localize17.0ms

rewrite29.0ms

series215.0ms

simplify68.0ms

prune438.0ms

localize149.0ms

rewrite27.0ms

series360.0ms

simplify103.0ms

prune510.0ms

localize23.0ms

rewrite89.0ms

series600.0ms

simplify63.0ms

prune913.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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