Details

sample101.0ms

Algorithm

intervals

Results

31.0ms	126×	body	160	valid
31.0ms	214×	body	80	nan
18.0ms	130×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.2b	(pow (/ t l) 2.0)
0.3b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite91.0ms

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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `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 → 138

Calls

4 calls:

52.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(pow (/ t l) 2.0)
0.0ms	(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)))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
63.0ms	(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))))))
327.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	664	1948
1	2106	1846
2	5001	1828

prune623.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.3b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite59.0ms

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×	`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--`

Counts

4 → 159

Calls

4 calls:

7.0ms	(pow (/ t l) 2.0)
41.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms	(asin (/ (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))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ t l) 2.0)
323.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	638	2554
1	2044	2381
2	5001	2370

prune748.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (* (/ (fabs (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 1)) (/ (sqrt (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.3b	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`asin-acos` `pow1/2`

Counts

4 → 62

Calls

4 calls:

0.0ms	(asin (* (/ (fabs (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 1)) (/ (sqrt (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
4.0ms	(sqrt (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))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(asin (* (/ (fabs (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (* (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 1)) (/ (sqrt (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
239.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
243.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify122.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	344	1028
1	1048	940
2	4395	930
3	5002	930

prune522.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.8b

localize28.0ms

Local error

Found 4 expressions with local error:

1.3b	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.2b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-div`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`pow1/2`

Counts

4 → 67

Calls

4 calls:

3.0ms	(sqrt (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))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
240.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
250.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
251.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify98.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	209	745
1	685	699
2	3145	686
3	5001	685

prune636.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.8b

regimes530.0ms

Accuracy

0% (0.0b remaining)

Error of 10.9b against oracle of 10.9b and baseline of 10.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	7961×	body	80	nan
976.0ms	3790×	body	160	valid
613.0ms	4210×	body	80	valid