Details

Time bar (total: 10.2s)

sample66.0ms

Algorithm
intervals
Results
19.0ms248×body80nan
17.0ms133×body160valid
8.0ms123×body80valid

simplify127.0ms

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: 9.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
1.0b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×pow-exp add-cbrt-cube add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 106
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 2.0)
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
33.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
62.0ms
(pow (/ Om Omc) 2.0)
19.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
324.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06951235
120431164
250021152

prune487.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.2b

localize19.0ms

Local error

Found 4 expressions with local error:

8.1b
(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)))))))
30.1b
(cbrt (pow (/ t l) 2.0))
30.1b
(cbrt (pow (/ t l) 2.0))
30.1b
(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:
30.0ms
(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)))))))
6.0ms
(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:
323.0ms
(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)))))))
263.0ms
(cbrt (pow (/ t l) 2.0))
264.0ms
(cbrt (pow (/ t l) 2.0))
267.0ms
(cbrt (pow (/ t l) 2.0))

simplify124.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
05162190
112052120
248302084
350012075

prune681.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.2b

localize37.0ms

Local error

Found 4 expressions with local error:

8.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
22.8b
(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
30.1b
(cbrt (pow (/ t l) 2.0))
30.1b
(cbrt (pow (/ t l) 2.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
47×times-frac
43×cbrt-prod
40×*-un-lft-identity
37×unpow-prod-down
34×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 → 109
Calls
4 calls:
33.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
2.0ms
(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt 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:
331.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (* (cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0)) (cbrt (pow (/ (cbrt t) (cbrt l)) 2.0))) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
273.0ms
(cbrt (pow (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) 2.0))
269.0ms
(cbrt (pow (/ t l) 2.0))
271.0ms
(cbrt (pow (/ t l) 2.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
06383111
114673006
250012946

prune955.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.2b

localize48.0ms

Local error

Found 4 expressions with local error:

30.1b
(cbrt (pow (/ t l) 2.0))
30.1b
(cbrt (pow (/ t l) 2.0))
30.1b
(cbrt (pow (/ t l) 2.0))
30.1b
(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:
276.0ms
(cbrt (pow (/ t l) 2.0))
267.0ms
(cbrt (pow (/ t l) 2.0))
275.0ms
(cbrt (pow (/ t l) 2.0))
272.0ms
(cbrt (pow (/ t l) 2.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
02371064
14891036
213031028
333351016
450011016

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.2b

regimes639.0ms

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.4b and baseline of 10.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.8s

Algorithm
intervals
Results
512.0ms8093×body80nan
498.0ms3825×body160valid
268.0ms4175×body80valid