Details

Time bar (total: 11.4s)

sample58.0ms

Algorithm
intervals
Results
12.0ms117×body160valid
12.0ms211×body80nan
8.0ms139×body80valid

simplify127.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
74×times-frac
59×*-un-lft-identity
45×add-cube-cbrt
40×unpow-prod-down
30×sqrt-prod
28×difference-of-squares
12×add-exp-log
9×sqr-pow
8×associate-/l*
7×pow1 distribute-lft-out--
6×pow-unpow add-cbrt-cube
4×expm1-log1p-u pow-exp associate-/r/ log1p-expm1-u div-inv add-log-exp
3×div-exp associate-/r*
2×pow-to-exp rem-sqrt-square pow-pow flip3-+ flip-+ associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 158
Calls
4 calls:
6.0ms
(pow (/ Om Omc) 2.0)
6.0ms
(pow (/ t l) 2.0)
70.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
43.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ Om Omc) 2.0)
56.0ms
(pow (/ t l) 2.0)
208.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
321.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
07211929
122571838
250011819

prune661.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.6b

localize19.0ms

Local error

Found 4 expressions with local error:

7.1b
(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)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.1b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
126×sqrt-prod
117×add-sqr-sqrt
80×cbrt-div
72×*-un-lft-identity
71×cbrt-prod
60×add-cube-cbrt
50×associate-/r/
40×flip3-+ flip-+
24×frac-times difference-of-squares
12×unpow-prod-down associate-*r/ associate-*l/
7×div-inv
6×distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 188
Calls
4 calls:
71.0ms
(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)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
315.0ms
(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)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
230.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
241.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
237.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify101.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
09546303
129456199
250016188

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0b
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.5b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
110×times-frac
92×cbrt-prod
80×*-un-lft-identity
54×add-cube-cbrt
52×difference-of-squares
33×sqrt-prod
26×unpow-prod-down
13×distribute-lft-out-- sqr-pow
8×associate-/r/ associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square cbrt-div pow1/3 associate-/r*
2×sqrt-pow1 associate-/l/
1×cbrt-undiv flip3-- frac-2neg pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
4 → 185
Calls
4 calls:
68.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
44.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
20.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
23.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
328.0ms
(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
326.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
335.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
05293368
114053279
250023253

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 7.6b

localize23.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.6b
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.6b
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.6b
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
154×add-sqr-sqrt
120×sqrt-prod
109×times-frac
99×cbrt-prod
79×*-un-lft-identity
55×add-cube-cbrt
48×difference-of-squares
24×unpow-prod-down
12×distribute-lft-out-- sqr-pow
8×associate-/r/
5×pow1
4×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
2×rem-sqrt-square
1×sqrt-pow1 pow1/2
Counts
4 → 176
Calls
4 calls:
40.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
24.0ms
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
21.0ms
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
22.0ms
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
314.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
335.0ms
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
340.0ms
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
331.0ms
(cbrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify118.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
04153616
18923526
232623496
350013469

prune1.0s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 7.6b

regimes491.0ms

Accuracy

0% (0.0b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.6s

Algorithm
intervals
Results
419.0ms7646×body80nan
402.0ms3722×body160valid
240.0ms4278×body80valid