Details

Time bar (total: 10.4s)

sample71.0ms

Algorithm
intervals
Results
21.0ms286×body80nan
18.0ms118×body160valid
10.0ms138×body80valid

simplify130.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5443210
6500210

prune8.0ms

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: 12.1b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite68.0ms

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 (/ Om Omc) 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))))))
25.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series641.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ Om Omc) 2.0)
221.0ms
(/ (- 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))))))
338.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06802644
121022540
250012519

prune521.0ms

Filtered
201 candidates to 135 candidates (32.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1956201
Fresh000
Picked101
Done000
Total1966202

Merged error: 12.0b

Counts
202 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
1346×sqrt-prod
1294×times-frac
1188×*-un-lft-identity
1107×add-sqr-sqrt
404×add-cube-cbrt
328×difference-of-squares
310×distribute-lft-out
168×unpow-prod-down
155×associate-*l*
128×sqrt-div
86×associate-/l*
84×sqr-pow
82×distribute-lft-out--
25×associate-/l/
24×associate-/r*
22×associate-/r/
13×flip3-+ flip-+
11×div-inv
10×hypot-def
9×rem-sqrt-square
8×unswap-sqr
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg sqrt-pow1 pow1/2 clear-num
2×flip3-- flip--
1×cbrt-undiv div-sub div-exp
Counts
4 → 833
Calls
4 calls:
31.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
99.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
347.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
185.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
183.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
329.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify240.0ms

Algorithm
egg-herbie
Counts
845 → 845
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0178224774
1500223347

prune1.2s

Filtered
845 candidates to 250 candidates (70.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New8423845
Fresh235
Picked011
Done000
Total8447851

Merged error: 12.0b

Counts
851 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
23×add-sqr-sqrt
15×cbrt-prod
8×add-cube-cbrt distribute-lft-out
6×cbrt-div
5×pow1 sqrt-prod hypot-def
4×add-exp-log expm1-log1p-u flip3-+ associate-*l* add-cbrt-cube flip-+ log1p-expm1-u add-log-exp unswap-sqr
3×pow1/3
2×unpow-prod-down sqrt-div
1×rem-sqrt-square sqrt-pow1 times-frac pow1/2 sqr-pow
Counts
4 → 75
Calls
4 calls:
13.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series954.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
263.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
253.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
248.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify81.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0197729
1648685
22792673
35002670

prune462.0ms

Filtered
87 candidates to 76 candidates (12.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New87087
Fresh055
Picked011
Done011
Total87794

Merged error: 12.0b

Counts
94 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
82×sqrt-prod
33×*-un-lft-identity
32×sqrt-div
26×sqrt-pow1
24×unswap-sqr
19×pow1
15×hypot-def
13×add-cube-cbrt associate-*l*
11×pow1/2 associate-*r*
10×rem-sqrt-square distribute-lft-out
9×flip3-+ flip-+
6×unpow-prod-down pow-prod-up
4×add-exp-log expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
3×times-frac pow-prod-down sqr-pow
2×associate-*r/ pow3 associate-*l/
1×*-commutative
Counts
4 → 139
Calls
4 calls:
36.0ms
(sqrt (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
13.0ms
(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))))

series889.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(sqrt (* (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
185.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
216.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
197.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify109.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
03141616
19601588
240681537
350011512

prune750.0ms

Filtered
151 candidates to 103 candidates (31.8%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1501151
Fresh134
Picked011
Done022
Total1517158

Merged error: 12.0b

Counts
158 → 7

regimes706.0ms

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
02017
12017

end0.0ms

sample2.0s

Algorithm
intervals
Results
593.0ms3839×body160valid
585.0ms7903×body80nan
315.0ms4161×body80valid