Details

sample66.0ms

Algorithm

intervals

Results

18.0ms	262×	body	80	nan
17.0ms	121×	body	160	valid
9.0ms	135×	body	80	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4432	10
6	5002	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 10.9b

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))))
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
102×	`times-frac`
48×	`difference-of-squares`
46×	`sqrt-prod`
43×	`add-cube-cbrt`
37×	`unpow-prod-down`
36×	`distribute-lft-out`
18×	`sqrt-div` `associate-l`
16×	`associate-/l*`
13×	`sqr-pow`
12×	`distribute-lft-out--`
10×	`associate-/r*`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`rem-sqrt-square` `flip3--` `frac-2neg` `flip3-+` `div-exp` `pow-exp` `clear-num` `flip--` `flip-+`
1×	`cbrt-undiv` `pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `pow1/2` `div-sub`

Counts

4 → 189

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
26.0ms	(/ (- 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))))))
29.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ t l) 2.0)
218.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
329.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	695	2647
1	2139	2540
2	5001	2520

prune536.0ms

Filtered

201 candidates to 135 candidates (67.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	8	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	8	202

Merged error: 10.8b

Counts

202 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.8b	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.5b	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

1363×	`add-sqr-sqrt`
1195×	`*-un-lft-identity`
1097×	`times-frac`
1001×	`unpow-prod-down`
684×	`difference-of-squares`
672×	`associate-l`
498×	`sqrt-prod`
457×	`sqr-pow`
336×	`distribute-lft-out`
280×	`associate-r`
219×	`add-cube-cbrt`
155×	`pow-unpow`
152×	`difference-cubes`
76×	`distribute-lft-out--`
57×	`unswap-sqr`
56×	`*-commutative`
54×	`associate-/l*`
50×	`sqrt-div`
36×	`associate-/r*`
16×	`associate-/r/`
12×	`add-exp-log` `flip3-+` `flip-+`
9×	`add-cbrt-cube`
8×	`frac-times`
6×	`pow1`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`rem-sqrt-square` `div-exp` `div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `pow-exp` `clear-num` `flip--`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod`

Counts

4 → 1160

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
102.0ms	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
124.0ms	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ t l) 2.0)
731.0ms	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
40.0ms	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
933.0ms	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify401.0ms

Algorithm

egg-herbie

Counts

1172 → 1172

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	3063	37130
1	5001	35926

prune3.6s

Filtered

1172 candidates to 597 candidates (50.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1169	3	1172
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	1172	8	1180

Merged error: 10.8b

Counts

1180 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.8b	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.5b	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite569.0ms

Algorithm

rewrite-expression-head

Rules

1363×	`add-sqr-sqrt`
1195×	`*-un-lft-identity`
1097×	`times-frac`
1001×	`unpow-prod-down`
684×	`difference-of-squares`
672×	`associate-l`
498×	`sqrt-prod`
457×	`sqr-pow`
336×	`distribute-lft-out`
280×	`associate-r`
219×	`add-cube-cbrt`
155×	`pow-unpow`
152×	`difference-cubes`
76×	`distribute-lft-out--`
57×	`unswap-sqr`
56×	`*-commutative`
54×	`associate-/l*`
50×	`sqrt-div`
36×	`associate-/r*`
16×	`associate-/r/`
12×	`add-exp-log` `flip3-+` `flip-+`
9×	`add-cbrt-cube`
8×	`frac-times`
6×	`pow1`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`rem-sqrt-square` `div-exp` `div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `pow-exp` `clear-num` `flip--`
1×	`pow-to-exp` `asin-acos` `pow-pow` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod`

Counts

4 → 1160

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
102.0ms	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
123.0ms	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ t l) 2.0)
744.0ms	(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
40.0ms	(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
941.0ms	(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify403.0ms

Algorithm

egg-herbie

Counts

1172 → 1172

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	3063	37130
1	5001	35926

prune4.0s

Filtered

1172 candidates to 597 candidates (50.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1170	2	1172
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	1172	8	1180

Merged error: 10.8b

Counts

1180 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(asin (sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
9.5b	(sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

5522×	`sqrt-prod`
4932×	`add-sqr-sqrt`
3436×	`unpow-prod-down`
3061×	`associate-/l*`
3050×	`*-un-lft-identity`
2769×	`sqrt-div`
2455×	`frac-times`
2376×	`difference-of-squares`
1650×	`associate-l`
1586×	`sqr-pow`
1432×	`associate-/r*`
1414×	`times-frac`
838×	`associate-r`
745×	`add-cube-cbrt`
624×	`distribute-lft-out`
528×	`difference-cubes` `pow-unpow`
266×	`unswap-sqr`
264×	`distribute-lft-out--`
204×	`associate-/l/`
103×	`clear-num`
102×	`flip3--` `frac-2neg` `flip--`
75×	`*-commutative`
59×	`associate-*l/`
45×	`associate-*r/`
38×	`rem-sqrt-square`
10×	`associate-/r/` `hypot-def`
9×	`pow1` `flip3-+` `flip-+`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`un-div-inv` `div-inv`
1×	`asin-acos` `pow-prod-down`

Counts

4 → 3617

Calls

4 calls:

1.0ms	(asin (sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.1s	(sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
14.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

43.0ms	(asin (sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
934.0ms	(sqrt (* (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
191.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.8s

Algorithm

egg-herbie

Counts

3629 → 3629

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	8747	187919

prune22.6s

Filtered

3629 candidates to 2254 candidates (62.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	3627	2	3629
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	3629	8	3637

Merged error: 10.8b

Counts

3637 → 8

regimes947.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	23
1	32	23

end0.0ms

sample2.0s

Algorithm

intervals

Results

594.0ms	8034×	body	80	nan
572.0ms	3815×	body	160	valid
308.0ms	4185×	body	80	valid