Details

Time bar (total: 9.7s)

sample70.0ms

Algorithm
intervals
Results
21.0ms263×body80nan
18.0ms124×body160valid
9.0ms132×body80valid

simplify126.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

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 (/ Om Omc) 2.0)
16.0ms
(/ (- 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))))))
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ Om Omc) 2.0)
213.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
319.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06341882
120171787
250011774

prune574.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
8.7b
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
8×add-sqr-sqrt sqrt-pow1
7×sqrt-div sqrt-prod
6×add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square pow1/2
2×flip3-+ flip-+
1×pow2 frac-times asin-acos pow-plus associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
Counts
4 → 57
Calls
4 calls:
1.0ms
(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
31.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (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))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(asin (sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
329.0ms
(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (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))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify95.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0259884
1753806
23224804
35001804

prune484.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.5b
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
190×sqrt-prod
164×add-sqr-sqrt
112×times-frac
78×*-un-lft-identity
54×add-cube-cbrt
48×difference-of-squares
24×unpow-prod-down
12×distribute-lft-out-- sqr-pow
10×pow1 rem-sqrt-square sqrt-pow1
8×associate-/r/
6×pow1/2 sqrt-div
4×add-exp-log flip3-+ add-cbrt-cube flip-+ div-inv add-log-exp
Counts
4 → 180
Calls
4 calls:
18.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms
(sqrt (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)))))
13.0ms
(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:
333.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
336.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
315.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
318.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
04143308
19113236
233593216
350023182

prune960.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

localize33.0ms

Local error

Found 4 expressions with local error:

10.7b
(sqrt (/ (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)))))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
21×add-sqr-sqrt
18×cbrt-div
14×times-frac
12×*-un-lft-identity
10×add-cube-cbrt
9×cbrt-prod flip3-+ flip-+
8×associate-/r/
5×pow1
4×add-exp-log frac-times add-cbrt-cube add-log-exp difference-of-squares
3×rem-sqrt-square pow1/3
2×unpow-prod-down associate-*r/ associate-*l/
1×sqrt-pow1 pow1/2 sqrt-div div-inv distribute-lft-out-- sqr-pow
Counts
4 → 75
Calls
4 calls:
18.0ms
(sqrt (/ (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)))))))
3.0ms
(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))))

series1.2s

Counts
4 → 12
Calls
4 calls:
451.0ms
(sqrt (/ (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)))))))
235.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
243.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
235.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify89.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
03671353
18171301
229241289
350021286

prune598.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

regimes642.0ms

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.6b and baseline of 10.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.9s

Algorithm
intervals
Results
556.0ms8082×body80nan
537.0ms3856×body160valid
293.0ms4144×body80valid