Details

Time bar (total: 8.5s)

sample83.0ms

Algorithm
intervals
Results
22.0ms124×body160valid
21.0ms225×body80nan
12.0ms132×body80valid

simplify126.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune9.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.3b

Counts
2 → 1

localize16.0ms

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))))))
11.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite37.0ms

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

series283.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ t l) 2.0)
103.0ms
(/ (- 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))))))
151.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
06621889
120991789
250021774

prune467.0ms

Filtered
142 candidates to 114 candidates (19.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1348142
Fresh000
Picked101
Done000
Total1358143

Merged error: 12.2b

Counts
143 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
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))))))
11.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
26×unpow-prod-down
22×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac
10×add-exp-log
7×pow1
6×pow-unpow
4×pow-exp add-cbrt-cube add-log-exp
3×sqrt-prod
2×pow-to-exp pow-pow sqrt-div div-exp div-inv sqr-pow
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 79
Calls
4 calls:
4.0ms
(pow (/ Om Omc) 2.0)
5.0ms
(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))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series95.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ Om Omc) 2.0)
14.0ms
(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))))))
51.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify52.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0632677
12160627
25001615

prune272.0ms

Filtered
91 candidates to 69 candidates (24.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New90191
Fresh077
Picked011
Done000
Total90999

Merged error: 12.2b

Counts
99 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

11.4b
(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)))))))
16.2b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.2b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.2b
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite90.0ms

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:
43.0ms
(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)))))))
12.0ms
(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)))))
13.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series760.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(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)))))))
162.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
287.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
161.0ms
(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04182874
110522786
250012729

prune1.0s

Filtered
160 candidates to 127 candidates (20.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1600160
Fresh077
Picked011
Done011
Total1609169

Merged error: 12.2b

Counts
169 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

11.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
14.4b
(cbrt (/ t l))
14.4b
(cbrt (/ t l))
14.4b
(cbrt (/ t l))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
55×times-frac
43×*-un-lft-identity
39×cbrt-prod
37×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×unpow-prod-down
5×pow1
4×add-exp-log add-cbrt-cube div-inv add-log-exp
3×cbrt-div pow1/3 distribute-lft-out-- sqr-pow
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 108
Calls
4 calls:
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
2.0ms
(cbrt (/ t l))
2.0ms
(cbrt (/ t l))
3.0ms
(cbrt (/ t l))

series190.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
13.0ms
(cbrt (/ t l))
17.0ms
(cbrt (/ t l))
14.0ms
(cbrt (/ t l))

simplify145.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
04141767
19941697
245161682
350011624

prune327.0ms

Filtered
120 candidates to 97 candidates (19.2%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1200120
Fresh066
Picked011
Done022
Total1209129

Merged error: 12.2b

Counts
129 → 9

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01911
11911

end0.0ms

sample2.6s

Algorithm
intervals
Results
758.0ms8070×body80nan
734.0ms3876×body160valid
383.0ms4124×body80valid

Profiling

Loading profile data...