Details

Time bar (total: 8.0s)

sample63.0ms

Algorithm
intervals
Results
17.0ms252×body80nan
16.0ms116×body160valid
10.0ms140×body80valid

simplify122.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.1b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite27.0ms

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×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u 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 → 114
Calls
4 calls:
5.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 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)))))

series594.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
63.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
449.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
07091289
120871218
250011206

prune475.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.3b
(pow (/ Om Omc) 2.0)
0.5b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite32.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 159
Calls
4 calls:
18.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (/ (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))))

series575.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
60.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(asin (/ (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))))

simplify65.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06242554
120152381
250022370

prune603.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.6b

localize18.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0b
(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 expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 80
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))))

series867.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
248.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
185.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify86.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0213762
1703740
23026738
35002730

prune457.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.6b

localize18.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0b
(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 expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 80
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))))

series863.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
250.0ms
(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
185.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify85.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0213762
1703740
23026738
35002730

prune433.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.6b

regimes632.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.8s

Algorithm
intervals
Results
550.0ms7672×body80nan
524.0ms3751×body160valid
308.0ms4249×body80valid