Details

sample104.0ms

Algorithm

intervals

Results

23.0ms	259×	body	80	nan
22.0ms	122×	body	160	valid
12.0ms	134×	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

prune8.0ms

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: 8.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(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))))))
7.0b	(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×	`pow-exp` `add-cbrt-cube` `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 → 106

Calls

4 calls:

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

series186.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (/ t l) 2.0)
13.0ms	(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))))))
142.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	724	1249
1	2152	1176
2	5001	1152

prune313.0ms

Filtered

92 candidates to 118 candidates (-28.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Merged error: 7.9b

Counts

119 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.9b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.9b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.4b	(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 (/ Om Omc) 2.0)
15.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (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))))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (/ Om Omc) 2.0)
138.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (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))))))
50.0ms	(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	689	2520
1	2332	2350
2	5001	2330

prune386.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	163	7	170

Merged error: 7.9b

Counts

170 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.5b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.5b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
66×	`sqrt-prod`
56×	`times-frac`
42×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
8×	`pow1`
6×	`rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r/` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

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

series351.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
139.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
34.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
37.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify94.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	388	1928
1	920	1854
2	3298	1846
3	5003	1822

prune580.0ms

Filtered

100 candidates to 122 candidates (-22.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	4	4
Picked	1	0	1
Done	1	1	2
Total	118	11	129

Merged error: 7.9b

Counts

129 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.5b	(sqrt (asin (* (fabs (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
7.5b	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
75×	`sqrt-prod`
66×	`times-frac`
48×	`*-un-lft-identity`
36×	`add-cube-cbrt`
25×	`cbrt-prod`
24×	`difference-of-squares`
12×	`unpow-prod-down`
8×	`pow1`
7×	`rem-sqrt-square`
6×	`distribute-lft-out--` `sqr-pow`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r/` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 120

Calls

4 calls:

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

series377.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (/ (cbrt (- 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)))))
51.0ms	(sqrt (asin (* (fabs (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
39.0ms	(sqrt (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	652	2357
1	1498	2275
2	5002	2268

prune756.0ms

Filtered

111 candidates to 132 candidates (-18.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	132	11	143

Merged error: 7.9b

Counts

143 → 11

regimes1.9s

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

sample2.4s

Algorithm

intervals

Results

705.0ms	7877×	body	80	nan
690.0ms	3768×	body	160	valid
392.0ms	4232×	body	80	valid

Details

sample104.0ms

simplify126.0ms

prune8.0ms

localize14.0ms

rewrite26.0ms

series186.0ms

simplify55.0ms

prune313.0ms

localize15.0ms

rewrite30.0ms

series217.0ms

simplify68.0ms

prune386.0ms

localize20.0ms

rewrite32.0ms

series351.0ms

simplify94.0ms

prune580.0ms

localize28.0ms

rewrite34.0ms

series377.0ms

simplify54.0ms

prune756.0ms

regimes1.9s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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