Details

Time bar (total: 8.7s)

sample68.0ms

Algorithm
intervals
Results
18.0ms264×body80nan
17.0ms121×body160valid
9.0ms135×body80valid

simplify123.0ms

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: 10.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite30.0ms

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:
5.0ms
(pow (/ Om Omc) 2.0)
5.0ms
(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))))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(pow (/ Om Omc) 2.0)
64.0ms
(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))))))
316.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
06951235
120431164
250021152

prune486.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.7b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.8b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
95×sqrt-prod
82×times-frac
65×*-un-lft-identity
51×add-cube-cbrt
28×difference-of-squares
27×unpow-prod-down
11×associate-/l*
9×add-exp-log
8×sqr-pow
7×distribute-lft-out--
6×pow1 sqrt-div associate-/r* add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos sqrt-undiv flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 151
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
15.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (fabs (/ (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))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ t l) 2.0)
315.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
179.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify64.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
06232507
119872333
250012323

prune649.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.2b

localize18.0ms

Local error

Found 4 expressions with local error:

9.3b
(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)))))))
27.5b
(cbrt (pow (/ t l) 2.0))
27.5b
(cbrt (pow (/ t l) 2.0))
27.5b
(cbrt (pow (/ t l) 2.0))

rewrite30.0ms

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:
13.0ms
(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)))))))
4.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(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)))))))
267.0ms
(cbrt (pow (/ t l) 2.0))
266.0ms
(cbrt (pow (/ t l) 2.0))
266.0ms
(cbrt (pow (/ t l) 2.0))

simplify125.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
05162189
112052120
248302084
350012075

prune704.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.2b

localize19.0ms

Local error

Found 4 expressions with local error:

7.6b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.6b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.9b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
Counts
4 → 72
Calls
4 calls:
3.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series850.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
247.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
178.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
177.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0201720
1658700
22858696
35002688

prune436.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.2b

regimes850.0ms

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
02012
12012

end0.0ms

sample1.8s

Algorithm
intervals
Results
551.0ms8034×body80nan
543.0ms3824×body160valid
293.0ms4176×body80valid