Details

Time bar (total: 12.8s)

sample61.0ms

Algorithm
intervals
Results
17.0ms284×body80nan
15.0ms128×body160valid
7.0ms128×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01619
12919
25118
310618
425218
575918
6271618
done500018

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
28×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
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 112
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)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
27.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
64.0ms
(pow (/ Om Omc) 2.0)
11.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
274.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify960.0ms

Counts
124 → 124
Iterations

Useful iterations: 3 (455.0ms)

IterNodesCost
03192298
15862196
211442088
327172082
done50002082

prune494.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.5b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.7b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
10.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite55.0ms

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 associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×sqrt-div div-exp pow-exp 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 → 155
Calls
4 calls:
4.0ms
(pow (/ Om Omc) 2.0)
40.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series445.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ Om Omc) 2.0)
270.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
12.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
103.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify948.0ms

Counts
167 → 167
Iterations

Useful iterations: 3 (440.0ms)

IterNodesCost
03124370
15314044
210223928
324693922
done50003922

prune623.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize21.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
7.8b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
10.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
1.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series452.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
122.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
100.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
105.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.4s

Counts
84 → 84
Iterations

Useful iterations: 5 (701.0ms)

IterNodesCost
0751116
1126960
2220922
3471922
41125886
53046870
done5000870

prune324.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

7.3b
(sqrt (/ 1 (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
7.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
10.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
10.2b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
116×sqrt-prod
104×add-sqr-sqrt
78×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
10×pow1 rem-sqrt-square
9×sqrt-pow1
6×distribute-lft-out-- sqr-pow
5×pow1/2
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-flip
2×sqrt-div div-inv
1×inv-pow
Counts
4 → 140
Calls
4 calls:
5.0ms
(sqrt (/ 1 (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series651.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(sqrt (/ 1 (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
305.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))))
102.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
109.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.7s

Counts
152 → 152
Iterations

Useful iterations: 4 (1.0s)

IterNodesCost
02933691
14643324
27623185
314693185
441303158
done50013158

prune530.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.3b

regimes383.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01720
done1720

end0.0ms

sample1.6s

Algorithm
intervals
Results
483.0ms7987×body80nan
452.0ms3799×body160valid
246.0ms4201×body80valid