Details

Time bar (total: 9.7s)

sample64.0ms

Algorithm
intervals
Results
20.0ms274×body80nan
14.0ms115×body160valid
8.0ms141×body80valid

simplify129.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- 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))))))
10.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite84.0ms

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:
4.0ms
(pow (/ t l) 2.0)
44.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
30.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series628.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ t l) 2.0)
225.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
326.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify206.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06481882
120471787
250011774

prune578.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.7b

localize19.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
55×times-frac
51×cbrt-prod
46×*-un-lft-identity
45×unpow-prod-down
40×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log add-cbrt-cube div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 117
Calls
4 calls:
33.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
319.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
261.0ms
(cbrt (pow (/ t l) 2.0))
262.0ms
(cbrt (pow (/ t l) 2.0))
262.0ms
(cbrt (pow (/ t l) 2.0))

simplify124.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
05162189
112052120
248302084
350012075

prune666.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.7b

localize25.0ms

Local error

Found 4 expressions with local error:

29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
68×cbrt-prod
52×unpow-prod-down
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
4×pow1 add-exp-log pow1/3 add-cbrt-cube div-inv add-log-exp sqr-pow
Counts
4 → 100
Calls
4 calls:
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
267.0ms
(cbrt (pow (/ t l) 2.0))
266.0ms
(cbrt (pow (/ t l) 2.0))
266.0ms
(cbrt (pow (/ t l) 2.0))
263.0ms
(cbrt (pow (/ t l) 2.0))

simplify80.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
02371064
14891036
213031028
333351016
450011016

prune696.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.7b

localize29.0ms

Local error

Found 4 expressions with local error:

29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))
29.9b
(cbrt (pow (/ t l) 2.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
68×cbrt-prod
52×unpow-prod-down
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
4×pow1 add-exp-log pow1/3 add-cbrt-cube div-inv add-log-exp sqr-pow
Counts
4 → 100
Calls
4 calls:
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
263.0ms
(cbrt (pow (/ t l) 2.0))
269.0ms
(cbrt (pow (/ t l) 2.0))
267.0ms
(cbrt (pow (/ t l) 2.0))
267.0ms
(cbrt (pow (/ t l) 2.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
02371064
14891036
213031028
333351016
450011016

prune717.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.7b

regimes664.0ms

Accuracy

0% (0.1b remaining)

Error of 10.8b against oracle of 10.8b and baseline of 10.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.6s

Algorithm
intervals
Results
462.0ms7961×body80nan
438.0ms3742×body160valid
256.0ms4258×body80valid