Details

Time bar (total: 17.0s)

sample148.0ms

Algorithm
intervals
Results
53.0ms114×body160valid
30.0ms231×body80nan
18.0ms142×body80valid

simplify127.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize27.0ms

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))))))
9.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite156.0ms

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:
7.0ms
(pow (/ t l) 2.0)
70.0ms
(/ (- 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))))))
73.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series996.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(pow (/ t l) 2.0)
388.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
21.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
502.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify52.0ms

Counts
142 → 142

prune959.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize57.0ms

Local error

Found 4 expressions with local error:

9.0b
(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))))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite171.0ms

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 add-cbrt-cube add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 180
Calls
4 calls:
128.0ms
(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))))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
553.0ms
(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))))))
421.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
343.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
358.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify152.0ms

Counts
192 → 192

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

localize66.0ms

Local error

Found 4 expressions with local error:

10.3b
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.4b
(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 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
251×sqrt-prod
172×add-sqr-sqrt
136×cbrt-prod
116×cbrt-div
105×*-un-lft-identity
87×add-cube-cbrt
74×associate-/r/
58×flip3-+ flip-+
36×frac-times difference-of-squares
18×unpow-prod-down associate-*r/ associate-*l/
10×div-inv
9×distribute-lft-out-- sqr-pow
7×rem-sqrt-square
5×pow1 sqrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2
Counts
4 → 245
Calls
4 calls:
4.0ms
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
88.0ms
(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 (sqrt (+ 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))))

series1.5s

Counts
4 → 12
Calls
4 calls:
347.0ms
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
561.0ms
(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 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
312.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
267.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify129.0ms

Counts
257 → 257

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.7b

localize69.0ms

Local error

Found 4 expressions with local error:

16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
354.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
297.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
289.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
362.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify67.0ms

Counts
64 → 64

prune768.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.7b

regimes731.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify120.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.3s7835×body80nan
936.0ms3785×body160valid
482.0ms4215×body80valid