Details

Time bar (total: 36.3s)

sample144.0ms

Algorithm
intervals
Results
37.0ms274×body80nan
33.0ms120×body160valid
19.0ms136×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.4b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
8.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 134
Calls
4 calls:
6.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
92.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
44.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series955.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (/ Om Omc) 2.0)
25.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
298.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
526.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.1s

Counts
146 → 146
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02763461
15123355
210953196
331763184
done50003181

prune864.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.4b
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
0.4b
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
8.8b
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
215×add-sqr-sqrt
151×unpow-prod-down
131×times-frac
120×difference-of-squares
90×cube-prod
67×sqr-pow
53×sqrt-prod
49×associate-/l*
46×*-un-lft-identity
16×add-cube-cbrt
15×distribute-lft-out--
12×add-exp-log
9×add-cbrt-cube
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×difference-cubes pow-unpow div-exp div-inv
2×cbrt-undiv pow-exp associate-/l/
1×pow-to-exp rem-sqrt-square asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub prod-exp clear-num associate-/r* flip-- cbrt-unprod
Counts
4 → 224
Calls
4 calls:
13.0ms
(pow (/ Om Omc) 2.0)
2.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
367.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
240.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))

series4.2s

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (/ Om Omc) 2.0)
32.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.7s
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.4s
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))

simplify1.5s

Counts
236 → 236
Iterations

Useful iterations: done (1.5s)

IterNodesCost
043610249
19319941
227979552
done50029547

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.4b
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
0.4b
(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
9.0b
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
405×add-sqr-sqrt
299×sqrt-prod
257×times-frac
243×unpow-prod-down
200×difference-of-squares
150×cube-prod
125×*-un-lft-identity
111×sqr-pow
75×add-cube-cbrt
52×associate-/l*
25×distribute-lft-out--
9×add-exp-log
8×pow1
6×add-cbrt-cube
5×difference-cubes
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×pow-unpow
2×sqrt-pow1 sqrt-div div-exp pow-exp div-inv associate-/l/
1×cbrt-undiv pow-to-exp asin-acos sqrt-undiv flip3-- pow-pow frac-2neg pow1/2 pow-prod-down clear-num flip--
Counts
4 → 334
Calls
4 calls:
12.0ms
(pow (/ Om Omc) 2.0)
213.0ms
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.0ms
(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
5.0ms
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series3.2s

Counts
4 → 12
Calls
4 calls:
78.0ms
(pow (/ Om Omc) 2.0)
1.9s
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
30.0ms
(asin (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
1.2s
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.6s

Counts
346 → 346
Iterations

Useful iterations: done (1.6s)

IterNodesCost
058220923
1105020298
2263419934
done500119926

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.6b

localize76.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
8.6b
(sqrt (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.0b
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
9.0b
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
16×sqrt-pow1
12×sqrt-prod
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity pow1/2
4×add-exp-log expm1-log1p-u pow-prod-down add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square
Counts
4 → 64
Calls
4 calls:
9.0ms
(sqrt (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
7.0ms
(sqrt (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
5.0ms
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
6.0ms
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series6.8s

Counts
4 → 12
Calls
4 calls:
2.0s
(sqrt (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
2.1s
(sqrt (sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
1.3s
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.4s
(sqrt (* (fma 1.0 1.0 (* (pow (/ Om Omc) 2.0) (+ 1.0 (pow (/ Om Omc) 2.0)))) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify884.0ms

Counts
76 → 76
Iterations

Useful iterations: done (881.0ms)

IterNodesCost
01522552
13682314
211522174
done50002110

prune904.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.6b

regimes1.0s

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.5b and baseline of 10.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02239
12539
done2539

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s8020×body80nan
1.1s4219×body80valid
993.0ms3781×body160valid