Details

Time bar (total: 8.7s)

sample68.0ms

Algorithm
intervals
Results
18.0ms262×body80nan
16.0ms113×body160valid
11.0ms143×body80valid

simplify125.0ms

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: 11.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(pow (/ t l) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite34.0ms

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)
10.0ms
(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)))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ Om Omc) 2.0)
65.0ms
(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))))))
325.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
06951235
120431164
250021152

prune449.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.5b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
0.6b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

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:
5.0ms
(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)))))))
16.0ms
(/ (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))))

series589.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ t l) 2.0)
18.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
326.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
182.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
06232507
119872333
250012323

prune598.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 11.5b

localize23.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.1b
(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
320×sqrt-prod
192×add-sqr-sqrt
152×times-frac
100×*-un-lft-identity
76×add-cube-cbrt
48×difference-of-squares
24×unpow-prod-down
12×rem-sqrt-square distribute-lft-out-- sqr-pow
10×sqrt-div
8×pow1
4×add-exp-log sqrt-pow1 flip3-+ pow1/2 associate-/r/ add-cbrt-cube flip-+ add-log-exp
2×div-inv
Counts
4 → 204
Calls
4 calls:
19.0ms
(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
19.0ms
(sqrt (/ (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))))

series1.1s

Counts
4 → 12
Calls
4 calls:
353.0ms
(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
359.0ms
(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
185.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
179.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify129.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
04574306
111084238
248224160
350014160

prune944.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 11.5b

localize19.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.9b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite14.0ms

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)))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series874.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
253.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
184.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
182.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify82.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0201720
1658700
22858696
35002688

prune541.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 11.5b

regimes488.0ms

Accuracy

0% (0.0b remaining)

Error of 9.9b against oracle of 9.8b and baseline of 9.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.9s

Algorithm
intervals
Results
547.0ms7843×body80nan
539.0ms3826×body160valid
307.0ms4174×body80valid